datafusion_optimizer/simplify_expressions/

expr_simplifier.rs

// Licensed to the Apache Software Foundation (ASF) under one
// or more contributor license agreements.  See the NOTICE file
// distributed with this work for additional information
// regarding copyright ownership.  The ASF licenses this file
// to you under the Apache License, Version 2.0 (the
// "License"); you may not use this file except in compliance
// with the License.  You may obtain a copy of the License at
//
//   http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing,
// software distributed under the License is distributed on an
// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.  See the License for the
// specific language governing permissions and limitations
// under the License.

//! Expression simplification API

use arrow::{
    array::{new_null_array, AsArray},
    datatypes::{DataType, Field, Schema},
    record_batch::RecordBatch,
};
use std::borrow::Cow;
use std::collections::HashSet;
use std::ops::Not;
use std::sync::Arc;

use datafusion_common::{
    cast::{as_large_list_array, as_list_array},
    metadata::FieldMetadata,
    tree_node::{Transformed, TransformedResult, TreeNode, TreeNodeRewriter},
};
use datafusion_common::{
    exec_datafusion_err, internal_err, DFSchema, DataFusionError, Result, ScalarValue,
};
use datafusion_expr::{
    and, binary::BinaryTypeCoercer, lit, or, BinaryExpr, Case, ColumnarValue, Expr, Like,
    Operator, Volatility,
};
use datafusion_expr::{expr::ScalarFunction, interval_arithmetic::NullableInterval};
use datafusion_expr::{
    expr::{InList, InSubquery},
    utils::{iter_conjunction, iter_conjunction_owned},
};
use datafusion_expr::{simplify::ExprSimplifyResult, Cast, TryCast};
use datafusion_physical_expr::{create_physical_expr, execution_props::ExecutionProps};

use super::inlist_simplifier::ShortenInListSimplifier;
use super::utils::*;
use crate::analyzer::type_coercion::TypeCoercionRewriter;
use crate::simplify_expressions::guarantees::GuaranteeRewriter;
use crate::simplify_expressions::regex::simplify_regex_expr;
use crate::simplify_expressions::unwrap_cast::{
    is_cast_expr_and_support_unwrap_cast_in_comparison_for_binary,
    is_cast_expr_and_support_unwrap_cast_in_comparison_for_inlist,
    unwrap_cast_in_comparison_for_binary,
};
use crate::simplify_expressions::SimplifyInfo;
use datafusion_expr_common::casts::try_cast_literal_to_type;
use indexmap::IndexSet;
use regex::Regex;

/// This structure handles API for expression simplification
///
/// Provides simplification information based on DFSchema and
/// [`ExecutionProps`]. This is the default implementation used by DataFusion
///
/// For example:
/// ```
/// use arrow::datatypes::{DataType, Field, Schema};
/// use datafusion_common::{DataFusionError, ToDFSchema};
/// use datafusion_expr::execution_props::ExecutionProps;
/// use datafusion_expr::simplify::SimplifyContext;
/// use datafusion_expr::{col, lit};
/// use datafusion_optimizer::simplify_expressions::ExprSimplifier;
///
/// // Create the schema
/// let schema = Schema::new(vec![Field::new("i", DataType::Int64, false)])
///     .to_dfschema_ref()
///     .unwrap();
///
/// // Create the simplifier
/// let props = ExecutionProps::new();
/// let context = SimplifyContext::new(&props).with_schema(schema);
/// let simplifier = ExprSimplifier::new(context);
///
/// // Use the simplifier
///
/// // b < 2 or (1 > 3)
/// let expr = col("b").lt(lit(2)).or(lit(1).gt(lit(3)));
///
/// // b < 2
/// let simplified = simplifier.simplify(expr).unwrap();
/// assert_eq!(simplified, col("b").lt(lit(2)));
/// ```
pub struct ExprSimplifier<S> {
    info: S,
    /// Guarantees about the values of columns. This is provided by the user
    /// in [ExprSimplifier::with_guarantees()].
    guarantees: Vec<(Expr, NullableInterval)>,
    /// Should expressions be canonicalized before simplification? Defaults to
    /// true
    canonicalize: bool,
    /// Maximum number of simplifier cycles
    max_simplifier_cycles: u32,
}

pub const THRESHOLD_INLINE_INLIST: usize = 3;
pub const DEFAULT_MAX_SIMPLIFIER_CYCLES: u32 = 3;

impl<S: SimplifyInfo> ExprSimplifier<S> {
    /// Create a new `ExprSimplifier` with the given `info` such as an
    /// instance of [`SimplifyContext`]. See
    /// [`simplify`](Self::simplify) for an example.
    ///
    /// [`SimplifyContext`]: datafusion_expr::simplify::SimplifyContext
    pub fn new(info: S) -> Self {
        Self {
            info,
            guarantees: vec![],
            canonicalize: true,
            max_simplifier_cycles: DEFAULT_MAX_SIMPLIFIER_CYCLES,
        }
    }

    /// Simplifies this [`Expr`] as much as possible, evaluating
    /// constants and applying algebraic simplifications.
    ///
    /// The types of the expression must match what operators expect,
    /// or else an error may occur trying to evaluate. See
    /// [`coerce`](Self::coerce) for a function to help.
    ///
    /// # Example:
    ///
    /// `b > 2 AND b > 2`
    ///
    /// can be written to
    ///
    /// `b > 2`
    ///
    /// ```
    /// use arrow::datatypes::DataType;
    /// use datafusion_common::DFSchema;
    /// use datafusion_common::Result;
    /// use datafusion_expr::execution_props::ExecutionProps;
    /// use datafusion_expr::simplify::SimplifyContext;
    /// use datafusion_expr::simplify::SimplifyInfo;
    /// use datafusion_expr::{col, lit, Expr};
    /// use datafusion_optimizer::simplify_expressions::ExprSimplifier;
    /// use std::sync::Arc;
    ///
    /// /// Simple implementation that provides `Simplifier` the information it needs
    /// /// See SimplifyContext for a structure that does this.
    /// #[derive(Default)]
    /// struct Info {
    ///     execution_props: ExecutionProps,
    /// };
    ///
    /// impl SimplifyInfo for Info {
    ///     fn is_boolean_type(&self, expr: &Expr) -> Result<bool> {
    ///         Ok(false)
    ///     }
    ///     fn nullable(&self, expr: &Expr) -> Result<bool> {
    ///         Ok(true)
    ///     }
    ///     fn execution_props(&self) -> &ExecutionProps {
    ///         &self.execution_props
    ///     }
    ///     fn get_data_type(&self, expr: &Expr) -> Result<DataType> {
    ///         Ok(DataType::Int32)
    ///     }
    /// }
    ///
    /// // Create the simplifier
    /// let simplifier = ExprSimplifier::new(Info::default());
    ///
    /// // b < 2
    /// let b_lt_2 = col("b").gt(lit(2));
    ///
    /// // (b < 2) OR (b < 2)
    /// let expr = b_lt_2.clone().or(b_lt_2.clone());
    ///
    /// // (b < 2) OR (b < 2) --> (b < 2)
    /// let expr = simplifier.simplify(expr).unwrap();
    /// assert_eq!(expr, b_lt_2);
    /// ```
    pub fn simplify(&self, expr: Expr) -> Result<Expr> {
        Ok(self.simplify_with_cycle_count_transformed(expr)?.0.data)
    }

    /// Like [Self::simplify], simplifies this [`Expr`] as much as possible, evaluating
    /// constants and applying algebraic simplifications. Additionally returns a `u32`
    /// representing the number of simplification cycles performed, which can be useful for testing
    /// optimizations.
    ///
    /// See [Self::simplify] for details and usage examples.
    #[deprecated(
        since = "48.0.0",
        note = "Use `simplify_with_cycle_count_transformed` instead"
    )]
    #[allow(unused_mut)]
    pub fn simplify_with_cycle_count(&self, mut expr: Expr) -> Result<(Expr, u32)> {
        let (transformed, cycle_count) =
            self.simplify_with_cycle_count_transformed(expr)?;
        Ok((transformed.data, cycle_count))
    }

    /// Like [Self::simplify], simplifies this [`Expr`] as much as possible, evaluating
    /// constants and applying algebraic simplifications. Additionally returns a `u32`
    /// representing the number of simplification cycles performed, which can be useful for testing
    /// optimizations.
    ///
    /// # Returns
    ///
    /// A tuple containing:
    /// - The simplified expression wrapped in a `Transformed<Expr>` indicating if changes were made
    /// - The number of simplification cycles that were performed
    ///
    /// See [Self::simplify] for details and usage examples.
    pub fn simplify_with_cycle_count_transformed(
        &self,
        mut expr: Expr,
    ) -> Result<(Transformed<Expr>, u32)> {
        let mut simplifier = Simplifier::new(&self.info);
        let mut const_evaluator = ConstEvaluator::try_new(self.info.execution_props())?;
        let mut shorten_in_list_simplifier = ShortenInListSimplifier::new();
        let mut guarantee_rewriter = GuaranteeRewriter::new(&self.guarantees);

        if self.canonicalize {
            expr = expr.rewrite(&mut Canonicalizer::new()).data()?
        }

        // Evaluating constants can enable new simplifications and
        // simplifications can enable new constant evaluation
        // see `Self::with_max_cycles`
        let mut num_cycles = 0;
        let mut has_transformed = false;
        loop {
            let Transformed {
                data, transformed, ..
            } = expr
                .rewrite(&mut const_evaluator)?
                .transform_data(|expr| expr.rewrite(&mut simplifier))?
                .transform_data(|expr| expr.rewrite(&mut guarantee_rewriter))?;
            expr = data;
            num_cycles += 1;
            // Track if any transformation occurred
            has_transformed = has_transformed || transformed;
            if !transformed || num_cycles >= self.max_simplifier_cycles {
                break;
            }
        }
        // shorten inlist should be started after other inlist rules are applied
        expr = expr.rewrite(&mut shorten_in_list_simplifier).data()?;
        Ok((
            Transformed::new_transformed(expr, has_transformed),
            num_cycles,
        ))
    }

    /// Apply type coercion to an [`Expr`] so that it can be
    /// evaluated as a [`PhysicalExpr`](datafusion_physical_expr::PhysicalExpr).
    ///
    /// See the [type coercion module](datafusion_expr::type_coercion)
    /// documentation for more details on type coercion
    pub fn coerce(&self, expr: Expr, schema: &DFSchema) -> Result<Expr> {
        let mut expr_rewrite = TypeCoercionRewriter { schema };
        expr.rewrite(&mut expr_rewrite).data()
    }

    /// Input guarantees about the values of columns.
    ///
    /// The guarantees can simplify expressions. For example, if a column `x` is
    /// guaranteed to be `3`, then the expression `x > 1` can be replaced by the
    /// literal `true`.
    ///
    /// The guarantees are provided as a `Vec<(Expr, NullableInterval)>`,
    /// where the [Expr] is a column reference and the [NullableInterval]
    /// is an interval representing the known possible values of that column.
    ///
    /// ```rust
    /// use arrow::datatypes::{DataType, Field, Schema};
    /// use datafusion_common::{Result, ScalarValue, ToDFSchema};
    /// use datafusion_expr::execution_props::ExecutionProps;
    /// use datafusion_expr::interval_arithmetic::{Interval, NullableInterval};
    /// use datafusion_expr::simplify::SimplifyContext;
    /// use datafusion_expr::{col, lit, Expr};
    /// use datafusion_optimizer::simplify_expressions::ExprSimplifier;
    ///
    /// let schema = Schema::new(vec![
    ///     Field::new("x", DataType::Int64, false),
    ///     Field::new("y", DataType::UInt32, false),
    ///     Field::new("z", DataType::Int64, false),
    /// ])
    /// .to_dfschema_ref()
    /// .unwrap();
    ///
    /// // Create the simplifier
    /// let props = ExecutionProps::new();
    /// let context = SimplifyContext::new(&props).with_schema(schema);
    ///
    /// // Expression: (x >= 3) AND (y + 2 < 10) AND (z > 5)
    /// let expr_x = col("x").gt_eq(lit(3_i64));
    /// let expr_y = (col("y") + lit(2_u32)).lt(lit(10_u32));
    /// let expr_z = col("z").gt(lit(5_i64));
    /// let expr = expr_x.and(expr_y).and(expr_z.clone());
    ///
    /// let guarantees = vec![
    ///     // x ∈ [3, 5]
    ///     (
    ///         col("x"),
    ///         NullableInterval::NotNull {
    ///             values: Interval::make(Some(3_i64), Some(5_i64)).unwrap(),
    ///         },
    ///     ),
    ///     // y = 3
    ///     (
    ///         col("y"),
    ///         NullableInterval::from(ScalarValue::UInt32(Some(3))),
    ///     ),
    /// ];
    /// let simplifier = ExprSimplifier::new(context).with_guarantees(guarantees);
    /// let output = simplifier.simplify(expr).unwrap();
    /// // Expression becomes: true AND true AND (z > 5), which simplifies to
    /// // z > 5.
    /// assert_eq!(output, expr_z);
    /// ```
    pub fn with_guarantees(mut self, guarantees: Vec<(Expr, NullableInterval)>) -> Self {
        self.guarantees = guarantees;
        self
    }

    /// Should `Canonicalizer` be applied before simplification?
    ///
    /// If true (the default), the expression will be rewritten to canonical
    /// form before simplification. This is useful to ensure that the simplifier
    /// can apply all possible simplifications.
    ///
    /// Some expressions, such as those in some Joins, can not be canonicalized
    /// without changing their meaning. In these cases, canonicalization should
    /// be disabled.
    ///
    /// ```rust
    /// use arrow::datatypes::{DataType, Field, Schema};
    /// use datafusion_common::{Result, ScalarValue, ToDFSchema};
    /// use datafusion_expr::execution_props::ExecutionProps;
    /// use datafusion_expr::interval_arithmetic::{Interval, NullableInterval};
    /// use datafusion_expr::simplify::SimplifyContext;
    /// use datafusion_expr::{col, lit, Expr};
    /// use datafusion_optimizer::simplify_expressions::ExprSimplifier;
    ///
    /// let schema = Schema::new(vec![
    ///     Field::new("a", DataType::Int64, false),
    ///     Field::new("b", DataType::Int64, false),
    ///     Field::new("c", DataType::Int64, false),
    /// ])
    /// .to_dfschema_ref()
    /// .unwrap();
    ///
    /// // Create the simplifier
    /// let props = ExecutionProps::new();
    /// let context = SimplifyContext::new(&props).with_schema(schema);
    /// let simplifier = ExprSimplifier::new(context);
    ///
    /// // Expression: a = c AND 1 = b
    /// let expr = col("a").eq(col("c")).and(lit(1).eq(col("b")));
    ///
    /// // With canonicalization, the expression is rewritten to canonical form
    /// // (though it is no simpler in this case):
    /// let canonical = simplifier.simplify(expr.clone()).unwrap();
    /// // Expression has been rewritten to: (c = a AND b = 1)
    /// assert_eq!(canonical, col("c").eq(col("a")).and(col("b").eq(lit(1))));
    ///
    /// // If canonicalization is disabled, the expression is not changed
    /// let non_canonicalized = simplifier
    ///     .with_canonicalize(false)
    ///     .simplify(expr.clone())
    ///     .unwrap();
    ///
    /// assert_eq!(non_canonicalized, expr);
    /// ```
    pub fn with_canonicalize(mut self, canonicalize: bool) -> Self {
        self.canonicalize = canonicalize;
        self
    }

    /// Specifies the maximum number of simplification cycles to run.
    ///
    /// The simplifier can perform multiple passes of simplification. This is
    /// because the output of one simplification step can allow more optimizations
    /// in another simplification step. For example, constant evaluation can allow more
    /// expression simplifications, and expression simplifications can allow more constant
    /// evaluations.
    ///
    /// This method specifies the maximum number of allowed iteration cycles before the simplifier
    /// returns an [Expr] output. However, it does not always perform the maximum number of cycles.
    /// The simplifier will attempt to detect when an [Expr] is unchanged by all the simplification
    /// passes, and return early. This avoids wasting time on unnecessary [Expr] tree traversals.
    ///
    /// If no maximum is specified, the value of [DEFAULT_MAX_SIMPLIFIER_CYCLES] is used
    /// instead.
    ///
    /// ```rust
    /// use arrow::datatypes::{DataType, Field, Schema};
    /// use datafusion_expr::{col, lit, Expr};
    /// use datafusion_common::{Result, ScalarValue, ToDFSchema};
    /// use datafusion_expr::execution_props::ExecutionProps;
    /// use datafusion_expr::simplify::SimplifyContext;
    /// use datafusion_optimizer::simplify_expressions::ExprSimplifier;
    ///
    /// let schema = Schema::new(vec![
    ///   Field::new("a", DataType::Int64, false),
    ///   ])
    ///   .to_dfschema_ref().unwrap();
    ///
    /// // Create the simplifier
    /// let props = ExecutionProps::new();
    /// let context = SimplifyContext::new(&props)
    ///    .with_schema(schema);
    /// let simplifier = ExprSimplifier::new(context);
    ///
    /// // Expression: a IS NOT NULL
    /// let expr = col("a").is_not_null();
    ///
    /// // When using default maximum cycles, 2 cycles will be performed.
    /// let (simplified_expr, count) = simplifier.simplify_with_cycle_count_transformed(expr.clone()).unwrap();
    /// assert_eq!(simplified_expr.data, lit(true));
    /// // 2 cycles were executed, but only 1 was needed
    /// assert_eq!(count, 2);
    ///
    /// // Only 1 simplification pass is necessary here, so we can set the maximum cycles to 1.
    /// let (simplified_expr, count) = simplifier.with_max_cycles(1).simplify_with_cycle_count_transformed(expr.clone()).unwrap();
    /// // Expression has been rewritten to: (c = a AND b = 1)
    /// assert_eq!(simplified_expr.data, lit(true));
    /// // Only 1 cycle was executed
    /// assert_eq!(count, 1);
    /// ```
    pub fn with_max_cycles(mut self, max_simplifier_cycles: u32) -> Self {
        self.max_simplifier_cycles = max_simplifier_cycles;
        self
    }
}

/// Canonicalize any BinaryExprs that are not in canonical form
///
/// `<literal> <op> <col>` is rewritten to `<col> <op> <literal>`
///
/// `<col1> <op> <col2>` is rewritten so that the name of `col1` sorts higher
/// than `col2` (`a > b` would be canonicalized to `b < a`)
struct Canonicalizer {}

impl Canonicalizer {
    fn new() -> Self {
        Self {}
    }
}

impl TreeNodeRewriter for Canonicalizer {
    type Node = Expr;

    fn f_up(&mut self, expr: Expr) -> Result<Transformed<Expr>> {
        let Expr::BinaryExpr(BinaryExpr { left, op, right }) = expr else {
            return Ok(Transformed::no(expr));
        };
        match (left.as_ref(), right.as_ref(), op.swap()) {
            // <col1> <op> <col2>
            (Expr::Column(left_col), Expr::Column(right_col), Some(swapped_op))
                if right_col > left_col =>
            {
                Ok(Transformed::yes(Expr::BinaryExpr(BinaryExpr {
                    left: right,
                    op: swapped_op,
                    right: left,
                })))
            }
            // <literal> <op> <col>
            (Expr::Literal(_a, _), Expr::Column(_b), Some(swapped_op)) => {
                Ok(Transformed::yes(Expr::BinaryExpr(BinaryExpr {
                    left: right,
                    op: swapped_op,
                    right: left,
                })))
            }
            _ => Ok(Transformed::no(Expr::BinaryExpr(BinaryExpr {
                left,
                op,
                right,
            }))),
        }
    }
}

#[allow(rustdoc::private_intra_doc_links)]
/// Partially evaluate `Expr`s so constant subtrees are evaluated at plan time.
///
/// Note it does not handle algebraic rewrites such as `(a or false)`
/// --> `a`, which is handled by [`Simplifier`]
struct ConstEvaluator<'a> {
    /// `can_evaluate` is used during the depth-first-search of the
    /// `Expr` tree to track if any siblings (or their descendants) were
    /// non evaluatable (e.g. had a column reference or volatile
    /// function)
    ///
    /// Specifically, `can_evaluate[N]` represents the state of
    /// traversal when we are N levels deep in the tree, one entry for
    /// this Expr and each of its parents.
    ///
    /// After visiting all siblings if `can_evaluate.top()` is true, that
    /// means there were no non evaluatable siblings (or their
    /// descendants) so this `Expr` can be evaluated
    can_evaluate: Vec<bool>,

    execution_props: &'a ExecutionProps,
    input_schema: DFSchema,
    input_batch: RecordBatch,
}

#[allow(dead_code)]
/// The simplify result of ConstEvaluator
enum ConstSimplifyResult {
    // Expr was simplified and contains the new expression
    Simplified(ScalarValue, Option<FieldMetadata>),
    // Expr was not simplified and original value is returned
    NotSimplified(ScalarValue, Option<FieldMetadata>),
    // Evaluation encountered an error, contains the original expression
    SimplifyRuntimeError(DataFusionError, Expr),
}

impl TreeNodeRewriter for ConstEvaluator<'_> {
    type Node = Expr;

    fn f_down(&mut self, expr: Expr) -> Result<Transformed<Expr>> {
        // Default to being able to evaluate this node
        self.can_evaluate.push(true);

        // if this expr is not ok to evaluate, mark entire parent
        // stack as not ok (as all parents have at least one child or
        // descendant that can not be evaluated

        if !Self::can_evaluate(&expr) {
            // walk back up stack, marking first parent that is not mutable
            let parent_iter = self.can_evaluate.iter_mut().rev();
            for p in parent_iter {
                if !*p {
                    // optimization: if we find an element on the
                    // stack already marked, know all elements above are also marked
                    break;
                }
                *p = false;
            }
        }

        // NB: do not short circuit recursion even if we find a non
        // evaluatable node (so we can fold other children, args to
        // functions, etc.)
        Ok(Transformed::no(expr))
    }

    fn f_up(&mut self, expr: Expr) -> Result<Transformed<Expr>> {
        match self.can_evaluate.pop() {
            // Certain expressions such as `CASE` and `COALESCE` are short-circuiting
            // and may not evaluate all their sub expressions. Thus, if
            // any error is countered during simplification, return the original
            // so that normal evaluation can occur
            Some(true) => match self.evaluate_to_scalar(expr) {
                ConstSimplifyResult::Simplified(s, m) => {
                    Ok(Transformed::yes(Expr::Literal(s, m)))
                }
                ConstSimplifyResult::NotSimplified(s, m) => {
                    Ok(Transformed::no(Expr::Literal(s, m)))
                }
                ConstSimplifyResult::SimplifyRuntimeError(err, expr) => {
                    // For CAST expressions with literal inputs, propagate the error at plan time rather than deferring to execution time.
                    // This provides clearer error messages and fails fast.
                    if let Expr::Cast(Cast { ref expr, .. })
                    | Expr::TryCast(TryCast { ref expr, .. }) = expr
                    {
                        if matches!(expr.as_ref(), Expr::Literal(_, _)) {
                            return Err(err);
                        }
                    }
                    // For other expressions (like CASE, COALESCE), preserve the original
                    // to allow short-circuit evaluation at execution time
                    Ok(Transformed::yes(expr))
                }
            },
            Some(false) => Ok(Transformed::no(expr)),
            _ => internal_err!("Failed to pop can_evaluate"),
        }
    }
}

impl<'a> ConstEvaluator<'a> {
    /// Create a new `ConstantEvaluator`. Session constants (such as
    /// the time for `now()` are taken from the passed
    /// `execution_props`.
    pub fn try_new(execution_props: &'a ExecutionProps) -> Result<Self> {
        // The dummy column name is unused and doesn't matter as only
        // expressions without column references can be evaluated
        static DUMMY_COL_NAME: &str = ".";
        let schema = Arc::new(Schema::new(vec![Field::new(
            DUMMY_COL_NAME,
            DataType::Null,
            true,
        )]));
        let input_schema = DFSchema::try_from(Arc::clone(&schema))?;
        // Need a single "input" row to produce a single output row
        let col = new_null_array(&DataType::Null, 1);
        let input_batch = RecordBatch::try_new(schema, vec![col])?;

        Ok(Self {
            can_evaluate: vec![],
            execution_props,
            input_schema,
            input_batch,
        })
    }

    /// Can a function of the specified volatility be evaluated?
    fn volatility_ok(volatility: Volatility) -> bool {
        match volatility {
            Volatility::Immutable => true,
            // Values for functions such as now() are taken from ExecutionProps
            Volatility::Stable => true,
            Volatility::Volatile => false,
        }
    }

    /// Can the expression be evaluated at plan time, (assuming all of
    /// its children can also be evaluated)?
    fn can_evaluate(expr: &Expr) -> bool {
        // check for reasons we can't evaluate this node
        //
        // NOTE all expr types are listed here so when new ones are
        // added they can be checked for their ability to be evaluated
        // at plan time
        match expr {
            // TODO: remove the next line after `Expr::Wildcard` is removed
            #[expect(deprecated)]
            Expr::AggregateFunction { .. }
            | Expr::ScalarVariable(_, _)
            | Expr::Column(_)
            | Expr::OuterReferenceColumn(_, _)
            | Expr::Exists { .. }
            | Expr::InSubquery(_)
            | Expr::ScalarSubquery(_)
            | Expr::WindowFunction { .. }
            | Expr::GroupingSet(_)
            | Expr::Wildcard { .. }
            | Expr::Placeholder(_) => false,
            Expr::ScalarFunction(ScalarFunction { func, .. }) => {
                Self::volatility_ok(func.signature().volatility)
            }
            Expr::Literal(_, _)
            | Expr::Alias(..)
            | Expr::Unnest(_)
            | Expr::BinaryExpr { .. }
            | Expr::Not(_)
            | Expr::IsNotNull(_)
            | Expr::IsNull(_)
            | Expr::IsTrue(_)
            | Expr::IsFalse(_)
            | Expr::IsUnknown(_)
            | Expr::IsNotTrue(_)
            | Expr::IsNotFalse(_)
            | Expr::IsNotUnknown(_)
            | Expr::Negative(_)
            | Expr::Between { .. }
            | Expr::Like { .. }
            | Expr::SimilarTo { .. }
            | Expr::Case(_)
            | Expr::Cast { .. }
            | Expr::TryCast { .. }
            | Expr::InList { .. } => true,
        }
    }

    /// Internal helper to evaluates an Expr
    pub(crate) fn evaluate_to_scalar(&mut self, expr: Expr) -> ConstSimplifyResult {
        if let Expr::Literal(s, m) = expr {
            return ConstSimplifyResult::NotSimplified(s, m);
        }

        let phys_expr =
            match create_physical_expr(&expr, &self.input_schema, self.execution_props) {
                Ok(e) => e,
                Err(err) => return ConstSimplifyResult::SimplifyRuntimeError(err, expr),
            };
        let metadata = phys_expr
            .return_field(self.input_batch.schema_ref())
            .ok()
            .and_then(|f| {
                let m = f.metadata();
                match m.is_empty() {
                    true => None,
                    false => Some(FieldMetadata::from(m)),
                }
            });
        let col_val = match phys_expr.evaluate(&self.input_batch) {
            Ok(v) => v,
            Err(err) => return ConstSimplifyResult::SimplifyRuntimeError(err, expr),
        };
        match col_val {
            ColumnarValue::Array(a) => {
                if a.len() != 1 {
                    ConstSimplifyResult::SimplifyRuntimeError(
                        exec_datafusion_err!("Could not evaluate the expression, found a result of length {}", a.len()),
                        expr,
                    )
                } else if as_list_array(&a).is_ok() {
                    ConstSimplifyResult::Simplified(
                        ScalarValue::List(a.as_list::<i32>().to_owned().into()),
                        metadata,
                    )
                } else if as_large_list_array(&a).is_ok() {
                    ConstSimplifyResult::Simplified(
                        ScalarValue::LargeList(a.as_list::<i64>().to_owned().into()),
                        metadata,
                    )
                } else {
                    // Non-ListArray
                    match ScalarValue::try_from_array(&a, 0) {
                        Ok(s) => ConstSimplifyResult::Simplified(s, metadata),
                        Err(err) => ConstSimplifyResult::SimplifyRuntimeError(err, expr),
                    }
                }
            }
            ColumnarValue::Scalar(s) => ConstSimplifyResult::Simplified(s, metadata),
        }
    }
}

/// Simplifies [`Expr`]s by applying algebraic transformation rules
///
/// Example transformations that are applied:
/// * `expr = true` and `expr != false` to `expr` when `expr` is of boolean type
/// * `expr = false` and `expr != true` to `!expr` when `expr` is of boolean type
/// * `true = true` and `false = false` to `true`
/// * `false = true` and `true = false` to `false`
/// * `!!expr` to `expr`
/// * `expr = null` and `expr != null` to `null`
struct Simplifier<'a, S> {
    info: &'a S,
}

impl<'a, S> Simplifier<'a, S> {
    pub fn new(info: &'a S) -> Self {
        Self { info }
    }
}

impl<S: SimplifyInfo> TreeNodeRewriter for Simplifier<'_, S> {
    type Node = Expr;

    /// rewrite the expression simplifying any constant expressions
    fn f_up(&mut self, expr: Expr) -> Result<Transformed<Expr>> {
        use datafusion_expr::Operator::{
            And, BitwiseAnd, BitwiseOr, BitwiseShiftLeft, BitwiseShiftRight, BitwiseXor,
            Divide, Eq, Modulo, Multiply, NotEq, Or, RegexIMatch, RegexMatch,
            RegexNotIMatch, RegexNotMatch,
        };

        let info = self.info;
        Ok(match expr {
            // `value op NULL` -> `NULL`
            // `NULL op value` -> `NULL`
            // except for few operators that can return non-null value even when one of the operands is NULL
            ref expr @ Expr::BinaryExpr(BinaryExpr {
                ref left,
                ref op,
                ref right,
            }) if op.returns_null_on_null()
                && (is_null(left.as_ref()) || is_null(right.as_ref())) =>
            {
                Transformed::yes(Expr::Literal(
                    ScalarValue::try_new_null(&info.get_data_type(expr)?)?,
                    None,
                ))
            }

            // `NULL {AND, OR} NULL` -> `NULL`
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And | Or,
                right,
            }) if is_null(&left) && is_null(&right) => Transformed::yes(lit_bool_null()),

            //
            // Rules for Eq
            //

            // true = A  --> A
            // false = A --> !A
            // null = A --> null
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Eq,
                right,
            }) if is_bool_lit(&left) && info.is_boolean_type(&right)? => {
                Transformed::yes(match as_bool_lit(&left)? {
                    Some(true) => *right,
                    Some(false) => Expr::Not(right),
                    None => lit_bool_null(),
                })
            }
            // A = true  --> A
            // A = false --> !A
            // A = null --> null
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Eq,
                right,
            }) if is_bool_lit(&right) && info.is_boolean_type(&left)? => {
                Transformed::yes(match as_bool_lit(&right)? {
                    Some(true) => *left,
                    Some(false) => Expr::Not(left),
                    None => lit_bool_null(),
                })
            }
            // According to SQL's null semantics, NULL = NULL evaluates to NULL
            // Both sides are the same expression (A = A) and A is non-volatile expression
            // A = A --> A IS NOT NULL OR NULL
            // A = A --> true (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Eq,
                right,
            }) if (left == right) & !left.is_volatile() => {
                Transformed::yes(match !info.nullable(&left)? {
                    true => lit(true),
                    false => Expr::BinaryExpr(BinaryExpr {
                        left: Box::new(Expr::IsNotNull(left)),
                        op: Or,
                        right: Box::new(lit_bool_null()),
                    }),
                })
            }

            // Rules for NotEq
            //

            // true != A  --> !A
            // false != A --> A
            // null != A --> null
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: NotEq,
                right,
            }) if is_bool_lit(&left) && info.is_boolean_type(&right)? => {
                Transformed::yes(match as_bool_lit(&left)? {
                    Some(true) => Expr::Not(right),
                    Some(false) => *right,
                    None => lit_bool_null(),
                })
            }
            // A != true  --> !A
            // A != false --> A
            // A != null --> null,
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: NotEq,
                right,
            }) if is_bool_lit(&right) && info.is_boolean_type(&left)? => {
                Transformed::yes(match as_bool_lit(&right)? {
                    Some(true) => Expr::Not(left),
                    Some(false) => *left,
                    None => lit_bool_null(),
                })
            }

            //
            // Rules for OR
            //

            // true OR A --> true (even if A is null)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Or,
                right: _,
            }) if is_true(&left) => Transformed::yes(*left),
            // false OR A --> A
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Or,
                right,
            }) if is_false(&left) => Transformed::yes(*right),
            // A OR true --> true (even if A is null)
            Expr::BinaryExpr(BinaryExpr {
                left: _,
                op: Or,
                right,
            }) if is_true(&right) => Transformed::yes(*right),
            // A OR false --> A
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Or,
                right,
            }) if is_false(&right) => Transformed::yes(*left),
            // A OR !A ---> true (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Or,
                right,
            }) if is_not_of(&right, &left) && !info.nullable(&left)? => {
                Transformed::yes(lit(true))
            }
            // !A OR A ---> true (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Or,
                right,
            }) if is_not_of(&left, &right) && !info.nullable(&right)? => {
                Transformed::yes(lit(true))
            }
            // (..A..) OR A --> (..A..)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Or,
                right,
            }) if expr_contains(&left, &right, Or) => Transformed::yes(*left),
            // A OR (..A..) --> (..A..)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Or,
                right,
            }) if expr_contains(&right, &left, Or) => Transformed::yes(*right),
            // A OR (A AND B) --> A
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Or,
                right,
            }) if is_op_with(And, &right, &left) => Transformed::yes(*left),
            // (A AND B) OR A --> A
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Or,
                right,
            }) if is_op_with(And, &left, &right) => Transformed::yes(*right),
            // Eliminate common factors in conjunctions e.g
            // (A AND B) OR (A AND C) -> A AND (B OR C)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Or,
                right,
            }) if has_common_conjunction(&left, &right) => {
                let lhs: IndexSet<Expr> = iter_conjunction_owned(*left).collect();
                let (common, rhs): (Vec<_>, Vec<_>) = iter_conjunction_owned(*right)
                    .partition(|e| lhs.contains(e) && !e.is_volatile());

                let new_rhs = rhs.into_iter().reduce(and);
                let new_lhs = lhs.into_iter().filter(|e| !common.contains(e)).reduce(and);
                let common_conjunction = common.into_iter().reduce(and).unwrap();

                let new_expr = match (new_lhs, new_rhs) {
                    (Some(lhs), Some(rhs)) => and(common_conjunction, or(lhs, rhs)),
                    (_, _) => common_conjunction,
                };
                Transformed::yes(new_expr)
            }

            //
            // Rules for AND
            //

            // true AND A --> A
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if is_true(&left) => Transformed::yes(*right),
            // false AND A --> false (even if A is null)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right: _,
            }) if is_false(&left) => Transformed::yes(*left),
            // A AND true --> A
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if is_true(&right) => Transformed::yes(*left),
            // A AND false --> false (even if A is null)
            Expr::BinaryExpr(BinaryExpr {
                left: _,
                op: And,
                right,
            }) if is_false(&right) => Transformed::yes(*right),
            // A AND !A ---> false (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if is_not_of(&right, &left) && !info.nullable(&left)? => {
                Transformed::yes(lit(false))
            }
            // !A AND A ---> false (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if is_not_of(&left, &right) && !info.nullable(&right)? => {
                Transformed::yes(lit(false))
            }
            // (..A..) AND A --> (..A..)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if expr_contains(&left, &right, And) => Transformed::yes(*left),
            // A AND (..A..) --> (..A..)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if expr_contains(&right, &left, And) => Transformed::yes(*right),
            // A AND (A OR B) --> A
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if is_op_with(Or, &right, &left) => Transformed::yes(*left),
            // (A OR B) AND A --> A
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if is_op_with(Or, &left, &right) => Transformed::yes(*right),
            // A >= constant AND constant <= A --> A = constant
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if can_reduce_to_equal_statement(&left, &right) => {
                if let Expr::BinaryExpr(BinaryExpr {
                    left: left_left,
                    right: left_right,
                    ..
                }) = *left
                {
                    Transformed::yes(Expr::BinaryExpr(BinaryExpr {
                        left: left_left,
                        op: Eq,
                        right: left_right,
                    }))
                } else {
                    return internal_err!("can_reduce_to_equal_statement should only be called with a BinaryExpr");
                }
            }

            //
            // Rules for Multiply
            //

            // A * 1 --> A (with type coercion if needed)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Multiply,
                right,
            }) if is_one(&right) => {
                simplify_right_is_one_case(info, left, &Multiply, &right)?
            }
            // 1 * A --> A
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Multiply,
                right,
            }) if is_one(&left) => {
                // 1 * A is equivalent to A * 1
                simplify_right_is_one_case(info, right, &Multiply, &left)?
            }

            // A * 0 --> 0 (if A is not null and not floating, since NAN * 0 -> NAN)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Multiply,
                right,
            }) if !info.nullable(&left)?
                && !info.get_data_type(&left)?.is_floating()
                && is_zero(&right) =>
            {
                Transformed::yes(*right)
            }
            // 0 * A --> 0 (if A is not null and not floating, since 0 * NAN -> NAN)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Multiply,
                right,
            }) if !info.nullable(&right)?
                && !info.get_data_type(&right)?.is_floating()
                && is_zero(&left) =>
            {
                Transformed::yes(*left)
            }

            //
            // Rules for Divide
            //

            // A / 1 --> A
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Divide,
                right,
            }) if is_one(&right) => {
                simplify_right_is_one_case(info, left, &Divide, &right)?
            }

            //
            // Rules for Modulo
            //

            // A % 1 --> 0 (if A is not nullable and not floating, since NAN % 1 --> NAN)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Modulo,
                right,
            }) if !info.nullable(&left)?
                && !info.get_data_type(&left)?.is_floating()
                && is_one(&right) =>
            {
                Transformed::yes(Expr::Literal(
                    ScalarValue::new_zero(&info.get_data_type(&left)?)?,
                    None,
                ))
            }

            //
            // Rules for BitwiseAnd
            //

            // A & 0 -> 0 (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseAnd,
                right,
            }) if !info.nullable(&left)? && is_zero(&right) => Transformed::yes(*right),

            // 0 & A -> 0 (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseAnd,
                right,
            }) if !info.nullable(&right)? && is_zero(&left) => Transformed::yes(*left),

            // !A & A -> 0 (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseAnd,
                right,
            }) if is_negative_of(&left, &right) && !info.nullable(&right)? => {
                Transformed::yes(Expr::Literal(
                    ScalarValue::new_zero(&info.get_data_type(&left)?)?,
                    None,
                ))
            }

            // A & !A -> 0 (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseAnd,
                right,
            }) if is_negative_of(&right, &left) && !info.nullable(&left)? => {
                Transformed::yes(Expr::Literal(
                    ScalarValue::new_zero(&info.get_data_type(&left)?)?,
                    None,
                ))
            }

            // (..A..) & A --> (..A..)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseAnd,
                right,
            }) if expr_contains(&left, &right, BitwiseAnd) => Transformed::yes(*left),

            // A & (..A..) --> (..A..)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseAnd,
                right,
            }) if expr_contains(&right, &left, BitwiseAnd) => Transformed::yes(*right),

            // A & (A | B) --> A (if B not null)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseAnd,
                right,
            }) if !info.nullable(&right)? && is_op_with(BitwiseOr, &right, &left) => {
                Transformed::yes(*left)
            }

            // (A | B) & A --> A (if B not null)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseAnd,
                right,
            }) if !info.nullable(&left)? && is_op_with(BitwiseOr, &left, &right) => {
                Transformed::yes(*right)
            }

            //
            // Rules for BitwiseOr
            //

            // A | 0 -> A (even if A is null)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseOr,
                right,
            }) if is_zero(&right) => Transformed::yes(*left),

            // 0 | A -> A (even if A is null)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseOr,
                right,
            }) if is_zero(&left) => Transformed::yes(*right),

            // !A | A -> -1 (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseOr,
                right,
            }) if is_negative_of(&left, &right) && !info.nullable(&right)? => {
                Transformed::yes(Expr::Literal(
                    ScalarValue::new_negative_one(&info.get_data_type(&left)?)?,
                    None,
                ))
            }

            // A | !A -> -1 (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseOr,
                right,
            }) if is_negative_of(&right, &left) && !info.nullable(&left)? => {
                Transformed::yes(Expr::Literal(
                    ScalarValue::new_negative_one(&info.get_data_type(&left)?)?,
                    None,
                ))
            }

            // (..A..) | A --> (..A..)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseOr,
                right,
            }) if expr_contains(&left, &right, BitwiseOr) => Transformed::yes(*left),

            // A | (..A..) --> (..A..)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseOr,
                right,
            }) if expr_contains(&right, &left, BitwiseOr) => Transformed::yes(*right),

            // A | (A & B) --> A (if B not null)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseOr,
                right,
            }) if !info.nullable(&right)? && is_op_with(BitwiseAnd, &right, &left) => {
                Transformed::yes(*left)
            }

            // (A & B) | A --> A (if B not null)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseOr,
                right,
            }) if !info.nullable(&left)? && is_op_with(BitwiseAnd, &left, &right) => {
                Transformed::yes(*right)
            }

            //
            // Rules for BitwiseXor
            //

            // A ^ 0 -> A (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseXor,
                right,
            }) if !info.nullable(&left)? && is_zero(&right) => Transformed::yes(*left),

            // 0 ^ A -> A (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseXor,
                right,
            }) if !info.nullable(&right)? && is_zero(&left) => Transformed::yes(*right),

            // !A ^ A -> -1 (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseXor,
                right,
            }) if is_negative_of(&left, &right) && !info.nullable(&right)? => {
                Transformed::yes(Expr::Literal(
                    ScalarValue::new_negative_one(&info.get_data_type(&left)?)?,
                    None,
                ))
            }

            // A ^ !A -> -1 (if A not nullable)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseXor,
                right,
            }) if is_negative_of(&right, &left) && !info.nullable(&left)? => {
                Transformed::yes(Expr::Literal(
                    ScalarValue::new_negative_one(&info.get_data_type(&left)?)?,
                    None,
                ))
            }

            // (..A..) ^ A --> (the expression without A, if number of A is odd, otherwise one A)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseXor,
                right,
            }) if expr_contains(&left, &right, BitwiseXor) => {
                let expr = delete_xor_in_complex_expr(&left, &right, false);
                Transformed::yes(if expr == *right {
                    Expr::Literal(
                        ScalarValue::new_zero(&info.get_data_type(&right)?)?,
                        None,
                    )
                } else {
                    expr
                })
            }

            // A ^ (..A..) --> (the expression without A, if number of A is odd, otherwise one A)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseXor,
                right,
            }) if expr_contains(&right, &left, BitwiseXor) => {
                let expr = delete_xor_in_complex_expr(&right, &left, true);
                Transformed::yes(if expr == *left {
                    Expr::Literal(
                        ScalarValue::new_zero(&info.get_data_type(&left)?)?,
                        None,
                    )
                } else {
                    expr
                })
            }

            //
            // Rules for BitwiseShiftRight
            //

            // A >> 0 -> A (even if A is null)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseShiftRight,
                right,
            }) if is_zero(&right) => Transformed::yes(*left),

            //
            // Rules for BitwiseShiftRight
            //

            // A << 0 -> A (even if A is null)
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: BitwiseShiftLeft,
                right,
            }) if is_zero(&right) => Transformed::yes(*left),

            //
            // Rules for Not
            //
            Expr::Not(inner) => Transformed::yes(negate_clause(*inner)),

            //
            // Rules for Negative
            //
            Expr::Negative(inner) => Transformed::yes(distribute_negation(*inner)),

            //
            // Rules for Case
            //

            // Inline a comparison to a literal with the case statement into the `THEN` clauses.
            // which can enable further simplifications
            // CASE WHEN X THEN "a" WHEN Y THEN "b" ... END = "a" --> CASE WHEN X THEN "a" = "a" WHEN Y THEN "b" = "a" END
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: op @ (Eq | NotEq),
                right,
            }) if is_case_with_literal_outputs(&left) && is_lit(&right) => {
                let case = into_case(*left)?;
                Transformed::yes(Expr::Case(Case {
                    expr: None,
                    when_then_expr: case
                        .when_then_expr
                        .into_iter()
                        .map(|(when, then)| {
                            (
                                when,
                                Box::new(Expr::BinaryExpr(BinaryExpr {
                                    left: then,
                                    op,
                                    right: right.clone(),
                                })),
                            )
                        })
                        .collect(),
                    else_expr: case.else_expr.map(|els| {
                        Box::new(Expr::BinaryExpr(BinaryExpr {
                            left: els,
                            op,
                            right,
                        }))
                    }),
                }))
            }

            // CASE WHEN true THEN A ... END --> A
            // CASE WHEN X THEN A WHEN TRUE THEN B ... END --> CASE WHEN X THEN A ELSE B END
            // CASE WHEN false THEN A END --> NULL
            // CASE WHEN false THEN A ELSE B END --> B
            // CASE WHEN X THEN A WHEN false THEN B END --> CASE WHEN X THEN A ELSE B END
            Expr::Case(Case {
                expr: None,
                when_then_expr,
                mut else_expr,
            }) if when_then_expr
                .iter()
                .any(|(when, _)| is_true(when.as_ref()) || is_false(when.as_ref())) =>
            {
                let out_type = info.get_data_type(&when_then_expr[0].1)?;
                let mut new_when_then_expr = Vec::with_capacity(when_then_expr.len());

                for (when, then) in when_then_expr.into_iter() {
                    if is_true(when.as_ref()) {
                        // Skip adding the rest of the when-then expressions after WHEN true
                        // CASE WHEN X THEN A WHEN TRUE THEN B ... END --> CASE WHEN X THEN A ELSE B END
                        else_expr = Some(then);
                        break;
                    } else if !is_false(when.as_ref()) {
                        new_when_then_expr.push((when, then));
                    }
                    // else: skip WHEN false cases
                }

                // Exclude CASE statement altogether if there are no when-then expressions left
                if new_when_then_expr.is_empty() {
                    // CASE WHEN false THEN A ELSE B END --> B
                    if let Some(else_expr) = else_expr {
                        return Ok(Transformed::yes(*else_expr));
                    // CASE WHEN false THEN A END --> NULL
                    } else {
                        let null =
                            Expr::Literal(ScalarValue::try_new_null(&out_type)?, None);
                        return Ok(Transformed::yes(null));
                    }
                }

                Transformed::yes(Expr::Case(Case {
                    expr: None,
                    when_then_expr: new_when_then_expr,
                    else_expr,
                }))
            }

            // CASE
            //   WHEN X THEN A
            //   WHEN Y THEN B
            //   ...
            //   ELSE Q
            // END
            //
            // ---> (X AND A) OR (Y AND B AND NOT X) OR ... (NOT (X OR Y) AND Q)
            //
            // Note: the rationale for this rewrite is that the expr can then be further
            // simplified using the existing rules for AND/OR
            Expr::Case(Case {
                expr: None,
                when_then_expr,
                else_expr,
            }) if !when_then_expr.is_empty()
                // The rewrite is O(n²) in general so limit to small number of when-thens that can be true
                && (when_then_expr.len() < 3 // small number of input whens
                    // or all thens are literal bools and a small number of them are true
                    || (when_then_expr.iter().all(|(_, then)| is_bool_lit(then))
                        && when_then_expr.iter().filter(|(_, then)| is_true(then)).count() < 3))
                && info.is_boolean_type(&when_then_expr[0].1)? =>
            {
                // String disjunction of all the when predicates encountered so far. Not nullable.
                let mut filter_expr = lit(false);
                // The disjunction of all the cases
                let mut out_expr = lit(false);

                for (when, then) in when_then_expr {
                    let when = is_exactly_true(*when, info)?;
                    let case_expr =
                        when.clone().and(filter_expr.clone().not()).and(*then);

                    out_expr = out_expr.or(case_expr);
                    filter_expr = filter_expr.or(when);
                }

                let else_expr = else_expr.map(|b| *b).unwrap_or_else(lit_bool_null);
                let case_expr = filter_expr.not().and(else_expr);
                out_expr = out_expr.or(case_expr);

                // Do a first pass at simplification
                out_expr.rewrite(self)?
            }
            // CASE
            //   WHEN X THEN true
            //   WHEN Y THEN true
            //   WHEN Z THEN false
            //   ...
            //   ELSE true
            // END
            //
            // --->
            //
            // NOT(CASE
            //   WHEN X THEN false
            //   WHEN Y THEN false
            //   WHEN Z THEN true
            //   ...
            //   ELSE false
            // END)
            //
            // Note: the rationale for this rewrite is that the case can then be further
            // simplified into a small number of ANDs and ORs
            Expr::Case(Case {
                expr: None,
                when_then_expr,
                else_expr,
            }) if !when_then_expr.is_empty()
                && when_then_expr
                    .iter()
                    .all(|(_, then)| is_bool_lit(then)) // all thens are literal bools
                // This simplification is only helpful if we end up with a small number of true thens
                && when_then_expr
                    .iter()
                    .filter(|(_, then)| is_false(then))
                    .count()
                    < 3
                && else_expr.as_deref().is_none_or(is_bool_lit) =>
            {
                Transformed::yes(
                    Expr::Case(Case {
                        expr: None,
                        when_then_expr: when_then_expr
                            .into_iter()
                            .map(|(when, then)| (when, Box::new(Expr::Not(then))))
                            .collect(),
                        else_expr: else_expr
                            .map(|else_expr| Box::new(Expr::Not(else_expr))),
                    })
                    .not(),
                )
            }
            Expr::ScalarFunction(ScalarFunction { func: udf, args }) => {
                match udf.simplify(args, info)? {
                    ExprSimplifyResult::Original(args) => {
                        Transformed::no(Expr::ScalarFunction(ScalarFunction {
                            func: udf,
                            args,
                        }))
                    }
                    ExprSimplifyResult::Simplified(expr) => Transformed::yes(expr),
                }
            }

            Expr::AggregateFunction(datafusion_expr::expr::AggregateFunction {
                ref func,
                ..
            }) => match (func.simplify(), expr) {
                (Some(simplify_function), Expr::AggregateFunction(af)) => {
                    Transformed::yes(simplify_function(af, info)?)
                }
                (_, expr) => Transformed::no(expr),
            },

            Expr::WindowFunction(ref window_fun) => match (window_fun.simplify(), expr) {
                (Some(simplify_function), Expr::WindowFunction(wf)) => {
                    Transformed::yes(simplify_function(*wf, info)?)
                }
                (_, expr) => Transformed::no(expr),
            },

            //
            // Rules for Between
            //

            // a between 3 and 5  -->  a >= 3 AND a <=5
            // a not between 3 and 5  -->  a < 3 OR a > 5
            Expr::Between(between) => Transformed::yes(if between.negated {
                let l = *between.expr.clone();
                let r = *between.expr;
                or(l.lt(*between.low), r.gt(*between.high))
            } else {
                and(
                    between.expr.clone().gt_eq(*between.low),
                    between.expr.lt_eq(*between.high),
                )
            }),

            //
            // Rules for regexes
            //
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: op @ (RegexMatch | RegexNotMatch | RegexIMatch | RegexNotIMatch),
                right,
            }) => Transformed::yes(simplify_regex_expr(left, op, right)?),

            // Rules for Like
            Expr::Like(like) => {
                // `\` is implicit escape, see https://github.com/apache/datafusion/issues/13291
                let escape_char = like.escape_char.unwrap_or('\\');
                match as_string_scalar(&like.pattern) {
                    Some((data_type, pattern_str)) => {
                        match pattern_str {
                            None => return Ok(Transformed::yes(lit_bool_null())),
                            Some(pattern_str) if pattern_str == "%" => {
                                // exp LIKE '%' is
                                //   - when exp is not NULL, it's true
                                //   - when exp is NULL, it's NULL
                                // exp NOT LIKE '%' is
                                //   - when exp is not NULL, it's false
                                //   - when exp is NULL, it's NULL
                                let result_for_non_null = lit(!like.negated);
                                Transformed::yes(if !info.nullable(&like.expr)? {
                                    result_for_non_null
                                } else {
                                    Expr::Case(Case {
                                        expr: Some(Box::new(Expr::IsNotNull(like.expr))),
                                        when_then_expr: vec![(
                                            Box::new(lit(true)),
                                            Box::new(result_for_non_null),
                                        )],
                                        else_expr: None,
                                    })
                                })
                            }
                            Some(pattern_str)
                                if pattern_str.contains("%%")
                                    && !pattern_str.contains(escape_char) =>
                            {
                                // Repeated occurrences of wildcard are redundant so remove them
                                // exp LIKE '%%'  --> exp LIKE '%'
                                let simplified_pattern = Regex::new("%%+")
                                    .unwrap()
                                    .replace_all(pattern_str, "%")
                                    .to_string();
                                Transformed::yes(Expr::Like(Like {
                                    pattern: Box::new(to_string_scalar(
                                        &data_type,
                                        Some(simplified_pattern),
                                    )),
                                    ..like
                                }))
                            }
                            Some(pattern_str)
                                if !like.case_insensitive
                                    && !pattern_str
                                        .contains(['%', '_', escape_char].as_ref()) =>
                            {
                                // If the pattern does not contain any wildcards, we can simplify the like expression to an equality expression
                                // TODO: handle escape characters
                                Transformed::yes(Expr::BinaryExpr(BinaryExpr {
                                    left: like.expr.clone(),
                                    op: if like.negated { NotEq } else { Eq },
                                    right: like.pattern.clone(),
                                }))
                            }

                            Some(_pattern_str) => Transformed::no(Expr::Like(like)),
                        }
                    }
                    None => Transformed::no(Expr::Like(like)),
                }
            }

            // a is not null/unknown --> true (if a is not nullable)
            Expr::IsNotNull(expr) | Expr::IsNotUnknown(expr)
                if !info.nullable(&expr)? =>
            {
                Transformed::yes(lit(true))
            }

            // a is null/unknown --> false (if a is not nullable)
            Expr::IsNull(expr) | Expr::IsUnknown(expr) if !info.nullable(&expr)? => {
                Transformed::yes(lit(false))
            }

            // expr IN () --> false
            // expr NOT IN () --> true
            Expr::InList(InList {
                expr: _,
                list,
                negated,
            }) if list.is_empty() => Transformed::yes(lit(negated)),

            // null in (x, y, z) --> null
            // null not in (x, y, z) --> null
            Expr::InList(InList {
                expr,
                list,
                negated: _,
            }) if is_null(expr.as_ref()) && !list.is_empty() => {
                Transformed::yes(lit_bool_null())
            }

            // expr IN ((subquery)) -> expr IN (subquery), see ##5529
            Expr::InList(InList {
                expr,
                mut list,
                negated,
            }) if list.len() == 1
                && matches!(list.first(), Some(Expr::ScalarSubquery { .. })) =>
            {
                let Expr::ScalarSubquery(subquery) = list.remove(0) else {
                    unreachable!()
                };

                Transformed::yes(Expr::InSubquery(InSubquery::new(
                    expr, subquery, negated,
                )))
            }

            // Combine multiple OR expressions into a single IN list expression if possible
            //
            // i.e. `a = 1 OR a = 2 OR a = 3` -> `a IN (1, 2, 3)`
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Or,
                right,
            }) if are_inlist_and_eq(left.as_ref(), right.as_ref()) => {
                let lhs = to_inlist(*left).unwrap();
                let rhs = to_inlist(*right).unwrap();
                let mut seen: HashSet<Expr> = HashSet::new();
                let list = lhs
                    .list
                    .into_iter()
                    .chain(rhs.list)
                    .filter(|e| seen.insert(e.to_owned()))
                    .collect::<Vec<_>>();

                let merged_inlist = InList {
                    expr: lhs.expr,
                    list,
                    negated: false,
                };

                Transformed::yes(Expr::InList(merged_inlist))
            }

            // Simplify expressions that is guaranteed to be true or false to a literal boolean expression
            //
            // Rules:
            // If both expressions are `IN` or `NOT IN`, then we can apply intersection or union on both lists
            //   Intersection:
            //     1. `a in (1,2,3) AND a in (4,5) -> a in (), which is false`
            //     2. `a in (1,2,3) AND a in (2,3,4) -> a in (2,3)`
            //     3. `a not in (1,2,3) OR a not in (3,4,5,6) -> a not in (3)`
            //   Union:
            //     4. `a not int (1,2,3) AND a not in (4,5,6) -> a not in (1,2,3,4,5,6)`
            //     # This rule is handled by `or_in_list_simplifier.rs`
            //     5. `a in (1,2,3) OR a in (4,5,6) -> a in (1,2,3,4,5,6)`
            // If one of the expressions is `IN` and another one is `NOT IN`, then we apply exception on `In` expression
            //     6. `a in (1,2,3,4) AND a not in (1,2,3,4,5) -> a in (), which is false`
            //     7. `a not in (1,2,3,4) AND a in (1,2,3,4,5) -> a = 5`
            //     8. `a in (1,2,3,4) AND a not in (5,6,7,8) -> a in (1,2,3,4)`
            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if are_inlist_and_eq_and_match_neg(
                left.as_ref(),
                right.as_ref(),
                false,
                false,
            ) =>
            {
                match (*left, *right) {
                    (Expr::InList(l1), Expr::InList(l2)) => {
                        return inlist_intersection(l1, &l2, false).map(Transformed::yes);
                    }
                    // Matched previously once
                    _ => unreachable!(),
                }
            }

            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if are_inlist_and_eq_and_match_neg(
                left.as_ref(),
                right.as_ref(),
                true,
                true,
            ) =>
            {
                match (*left, *right) {
                    (Expr::InList(l1), Expr::InList(l2)) => {
                        return inlist_union(l1, l2, true).map(Transformed::yes);
                    }
                    // Matched previously once
                    _ => unreachable!(),
                }
            }

            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if are_inlist_and_eq_and_match_neg(
                left.as_ref(),
                right.as_ref(),
                false,
                true,
            ) =>
            {
                match (*left, *right) {
                    (Expr::InList(l1), Expr::InList(l2)) => {
                        return inlist_except(l1, &l2).map(Transformed::yes);
                    }
                    // Matched previously once
                    _ => unreachable!(),
                }
            }

            Expr::BinaryExpr(BinaryExpr {
                left,
                op: And,
                right,
            }) if are_inlist_and_eq_and_match_neg(
                left.as_ref(),
                right.as_ref(),
                true,
                false,
            ) =>
            {
                match (*left, *right) {
                    (Expr::InList(l1), Expr::InList(l2)) => {
                        return inlist_except(l2, &l1).map(Transformed::yes);
                    }
                    // Matched previously once
                    _ => unreachable!(),
                }
            }

            Expr::BinaryExpr(BinaryExpr {
                left,
                op: Or,
                right,
            }) if are_inlist_and_eq_and_match_neg(
                left.as_ref(),
                right.as_ref(),
                true,
                true,
            ) =>
            {
                match (*left, *right) {
                    (Expr::InList(l1), Expr::InList(l2)) => {
                        return inlist_intersection(l1, &l2, true).map(Transformed::yes);
                    }
                    // Matched previously once
                    _ => unreachable!(),
                }
            }

            // =======================================
            // unwrap_cast_in_comparison
            // =======================================
            //
            // For case:
            // try_cast/cast(expr as data_type) op literal
            Expr::BinaryExpr(BinaryExpr { left, op, right })
                if is_cast_expr_and_support_unwrap_cast_in_comparison_for_binary(
                    info, &left, op, &right,
                ) && op.supports_propagation() =>
            {
                unwrap_cast_in_comparison_for_binary(info, *left, *right, op)?
            }
            // literal op try_cast/cast(expr as data_type)
            // -->
            // try_cast/cast(expr as data_type) op_swap literal
            Expr::BinaryExpr(BinaryExpr { left, op, right })
                if is_cast_expr_and_support_unwrap_cast_in_comparison_for_binary(
                    info, &right, op, &left,
                ) && op.supports_propagation()
                    && op.swap().is_some() =>
            {
                unwrap_cast_in_comparison_for_binary(
                    info,
                    *right,
                    *left,
                    op.swap().unwrap(),
                )?
            }
            // For case:
            // try_cast/cast(expr as left_type) in (expr1,expr2,expr3)
            Expr::InList(InList {
                expr: mut left,
                list,
                negated,
            }) if is_cast_expr_and_support_unwrap_cast_in_comparison_for_inlist(
                info, &left, &list,
            ) =>
            {
                let (Expr::TryCast(TryCast {
                    expr: left_expr, ..
                })
                | Expr::Cast(Cast {
                    expr: left_expr, ..
                })) = left.as_mut()
                else {
                    return internal_err!("Expect cast expr, but got {:?}", left)?;
                };

                let expr_type = info.get_data_type(left_expr)?;
                let right_exprs = list
                    .into_iter()
                    .map(|right| {
                        match right {
                            Expr::Literal(right_lit_value, _) => {
                                // if the right_lit_value can be casted to the type of internal_left_expr
                                // we need to unwrap the cast for cast/try_cast expr, and add cast to the literal
                                let Some(value) = try_cast_literal_to_type(&right_lit_value, &expr_type) else {
                                    internal_err!(
                                        "Can't cast the list expr {:?} to type {}",
                                        right_lit_value, &expr_type
                                    )?
                                };
                                Ok(lit(value))
                            }
                            other_expr => internal_err!(
                                "Only support literal expr to optimize, but the expr is {:?}",
                                &other_expr
                            ),
                        }
                    })
                    .collect::<Result<Vec<_>>>()?;

                Transformed::yes(Expr::InList(InList {
                    expr: std::mem::take(left_expr),
                    list: right_exprs,
                    negated,
                }))
            }

            // no additional rewrites possible
            expr => Transformed::no(expr),
        })
    }
}

fn as_string_scalar(expr: &Expr) -> Option<(DataType, &Option<String>)> {
    match expr {
        Expr::Literal(ScalarValue::Utf8(s), _) => Some((DataType::Utf8, s)),
        Expr::Literal(ScalarValue::LargeUtf8(s), _) => Some((DataType::LargeUtf8, s)),
        Expr::Literal(ScalarValue::Utf8View(s), _) => Some((DataType::Utf8View, s)),
        _ => None,
    }
}

fn to_string_scalar(data_type: &DataType, value: Option<String>) -> Expr {
    match data_type {
        DataType::Utf8 => Expr::Literal(ScalarValue::Utf8(value), None),
        DataType::LargeUtf8 => Expr::Literal(ScalarValue::LargeUtf8(value), None),
        DataType::Utf8View => Expr::Literal(ScalarValue::Utf8View(value), None),
        _ => unreachable!(),
    }
}

fn has_common_conjunction(lhs: &Expr, rhs: &Expr) -> bool {
    let lhs_set: HashSet<&Expr> = iter_conjunction(lhs).collect();
    iter_conjunction(rhs).any(|e| lhs_set.contains(&e) && !e.is_volatile())
}

// TODO: We might not need this after defer pattern for Box is stabilized. https://github.com/rust-lang/rust/issues/87121
fn are_inlist_and_eq_and_match_neg(
    left: &Expr,
    right: &Expr,
    is_left_neg: bool,
    is_right_neg: bool,
) -> bool {
    match (left, right) {
        (Expr::InList(l), Expr::InList(r)) => {
            l.expr == r.expr && l.negated == is_left_neg && r.negated == is_right_neg
        }
        _ => false,
    }
}

// TODO: We might not need this after defer pattern for Box is stabilized. https://github.com/rust-lang/rust/issues/87121
fn are_inlist_and_eq(left: &Expr, right: &Expr) -> bool {
    let left = as_inlist(left);
    let right = as_inlist(right);
    if let (Some(lhs), Some(rhs)) = (left, right) {
        matches!(lhs.expr.as_ref(), Expr::Column(_))
            && matches!(rhs.expr.as_ref(), Expr::Column(_))
            && lhs.expr == rhs.expr
            && !lhs.negated
            && !rhs.negated
    } else {
        false
    }
}

/// Try to convert an expression to an in-list expression
fn as_inlist(expr: &'_ Expr) -> Option<Cow<'_, InList>> {
    match expr {
        Expr::InList(inlist) => Some(Cow::Borrowed(inlist)),
        Expr::BinaryExpr(BinaryExpr { left, op, right }) if *op == Operator::Eq => {
            match (left.as_ref(), right.as_ref()) {
                (Expr::Column(_), Expr::Literal(_, _)) => Some(Cow::Owned(InList {
                    expr: left.clone(),
                    list: vec![*right.clone()],
                    negated: false,
                })),
                (Expr::Literal(_, _), Expr::Column(_)) => Some(Cow::Owned(InList {
                    expr: right.clone(),
                    list: vec![*left.clone()],
                    negated: false,
                })),
                _ => None,
            }
        }
        _ => None,
    }
}

fn to_inlist(expr: Expr) -> Option<InList> {
    match expr {
        Expr::InList(inlist) => Some(inlist),
        Expr::BinaryExpr(BinaryExpr {
            left,
            op: Operator::Eq,
            right,
        }) => match (left.as_ref(), right.as_ref()) {
            (Expr::Column(_), Expr::Literal(_, _)) => Some(InList {
                expr: left,
                list: vec![*right],
                negated: false,
            }),
            (Expr::Literal(_, _), Expr::Column(_)) => Some(InList {
                expr: right,
                list: vec![*left],
                negated: false,
            }),
            _ => None,
        },
        _ => None,
    }
}

/// Return the union of two inlist expressions
/// maintaining the order of the elements in the two lists
fn inlist_union(mut l1: InList, l2: InList, negated: bool) -> Result<Expr> {
    // extend the list in l1 with the elements in l2 that are not already in l1
    let l1_items: HashSet<_> = l1.list.iter().collect();

    // keep all l2 items that do not also appear in l1
    let keep_l2: Vec<_> = l2
        .list
        .into_iter()
        .filter_map(|e| if l1_items.contains(&e) { None } else { Some(e) })
        .collect();

    l1.list.extend(keep_l2);
    l1.negated = negated;
    Ok(Expr::InList(l1))
}

/// Return the intersection of two inlist expressions
/// maintaining the order of the elements in the two lists
fn inlist_intersection(mut l1: InList, l2: &InList, negated: bool) -> Result<Expr> {
    let l2_items = l2.list.iter().collect::<HashSet<_>>();

    // remove all items from l1 that are not in l2
    l1.list.retain(|e| l2_items.contains(e));

    // e in () is always false
    // e not in () is always true
    if l1.list.is_empty() {
        return Ok(lit(negated));
    }
    Ok(Expr::InList(l1))
}

/// Return the all items in l1 that are not in l2
/// maintaining the order of the elements in the two lists
fn inlist_except(mut l1: InList, l2: &InList) -> Result<Expr> {
    let l2_items = l2.list.iter().collect::<HashSet<_>>();

    // keep only items from l1 that are not in l2
    l1.list.retain(|e| !l2_items.contains(e));

    if l1.list.is_empty() {
        return Ok(lit(false));
    }
    Ok(Expr::InList(l1))
}

/// Returns expression testing a boolean `expr` for being exactly `true` (not `false` or NULL).
fn is_exactly_true(expr: Expr, info: &impl SimplifyInfo) -> Result<Expr> {
    if !info.nullable(&expr)? {
        Ok(expr)
    } else {
        Ok(Expr::BinaryExpr(BinaryExpr {
            left: Box::new(expr),
            op: Operator::IsNotDistinctFrom,
            right: Box::new(lit(true)),
        }))
    }
}

// A * 1 -> A
// A / 1 -> A
//
// Move this function body out of the large match branch avoid stack overflow
fn simplify_right_is_one_case<S: SimplifyInfo>(
    info: &S,
    left: Box<Expr>,
    op: &Operator,
    right: &Expr,
) -> Result<Transformed<Expr>> {
    // Check if resulting type would be different due to coercion
    let left_type = info.get_data_type(&left)?;
    let right_type = info.get_data_type(right)?;
    match BinaryTypeCoercer::new(&left_type, op, &right_type).get_result_type() {
        Ok(result_type) => {
            // Only cast if the types differ
            if left_type != result_type {
                Ok(Transformed::yes(Expr::Cast(Cast::new(left, result_type))))
            } else {
                Ok(Transformed::yes(*left))
            }
        }
        Err(_) => Ok(Transformed::yes(*left)),
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::simplify_expressions::SimplifyContext;
    use crate::test::test_table_scan_with_name;
    use arrow::datatypes::FieldRef;
    use datafusion_common::{assert_contains, DFSchemaRef, ToDFSchema};
    use datafusion_expr::{
        expr::WindowFunction,
        function::{
            AccumulatorArgs, AggregateFunctionSimplification,
            WindowFunctionSimplification,
        },
        interval_arithmetic::Interval,
        *,
    };
    use datafusion_functions_window_common::field::WindowUDFFieldArgs;
    use datafusion_functions_window_common::partition::PartitionEvaluatorArgs;
    use datafusion_physical_expr::PhysicalExpr;
    use std::hash::Hash;
    use std::sync::LazyLock;
    use std::{
        collections::HashMap,
        ops::{BitAnd, BitOr, BitXor},
        sync::Arc,
    };

    // ------------------------------
    // --- ExprSimplifier tests -----
    // ------------------------------
    #[test]
    fn api_basic() {
        let props = ExecutionProps::new();
        let simplifier =
            ExprSimplifier::new(SimplifyContext::new(&props).with_schema(test_schema()));

        let expr = lit(1) + lit(2);
        let expected = lit(3);
        assert_eq!(expected, simplifier.simplify(expr).unwrap());
    }

    #[test]
    fn basic_coercion() {
        let schema = test_schema();
        let props = ExecutionProps::new();
        let simplifier = ExprSimplifier::new(
            SimplifyContext::new(&props).with_schema(Arc::clone(&schema)),
        );

        // Note expr type is int32 (not int64)
        // (1i64 + 2i32) < i
        let expr = (lit(1i64) + lit(2i32)).lt(col("i"));
        // should fully simplify to 3 < i (though i has been coerced to i64)
        let expected = lit(3i64).lt(col("i"));

        let expr = simplifier.coerce(expr, &schema).unwrap();

        assert_eq!(expected, simplifier.simplify(expr).unwrap());
    }

    fn test_schema() -> DFSchemaRef {
        static TEST_SCHEMA: LazyLock<DFSchemaRef> = LazyLock::new(|| {
            Schema::new(vec![
                Field::new("i", DataType::Int64, false),
                Field::new("b", DataType::Boolean, true),
            ])
            .to_dfschema_ref()
            .unwrap()
        });
        Arc::clone(&TEST_SCHEMA)
    }

    #[test]
    fn simplify_and_constant_prop() {
        let props = ExecutionProps::new();
        let simplifier =
            ExprSimplifier::new(SimplifyContext::new(&props).with_schema(test_schema()));

        // should be able to simplify to false
        // (i * (1 - 2)) > 0
        let expr = (col("i") * (lit(1) - lit(1))).gt(lit(0));
        let expected = lit(false);
        assert_eq!(expected, simplifier.simplify(expr).unwrap());
    }

    #[test]
    fn simplify_and_constant_prop_with_case() {
        let props = ExecutionProps::new();
        let simplifier =
            ExprSimplifier::new(SimplifyContext::new(&props).with_schema(test_schema()));

        //   CASE
        //     WHEN i>5 AND false THEN i > 5
        //     WHEN i<5 AND true THEN i < 5
        //     ELSE false
        //   END
        //
        // Can be simplified to `i < 5`
        let expr = when(col("i").gt(lit(5)).and(lit(false)), col("i").gt(lit(5)))
            .when(col("i").lt(lit(5)).and(lit(true)), col("i").lt(lit(5)))
            .otherwise(lit(false))
            .unwrap();
        let expected = col("i").lt(lit(5));
        assert_eq!(expected, simplifier.simplify(expr).unwrap());
    }

    // ------------------------------
    // --- Simplifier tests -----
    // ------------------------------

    #[test]
    fn test_simplify_canonicalize() {
        {
            let expr = lit(1).lt(col("c2")).and(col("c2").gt(lit(1)));
            let expected = col("c2").gt(lit(1));
            assert_eq!(simplify(expr), expected);
        }
        {
            let expr = col("c1").lt(col("c2")).and(col("c2").gt(col("c1")));
            let expected = col("c2").gt(col("c1"));
            assert_eq!(simplify(expr), expected);
        }
        {
            let expr = col("c1")
                .eq(lit(1))
                .and(lit(1).eq(col("c1")))
                .and(col("c1").eq(lit(3)));
            let expected = col("c1").eq(lit(1)).and(col("c1").eq(lit(3)));
            assert_eq!(simplify(expr), expected);
        }
        {
            let expr = col("c1")
                .eq(col("c2"))
                .and(col("c1").gt(lit(5)))
                .and(col("c2").eq(col("c1")));
            let expected = col("c2").eq(col("c1")).and(col("c1").gt(lit(5)));
            assert_eq!(simplify(expr), expected);
        }
        {
            let expr = col("c1")
                .eq(lit(1))
                .and(col("c2").gt(lit(3)).or(lit(3).lt(col("c2"))));
            let expected = col("c1").eq(lit(1)).and(col("c2").gt(lit(3)));
            assert_eq!(simplify(expr), expected);
        }
        {
            let expr = col("c1").lt(lit(5)).and(col("c1").gt_eq(lit(5)));
            let expected = col("c1").lt(lit(5)).and(col("c1").gt_eq(lit(5)));
            assert_eq!(simplify(expr), expected);
        }
        {
            let expr = col("c1").lt(lit(5)).and(col("c1").gt_eq(lit(5)));
            let expected = col("c1").lt(lit(5)).and(col("c1").gt_eq(lit(5)));
            assert_eq!(simplify(expr), expected);
        }
        {
            let expr = col("c1").gt(col("c2")).and(col("c1").gt(col("c2")));
            let expected = col("c2").lt(col("c1"));
            assert_eq!(simplify(expr), expected);
        }
    }

    #[test]
    fn test_simplify_eq_not_self() {
        // `expr_a`: column `c2` is nullable, so `c2 = c2` simplifies to `c2 IS NOT NULL OR NULL`
        // This ensures the expression is only true when `c2` is not NULL, accounting for SQL's NULL semantics.
        let expr_a = col("c2").eq(col("c2"));
        let expected_a = col("c2").is_not_null().or(lit_bool_null());

        // `expr_b`: column `c2_non_null` is explicitly non-nullable, so `c2_non_null = c2_non_null` is always true
        let expr_b = col("c2_non_null").eq(col("c2_non_null"));
        let expected_b = lit(true);

        assert_eq!(simplify(expr_a), expected_a);
        assert_eq!(simplify(expr_b), expected_b);
    }

    #[test]
    fn test_simplify_or_true() {
        let expr_a = col("c2").or(lit(true));
        let expr_b = lit(true).or(col("c2"));
        let expected = lit(true);

        assert_eq!(simplify(expr_a), expected);
        assert_eq!(simplify(expr_b), expected);
    }

    #[test]
    fn test_simplify_or_false() {
        let expr_a = lit(false).or(col("c2"));
        let expr_b = col("c2").or(lit(false));
        let expected = col("c2");

        assert_eq!(simplify(expr_a), expected);
        assert_eq!(simplify(expr_b), expected);
    }

    #[test]
    fn test_simplify_or_same() {
        let expr = col("c2").or(col("c2"));
        let expected = col("c2");

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_or_not_self() {
        // A OR !A if A is not nullable --> true
        // !A OR A if A is not nullable --> true
        let expr_a = col("c2_non_null").or(col("c2_non_null").not());
        let expr_b = col("c2_non_null").not().or(col("c2_non_null"));
        let expected = lit(true);

        assert_eq!(simplify(expr_a), expected);
        assert_eq!(simplify(expr_b), expected);
    }

    #[test]
    fn test_simplify_and_false() {
        let expr_a = lit(false).and(col("c2"));
        let expr_b = col("c2").and(lit(false));
        let expected = lit(false);

        assert_eq!(simplify(expr_a), expected);
        assert_eq!(simplify(expr_b), expected);
    }

    #[test]
    fn test_simplify_and_same() {
        let expr = col("c2").and(col("c2"));
        let expected = col("c2");

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_and_true() {
        let expr_a = lit(true).and(col("c2"));
        let expr_b = col("c2").and(lit(true));
        let expected = col("c2");

        assert_eq!(simplify(expr_a), expected);
        assert_eq!(simplify(expr_b), expected);
    }

    #[test]
    fn test_simplify_and_not_self() {
        // A AND !A if A is not nullable --> false
        // !A AND A if A is not nullable --> false
        let expr_a = col("c2_non_null").and(col("c2_non_null").not());
        let expr_b = col("c2_non_null").not().and(col("c2_non_null"));
        let expected = lit(false);

        assert_eq!(simplify(expr_a), expected);
        assert_eq!(simplify(expr_b), expected);
    }

    #[test]
    fn test_simplify_multiply_by_one() {
        let expr_a = col("c2") * lit(1);
        let expr_b = lit(1) * col("c2");
        let expected = col("c2");

        assert_eq!(simplify(expr_a), expected);
        assert_eq!(simplify(expr_b), expected);

        let expr = col("c2") * lit(ScalarValue::Decimal128(Some(10000000000), 38, 10));
        assert_eq!(simplify(expr), expected);

        let expr = lit(ScalarValue::Decimal128(Some(10000000000), 31, 10)) * col("c2");
        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_multiply_by_null() {
        let null = lit(ScalarValue::Int64(None));
        // A * null --> null
        {
            let expr = col("c3") * null.clone();
            assert_eq!(simplify(expr), null);
        }
        // null * A --> null
        {
            let expr = null.clone() * col("c3");
            assert_eq!(simplify(expr), null);
        }
    }

    #[test]
    fn test_simplify_multiply_by_zero() {
        // cannot optimize A * null (null * A) if A is nullable
        {
            let expr_a = col("c2") * lit(0);
            let expr_b = lit(0) * col("c2");

            assert_eq!(simplify(expr_a.clone()), expr_a);
            assert_eq!(simplify(expr_b.clone()), expr_b);
        }
        // 0 * A --> 0 if A is not nullable
        {
            let expr = lit(0) * col("c2_non_null");
            assert_eq!(simplify(expr), lit(0));
        }
        // A * 0 --> 0 if A is not nullable
        {
            let expr = col("c2_non_null") * lit(0);
            assert_eq!(simplify(expr), lit(0));
        }
        // A * Decimal128(0) --> 0 if A is not nullable
        {
            let expr = col("c2_non_null") * lit(ScalarValue::Decimal128(Some(0), 31, 10));
            assert_eq!(
                simplify(expr),
                lit(ScalarValue::Decimal128(Some(0), 31, 10))
            );
            let expr = binary_expr(
                lit(ScalarValue::Decimal128(Some(0), 31, 10)),
                Operator::Multiply,
                col("c2_non_null"),
            );
            assert_eq!(
                simplify(expr),
                lit(ScalarValue::Decimal128(Some(0), 31, 10))
            );
        }
    }

    #[test]
    fn test_simplify_divide_by_one() {
        let expr = binary_expr(col("c2"), Operator::Divide, lit(1));
        let expected = col("c2");
        assert_eq!(simplify(expr), expected);
        let expr = col("c2") / lit(ScalarValue::Decimal128(Some(10000000000), 31, 10));
        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_divide_null() {
        // A / null --> null
        let null = lit(ScalarValue::Int64(None));
        {
            let expr = col("c3") / null.clone();
            assert_eq!(simplify(expr), null);
        }
        // null / A --> null
        {
            let expr = null.clone() / col("c3");
            assert_eq!(simplify(expr), null);
        }
    }

    #[test]
    fn test_simplify_divide_by_same() {
        let expr = col("c2") / col("c2");
        // if c2 is null, c2 / c2 = null, so can't simplify
        let expected = expr.clone();

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_modulo_by_null() {
        let null = lit(ScalarValue::Int64(None));
        // A % null --> null
        {
            let expr = col("c3") % null.clone();
            assert_eq!(simplify(expr), null);
        }
        // null % A --> null
        {
            let expr = null.clone() % col("c3");
            assert_eq!(simplify(expr), null);
        }
    }

    #[test]
    fn test_simplify_modulo_by_one() {
        let expr = col("c2") % lit(1);
        // if c2 is null, c2 % 1 = null, so can't simplify
        let expected = expr.clone();

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_divide_zero_by_zero() {
        // because divide by 0 maybe occur in short-circuit expression
        // so we should not simplify this, and throw error in runtime
        let expr = lit(0) / lit(0);
        let expected = expr.clone();

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_divide_by_zero() {
        // because divide by 0 maybe occur in short-circuit expression
        // so we should not simplify this, and throw error in runtime
        let expr = col("c2_non_null") / lit(0);
        let expected = expr.clone();

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_modulo_by_one_non_null() {
        let expr = col("c3_non_null") % lit(1);
        let expected = lit(0_i64);
        assert_eq!(simplify(expr), expected);
        let expr =
            col("c3_non_null") % lit(ScalarValue::Decimal128(Some(10000000000), 31, 10));
        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_bitwise_xor_by_null() {
        let null = lit(ScalarValue::Int64(None));
        // A ^ null --> null
        {
            let expr = col("c3") ^ null.clone();
            assert_eq!(simplify(expr), null);
        }
        // null ^ A --> null
        {
            let expr = null.clone() ^ col("c3");
            assert_eq!(simplify(expr), null);
        }
    }

    #[test]
    fn test_simplify_bitwise_shift_right_by_null() {
        let null = lit(ScalarValue::Int64(None));
        // A >> null --> null
        {
            let expr = col("c3") >> null.clone();
            assert_eq!(simplify(expr), null);
        }
        // null >> A --> null
        {
            let expr = null.clone() >> col("c3");
            assert_eq!(simplify(expr), null);
        }
    }

    #[test]
    fn test_simplify_bitwise_shift_left_by_null() {
        let null = lit(ScalarValue::Int64(None));
        // A << null --> null
        {
            let expr = col("c3") << null.clone();
            assert_eq!(simplify(expr), null);
        }
        // null << A --> null
        {
            let expr = null.clone() << col("c3");
            assert_eq!(simplify(expr), null);
        }
    }

    #[test]
    fn test_simplify_bitwise_and_by_zero() {
        // A & 0 --> 0
        {
            let expr = col("c2_non_null") & lit(0);
            assert_eq!(simplify(expr), lit(0));
        }
        // 0 & A --> 0
        {
            let expr = lit(0) & col("c2_non_null");
            assert_eq!(simplify(expr), lit(0));
        }
    }

    #[test]
    fn test_simplify_bitwise_or_by_zero() {
        // A | 0 --> A
        {
            let expr = col("c2_non_null") | lit(0);
            assert_eq!(simplify(expr), col("c2_non_null"));
        }
        // 0 | A --> A
        {
            let expr = lit(0) | col("c2_non_null");
            assert_eq!(simplify(expr), col("c2_non_null"));
        }
    }

    #[test]
    fn test_simplify_bitwise_xor_by_zero() {
        // A ^ 0 --> A
        {
            let expr = col("c2_non_null") ^ lit(0);
            assert_eq!(simplify(expr), col("c2_non_null"));
        }
        // 0 ^ A --> A
        {
            let expr = lit(0) ^ col("c2_non_null");
            assert_eq!(simplify(expr), col("c2_non_null"));
        }
    }

    #[test]
    fn test_simplify_bitwise_bitwise_shift_right_by_zero() {
        // A >> 0 --> A
        {
            let expr = col("c2_non_null") >> lit(0);
            assert_eq!(simplify(expr), col("c2_non_null"));
        }
    }

    #[test]
    fn test_simplify_bitwise_bitwise_shift_left_by_zero() {
        // A << 0 --> A
        {
            let expr = col("c2_non_null") << lit(0);
            assert_eq!(simplify(expr), col("c2_non_null"));
        }
    }

    #[test]
    fn test_simplify_bitwise_and_by_null() {
        let null = Expr::Literal(ScalarValue::Int64(None), None);
        // A & null --> null
        {
            let expr = col("c3") & null.clone();
            assert_eq!(simplify(expr), null);
        }
        // null & A --> null
        {
            let expr = null.clone() & col("c3");
            assert_eq!(simplify(expr), null);
        }
    }

    #[test]
    fn test_simplify_composed_bitwise_and() {
        // ((c2 > 5) & (c1 < 6)) & (c2 > 5) --> (c2 > 5) & (c1 < 6)

        let expr = bitwise_and(
            bitwise_and(col("c2").gt(lit(5)), col("c1").lt(lit(6))),
            col("c2").gt(lit(5)),
        );
        let expected = bitwise_and(col("c2").gt(lit(5)), col("c1").lt(lit(6)));

        assert_eq!(simplify(expr), expected);

        // (c2 > 5) & ((c2 > 5) & (c1 < 6)) --> (c2 > 5) & (c1 < 6)

        let expr = bitwise_and(
            col("c2").gt(lit(5)),
            bitwise_and(col("c2").gt(lit(5)), col("c1").lt(lit(6))),
        );
        let expected = bitwise_and(col("c2").gt(lit(5)), col("c1").lt(lit(6)));
        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_composed_bitwise_or() {
        // ((c2 > 5) | (c1 < 6)) | (c2 > 5) --> (c2 > 5) | (c1 < 6)

        let expr = bitwise_or(
            bitwise_or(col("c2").gt(lit(5)), col("c1").lt(lit(6))),
            col("c2").gt(lit(5)),
        );
        let expected = bitwise_or(col("c2").gt(lit(5)), col("c1").lt(lit(6)));

        assert_eq!(simplify(expr), expected);

        // (c2 > 5) | ((c2 > 5) | (c1 < 6)) --> (c2 > 5) | (c1 < 6)

        let expr = bitwise_or(
            col("c2").gt(lit(5)),
            bitwise_or(col("c2").gt(lit(5)), col("c1").lt(lit(6))),
        );
        let expected = bitwise_or(col("c2").gt(lit(5)), col("c1").lt(lit(6)));

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_composed_bitwise_xor() {
        // with an even number of the column "c2"
        // c2 ^ ((c2 ^ (c2 | c1)) ^ (c1 & c2)) --> (c2 | c1) ^ (c1 & c2)

        let expr = bitwise_xor(
            col("c2"),
            bitwise_xor(
                bitwise_xor(col("c2"), bitwise_or(col("c2"), col("c1"))),
                bitwise_and(col("c1"), col("c2")),
            ),
        );

        let expected = bitwise_xor(
            bitwise_or(col("c2"), col("c1")),
            bitwise_and(col("c1"), col("c2")),
        );

        assert_eq!(simplify(expr), expected);

        // with an odd number of the column "c2"
        // c2 ^ (c2 ^ (c2 | c1)) ^ ((c1 & c2) ^ c2) --> c2 ^ ((c2 | c1) ^ (c1 & c2))

        let expr = bitwise_xor(
            col("c2"),
            bitwise_xor(
                bitwise_xor(col("c2"), bitwise_or(col("c2"), col("c1"))),
                bitwise_xor(bitwise_and(col("c1"), col("c2")), col("c2")),
            ),
        );

        let expected = bitwise_xor(
            col("c2"),
            bitwise_xor(
                bitwise_or(col("c2"), col("c1")),
                bitwise_and(col("c1"), col("c2")),
            ),
        );

        assert_eq!(simplify(expr), expected);

        // with an even number of the column "c2"
        // ((c2 ^ (c2 | c1)) ^ (c1 & c2)) ^ c2 --> (c2 | c1) ^ (c1 & c2)

        let expr = bitwise_xor(
            bitwise_xor(
                bitwise_xor(col("c2"), bitwise_or(col("c2"), col("c1"))),
                bitwise_and(col("c1"), col("c2")),
            ),
            col("c2"),
        );

        let expected = bitwise_xor(
            bitwise_or(col("c2"), col("c1")),
            bitwise_and(col("c1"), col("c2")),
        );

        assert_eq!(simplify(expr), expected);

        // with an odd number of the column "c2"
        // (c2 ^ (c2 | c1)) ^ ((c1 & c2) ^ c2) ^ c2 --> ((c2 | c1) ^ (c1 & c2)) ^ c2

        let expr = bitwise_xor(
            bitwise_xor(
                bitwise_xor(col("c2"), bitwise_or(col("c2"), col("c1"))),
                bitwise_xor(bitwise_and(col("c1"), col("c2")), col("c2")),
            ),
            col("c2"),
        );

        let expected = bitwise_xor(
            bitwise_xor(
                bitwise_or(col("c2"), col("c1")),
                bitwise_and(col("c1"), col("c2")),
            ),
            col("c2"),
        );

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_negated_bitwise_and() {
        // !c4 & c4 --> 0
        let expr = (-col("c4_non_null")) & col("c4_non_null");
        let expected = lit(0u32);

        assert_eq!(simplify(expr), expected);
        // c4 & !c4 --> 0
        let expr = col("c4_non_null") & (-col("c4_non_null"));
        let expected = lit(0u32);

        assert_eq!(simplify(expr), expected);

        // !c3 & c3 --> 0
        let expr = (-col("c3_non_null")) & col("c3_non_null");
        let expected = lit(0i64);

        assert_eq!(simplify(expr), expected);
        // c3 & !c3 --> 0
        let expr = col("c3_non_null") & (-col("c3_non_null"));
        let expected = lit(0i64);

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_negated_bitwise_or() {
        // !c4 | c4 --> -1
        let expr = (-col("c4_non_null")) | col("c4_non_null");
        let expected = lit(-1i32);

        assert_eq!(simplify(expr), expected);

        // c4 | !c4 --> -1
        let expr = col("c4_non_null") | (-col("c4_non_null"));
        let expected = lit(-1i32);

        assert_eq!(simplify(expr), expected);

        // !c3 | c3 --> -1
        let expr = (-col("c3_non_null")) | col("c3_non_null");
        let expected = lit(-1i64);

        assert_eq!(simplify(expr), expected);

        // c3 | !c3 --> -1
        let expr = col("c3_non_null") | (-col("c3_non_null"));
        let expected = lit(-1i64);

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_negated_bitwise_xor() {
        // !c4 ^ c4 --> -1
        let expr = (-col("c4_non_null")) ^ col("c4_non_null");
        let expected = lit(-1i32);

        assert_eq!(simplify(expr), expected);

        // c4 ^ !c4 --> -1
        let expr = col("c4_non_null") ^ (-col("c4_non_null"));
        let expected = lit(-1i32);

        assert_eq!(simplify(expr), expected);

        // !c3 ^ c3 --> -1
        let expr = (-col("c3_non_null")) ^ col("c3_non_null");
        let expected = lit(-1i64);

        assert_eq!(simplify(expr), expected);

        // c3 ^ !c3 --> -1
        let expr = col("c3_non_null") ^ (-col("c3_non_null"));
        let expected = lit(-1i64);

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_bitwise_and_or() {
        // (c2 < 3) & ((c2 < 3) | c1) -> (c2 < 3)
        let expr = bitwise_and(
            col("c2_non_null").lt(lit(3)),
            bitwise_or(col("c2_non_null").lt(lit(3)), col("c1_non_null")),
        );
        let expected = col("c2_non_null").lt(lit(3));

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_bitwise_or_and() {
        // (c2 < 3) | ((c2 < 3) & c1) -> (c2 < 3)
        let expr = bitwise_or(
            col("c2_non_null").lt(lit(3)),
            bitwise_and(col("c2_non_null").lt(lit(3)), col("c1_non_null")),
        );
        let expected = col("c2_non_null").lt(lit(3));

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_simple_bitwise_and() {
        // (c2 > 5) & (c2 > 5) -> (c2 > 5)
        let expr = (col("c2").gt(lit(5))).bitand(col("c2").gt(lit(5)));
        let expected = col("c2").gt(lit(5));

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_simple_bitwise_or() {
        // (c2 > 5) | (c2 > 5) -> (c2 > 5)
        let expr = (col("c2").gt(lit(5))).bitor(col("c2").gt(lit(5)));
        let expected = col("c2").gt(lit(5));

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_simple_bitwise_xor() {
        // c4 ^ c4 -> 0
        let expr = (col("c4")).bitxor(col("c4"));
        let expected = lit(0u32);

        assert_eq!(simplify(expr), expected);

        // c3 ^ c3 -> 0
        let expr = col("c3").bitxor(col("c3"));
        let expected = lit(0i64);

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_modulo_by_zero_non_null() {
        // because modulo by 0 maybe occur in short-circuit expression
        // so we should not simplify this, and throw error in runtime.
        let expr = col("c2_non_null") % lit(0);
        let expected = expr.clone();

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_simple_and() {
        // (c2 > 5) AND (c2 > 5) -> (c2 > 5)
        let expr = (col("c2").gt(lit(5))).and(col("c2").gt(lit(5)));
        let expected = col("c2").gt(lit(5));

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_composed_and() {
        // ((c2 > 5) AND (c1 < 6)) AND (c2 > 5)
        let expr = and(
            and(col("c2").gt(lit(5)), col("c1").lt(lit(6))),
            col("c2").gt(lit(5)),
        );
        let expected = and(col("c2").gt(lit(5)), col("c1").lt(lit(6)));

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_negated_and() {
        // (c2 > 5) AND !(c2 > 5) --> (c2 > 5) AND (c2 <= 5)
        let expr = and(col("c2").gt(lit(5)), Expr::not(col("c2").gt(lit(5))));
        let expected = col("c2").gt(lit(5)).and(col("c2").lt_eq(lit(5)));

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_or_and() {
        let l = col("c2").gt(lit(5));
        let r = and(col("c1").lt(lit(6)), col("c2").gt(lit(5)));

        // (c2 > 5) OR ((c1 < 6) AND (c2 > 5))
        let expr = or(l.clone(), r.clone());

        let expected = l.clone();
        assert_eq!(simplify(expr), expected);

        // ((c1 < 6) AND (c2 > 5)) OR (c2 > 5)
        let expr = or(r, l);
        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_or_and_non_null() {
        let l = col("c2_non_null").gt(lit(5));
        let r = and(col("c1_non_null").lt(lit(6)), col("c2_non_null").gt(lit(5)));

        // (c2 > 5) OR ((c1 < 6) AND (c2 > 5)) --> c2 > 5
        let expr = or(l.clone(), r.clone());

        // This is only true if `c1 < 6` is not nullable / can not be null.
        let expected = col("c2_non_null").gt(lit(5));

        assert_eq!(simplify(expr), expected);

        // ((c1 < 6) AND (c2 > 5)) OR (c2 > 5) --> c2 > 5
        let expr = or(l, r);

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_and_or() {
        let l = col("c2").gt(lit(5));
        let r = or(col("c1").lt(lit(6)), col("c2").gt(lit(5)));

        // (c2 > 5) AND ((c1 < 6) OR (c2 > 5)) --> c2 > 5
        let expr = and(l.clone(), r.clone());

        let expected = l.clone();
        assert_eq!(simplify(expr), expected);

        // ((c1 < 6) OR (c2 > 5)) AND (c2 > 5) --> c2 > 5
        let expr = and(r, l);
        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_and_or_non_null() {
        let l = col("c2_non_null").gt(lit(5));
        let r = or(col("c1_non_null").lt(lit(6)), col("c2_non_null").gt(lit(5)));

        // (c2 > 5) AND ((c1 < 6) OR (c2 > 5)) --> c2 > 5
        let expr = and(l.clone(), r.clone());

        // This is only true if `c1 < 6` is not nullable / can not be null.
        let expected = col("c2_non_null").gt(lit(5));

        assert_eq!(simplify(expr), expected);

        // ((c1 < 6) OR (c2 > 5)) AND (c2 > 5) --> c2 > 5
        let expr = and(l, r);

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_by_de_morgan_laws() {
        // Laws with logical operations
        // !(c3 AND c4) --> !c3 OR !c4
        let expr = and(col("c3"), col("c4")).not();
        let expected = or(col("c3").not(), col("c4").not());
        assert_eq!(simplify(expr), expected);
        // !(c3 OR c4) --> !c3 AND !c4
        let expr = or(col("c3"), col("c4")).not();
        let expected = and(col("c3").not(), col("c4").not());
        assert_eq!(simplify(expr), expected);
        // !(!c3) --> c3
        let expr = col("c3").not().not();
        let expected = col("c3");
        assert_eq!(simplify(expr), expected);

        // Laws with bitwise operations
        // !(c3 & c4) --> !c3 | !c4
        let expr = -bitwise_and(col("c3"), col("c4"));
        let expected = bitwise_or(-col("c3"), -col("c4"));
        assert_eq!(simplify(expr), expected);
        // !(c3 | c4) --> !c3 & !c4
        let expr = -bitwise_or(col("c3"), col("c4"));
        let expected = bitwise_and(-col("c3"), -col("c4"));
        assert_eq!(simplify(expr), expected);
        // !(!c3) --> c3
        let expr = -(-col("c3"));
        let expected = col("c3");
        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_null_and_false() {
        let expr = and(lit_bool_null(), lit(false));
        let expr_eq = lit(false);

        assert_eq!(simplify(expr), expr_eq);
    }

    #[test]
    fn test_simplify_divide_null_by_null() {
        let null = lit(ScalarValue::Int32(None));
        let expr_plus = null.clone() / null.clone();
        let expr_eq = null;

        assert_eq!(simplify(expr_plus), expr_eq);
    }

    #[test]
    fn test_simplify_simplify_arithmetic_expr() {
        let expr_plus = lit(1) + lit(1);

        assert_eq!(simplify(expr_plus), lit(2));
    }

    #[test]
    fn test_simplify_simplify_eq_expr() {
        let expr_eq = binary_expr(lit(1), Operator::Eq, lit(1));

        assert_eq!(simplify(expr_eq), lit(true));
    }

    #[test]
    fn test_simplify_regex() {
        // malformed regex
        assert_contains!(
            try_simplify(regex_match(col("c1"), lit("foo{")))
                .unwrap_err()
                .to_string(),
            "regex parse error"
        );

        // unsupported cases
        assert_no_change(regex_match(col("c1"), lit("foo.*")));
        assert_no_change(regex_match(col("c1"), lit("(foo)")));
        assert_no_change(regex_match(col("c1"), lit("%")));
        assert_no_change(regex_match(col("c1"), lit("_")));
        assert_no_change(regex_match(col("c1"), lit("f%o")));
        assert_no_change(regex_match(col("c1"), lit("^f%o")));
        assert_no_change(regex_match(col("c1"), lit("f_o")));

        // empty cases
        assert_change(
            regex_match(col("c1"), lit("")),
            if_not_null(col("c1"), true),
        );
        assert_change(
            regex_not_match(col("c1"), lit("")),
            if_not_null(col("c1"), false),
        );
        assert_change(
            regex_imatch(col("c1"), lit("")),
            if_not_null(col("c1"), true),
        );
        assert_change(
            regex_not_imatch(col("c1"), lit("")),
            if_not_null(col("c1"), false),
        );

        // single character
        assert_change(regex_match(col("c1"), lit("x")), col("c1").like(lit("%x%")));

        // single word
        assert_change(
            regex_match(col("c1"), lit("foo")),
            col("c1").like(lit("%foo%")),
        );

        // regular expressions that match an exact literal
        assert_change(regex_match(col("c1"), lit("^$")), col("c1").eq(lit("")));
        assert_change(
            regex_not_match(col("c1"), lit("^$")),
            col("c1").not_eq(lit("")),
        );
        assert_change(
            regex_match(col("c1"), lit("^foo$")),
            col("c1").eq(lit("foo")),
        );
        assert_change(
            regex_not_match(col("c1"), lit("^foo$")),
            col("c1").not_eq(lit("foo")),
        );

        // regular expressions that match exact captured literals
        assert_change(
            regex_match(col("c1"), lit("^(foo|bar)$")),
            col("c1").eq(lit("foo")).or(col("c1").eq(lit("bar"))),
        );
        assert_change(
            regex_not_match(col("c1"), lit("^(foo|bar)$")),
            col("c1")
                .not_eq(lit("foo"))
                .and(col("c1").not_eq(lit("bar"))),
        );
        assert_change(
            regex_match(col("c1"), lit("^(foo)$")),
            col("c1").eq(lit("foo")),
        );
        assert_change(
            regex_match(col("c1"), lit("^(foo|bar|baz)$")),
            ((col("c1").eq(lit("foo"))).or(col("c1").eq(lit("bar"))))
                .or(col("c1").eq(lit("baz"))),
        );
        assert_change(
            regex_match(col("c1"), lit("^(foo|bar|baz|qux)$")),
            col("c1")
                .in_list(vec![lit("foo"), lit("bar"), lit("baz"), lit("qux")], false),
        );
        assert_change(
            regex_match(col("c1"), lit("^(fo_o)$")),
            col("c1").eq(lit("fo_o")),
        );
        assert_change(
            regex_match(col("c1"), lit("^(fo_o)$")),
            col("c1").eq(lit("fo_o")),
        );
        assert_change(
            regex_match(col("c1"), lit("^(fo_o|ba_r)$")),
            col("c1").eq(lit("fo_o")).or(col("c1").eq(lit("ba_r"))),
        );
        assert_change(
            regex_not_match(col("c1"), lit("^(fo_o|ba_r)$")),
            col("c1")
                .not_eq(lit("fo_o"))
                .and(col("c1").not_eq(lit("ba_r"))),
        );
        assert_change(
            regex_match(col("c1"), lit("^(fo_o|ba_r|ba_z)$")),
            ((col("c1").eq(lit("fo_o"))).or(col("c1").eq(lit("ba_r"))))
                .or(col("c1").eq(lit("ba_z"))),
        );
        assert_change(
            regex_match(col("c1"), lit("^(fo_o|ba_r|baz|qu_x)$")),
            col("c1").in_list(
                vec![lit("fo_o"), lit("ba_r"), lit("baz"), lit("qu_x")],
                false,
            ),
        );

        // regular expressions that mismatch captured literals
        assert_no_change(regex_match(col("c1"), lit("(foo|bar)")));
        assert_no_change(regex_match(col("c1"), lit("(foo|bar)*")));
        assert_no_change(regex_match(col("c1"), lit("(fo_o|b_ar)")));
        assert_no_change(regex_match(col("c1"), lit("(foo|ba_r)*")));
        assert_no_change(regex_match(col("c1"), lit("(fo_o|ba_r)*")));
        assert_no_change(regex_match(col("c1"), lit("^(foo|bar)*")));
        assert_no_change(regex_match(col("c1"), lit("^(foo)(bar)$")));
        assert_no_change(regex_match(col("c1"), lit("^")));
        assert_no_change(regex_match(col("c1"), lit("$")));
        assert_no_change(regex_match(col("c1"), lit("$^")));
        assert_no_change(regex_match(col("c1"), lit("$foo^")));

        // regular expressions that match a partial literal
        assert_change(
            regex_match(col("c1"), lit("^foo")),
            col("c1").like(lit("foo%")),
        );
        assert_change(
            regex_match(col("c1"), lit("foo$")),
            col("c1").like(lit("%foo")),
        );
        assert_change(
            regex_match(col("c1"), lit("^foo|bar$")),
            col("c1").like(lit("foo%")).or(col("c1").like(lit("%bar"))),
        );

        // OR-chain
        assert_change(
            regex_match(col("c1"), lit("foo|bar|baz")),
            col("c1")
                .like(lit("%foo%"))
                .or(col("c1").like(lit("%bar%")))
                .or(col("c1").like(lit("%baz%"))),
        );
        assert_change(
            regex_match(col("c1"), lit("foo|x|baz")),
            col("c1")
                .like(lit("%foo%"))
                .or(col("c1").like(lit("%x%")))
                .or(col("c1").like(lit("%baz%"))),
        );
        assert_change(
            regex_not_match(col("c1"), lit("foo|bar|baz")),
            col("c1")
                .not_like(lit("%foo%"))
                .and(col("c1").not_like(lit("%bar%")))
                .and(col("c1").not_like(lit("%baz%"))),
        );
        // both anchored expressions (translated to equality) and unanchored
        assert_change(
            regex_match(col("c1"), lit("foo|^x$|baz")),
            col("c1")
                .like(lit("%foo%"))
                .or(col("c1").eq(lit("x")))
                .or(col("c1").like(lit("%baz%"))),
        );
        assert_change(
            regex_not_match(col("c1"), lit("foo|^bar$|baz")),
            col("c1")
                .not_like(lit("%foo%"))
                .and(col("c1").not_eq(lit("bar")))
                .and(col("c1").not_like(lit("%baz%"))),
        );
        // Too many patterns (MAX_REGEX_ALTERNATIONS_EXPANSION)
        assert_no_change(regex_match(col("c1"), lit("foo|bar|baz|blarg|bozo|etc")));
    }

    #[track_caller]
    fn assert_no_change(expr: Expr) {
        let optimized = simplify(expr.clone());
        assert_eq!(expr, optimized);
    }

    #[track_caller]
    fn assert_change(expr: Expr, expected: Expr) {
        let optimized = simplify(expr);
        assert_eq!(optimized, expected);
    }

    fn regex_match(left: Expr, right: Expr) -> Expr {
        Expr::BinaryExpr(BinaryExpr {
            left: Box::new(left),
            op: Operator::RegexMatch,
            right: Box::new(right),
        })
    }

    fn regex_not_match(left: Expr, right: Expr) -> Expr {
        Expr::BinaryExpr(BinaryExpr {
            left: Box::new(left),
            op: Operator::RegexNotMatch,
            right: Box::new(right),
        })
    }

    fn regex_imatch(left: Expr, right: Expr) -> Expr {
        Expr::BinaryExpr(BinaryExpr {
            left: Box::new(left),
            op: Operator::RegexIMatch,
            right: Box::new(right),
        })
    }

    fn regex_not_imatch(left: Expr, right: Expr) -> Expr {
        Expr::BinaryExpr(BinaryExpr {
            left: Box::new(left),
            op: Operator::RegexNotIMatch,
            right: Box::new(right),
        })
    }

    // ------------------------------
    // ----- Simplifier tests -------
    // ------------------------------

    fn try_simplify(expr: Expr) -> Result<Expr> {
        let schema = expr_test_schema();
        let execution_props = ExecutionProps::new();
        let simplifier = ExprSimplifier::new(
            SimplifyContext::new(&execution_props).with_schema(schema),
        );
        simplifier.simplify(expr)
    }

    fn coerce(expr: Expr) -> Expr {
        let schema = expr_test_schema();
        let execution_props = ExecutionProps::new();
        let simplifier = ExprSimplifier::new(
            SimplifyContext::new(&execution_props).with_schema(Arc::clone(&schema)),
        );
        simplifier.coerce(expr, schema.as_ref()).unwrap()
    }

    fn simplify(expr: Expr) -> Expr {
        try_simplify(expr).unwrap()
    }

    fn try_simplify_with_cycle_count(expr: Expr) -> Result<(Expr, u32)> {
        let schema = expr_test_schema();
        let execution_props = ExecutionProps::new();
        let simplifier = ExprSimplifier::new(
            SimplifyContext::new(&execution_props).with_schema(schema),
        );
        let (expr, count) = simplifier.simplify_with_cycle_count_transformed(expr)?;
        Ok((expr.data, count))
    }

    fn simplify_with_cycle_count(expr: Expr) -> (Expr, u32) {
        try_simplify_with_cycle_count(expr).unwrap()
    }

    fn simplify_with_guarantee(
        expr: Expr,
        guarantees: Vec<(Expr, NullableInterval)>,
    ) -> Expr {
        let schema = expr_test_schema();
        let execution_props = ExecutionProps::new();
        let simplifier = ExprSimplifier::new(
            SimplifyContext::new(&execution_props).with_schema(schema),
        )
        .with_guarantees(guarantees);
        simplifier.simplify(expr).unwrap()
    }

    fn expr_test_schema() -> DFSchemaRef {
        static EXPR_TEST_SCHEMA: LazyLock<DFSchemaRef> = LazyLock::new(|| {
            Arc::new(
                DFSchema::from_unqualified_fields(
                    vec![
                        Field::new("c1", DataType::Utf8, true),
                        Field::new("c2", DataType::Boolean, true),
                        Field::new("c3", DataType::Int64, true),
                        Field::new("c4", DataType::UInt32, true),
                        Field::new("c1_non_null", DataType::Utf8, false),
                        Field::new("c2_non_null", DataType::Boolean, false),
                        Field::new("c3_non_null", DataType::Int64, false),
                        Field::new("c4_non_null", DataType::UInt32, false),
                        Field::new("c5", DataType::FixedSizeBinary(3), true),
                    ]
                    .into(),
                    HashMap::new(),
                )
                .unwrap(),
            )
        });
        Arc::clone(&EXPR_TEST_SCHEMA)
    }

    #[test]
    fn simplify_expr_null_comparison() {
        // x = null is always null
        assert_eq!(
            simplify(lit(true).eq(lit(ScalarValue::Boolean(None)))),
            lit(ScalarValue::Boolean(None)),
        );

        // null != null is always null
        assert_eq!(
            simplify(
                lit(ScalarValue::Boolean(None)).not_eq(lit(ScalarValue::Boolean(None)))
            ),
            lit(ScalarValue::Boolean(None)),
        );

        // x != null is always null
        assert_eq!(
            simplify(col("c2").not_eq(lit(ScalarValue::Boolean(None)))),
            lit(ScalarValue::Boolean(None)),
        );

        // null = x is always null
        assert_eq!(
            simplify(lit(ScalarValue::Boolean(None)).eq(col("c2"))),
            lit(ScalarValue::Boolean(None)),
        );
    }

    #[test]
    fn simplify_expr_is_not_null() {
        assert_eq!(
            simplify(Expr::IsNotNull(Box::new(col("c1")))),
            Expr::IsNotNull(Box::new(col("c1")))
        );

        // 'c1_non_null IS NOT NULL' is always true
        assert_eq!(
            simplify(Expr::IsNotNull(Box::new(col("c1_non_null")))),
            lit(true)
        );
    }

    #[test]
    fn simplify_expr_is_null() {
        assert_eq!(
            simplify(Expr::IsNull(Box::new(col("c1")))),
            Expr::IsNull(Box::new(col("c1")))
        );

        // 'c1_non_null IS NULL' is always false
        assert_eq!(
            simplify(Expr::IsNull(Box::new(col("c1_non_null")))),
            lit(false)
        );
    }

    #[test]
    fn simplify_expr_is_unknown() {
        assert_eq!(simplify(col("c2").is_unknown()), col("c2").is_unknown(),);

        // 'c2_non_null is unknown' is always false
        assert_eq!(simplify(col("c2_non_null").is_unknown()), lit(false));
    }

    #[test]
    fn simplify_expr_is_not_known() {
        assert_eq!(
            simplify(col("c2").is_not_unknown()),
            col("c2").is_not_unknown()
        );

        // 'c2_non_null is not unknown' is always true
        assert_eq!(simplify(col("c2_non_null").is_not_unknown()), lit(true));
    }

    #[test]
    fn simplify_expr_eq() {
        let schema = expr_test_schema();
        assert_eq!(col("c2").get_type(&schema).unwrap(), DataType::Boolean);

        // true = true -> true
        assert_eq!(simplify(lit(true).eq(lit(true))), lit(true));

        // true = false -> false
        assert_eq!(simplify(lit(true).eq(lit(false))), lit(false),);

        // c2 = true -> c2
        assert_eq!(simplify(col("c2").eq(lit(true))), col("c2"));

        // c2 = false => !c2
        assert_eq!(simplify(col("c2").eq(lit(false))), col("c2").not(),);
    }

    #[test]
    fn simplify_expr_eq_skip_nonboolean_type() {
        let schema = expr_test_schema();

        // When one of the operand is not of boolean type, folding the
        // other boolean constant will change return type of
        // expression to non-boolean.
        //
        // Make sure c1 column to be used in tests is not boolean type
        assert_eq!(col("c1").get_type(&schema).unwrap(), DataType::Utf8);

        // don't fold c1 = foo
        assert_eq!(simplify(col("c1").eq(lit("foo"))), col("c1").eq(lit("foo")),);
    }

    #[test]
    fn simplify_expr_not_eq() {
        let schema = expr_test_schema();

        assert_eq!(col("c2").get_type(&schema).unwrap(), DataType::Boolean);

        // c2 != true -> !c2
        assert_eq!(simplify(col("c2").not_eq(lit(true))), col("c2").not(),);

        // c2 != false -> c2
        assert_eq!(simplify(col("c2").not_eq(lit(false))), col("c2"),);

        // test constant
        assert_eq!(simplify(lit(true).not_eq(lit(true))), lit(false),);

        assert_eq!(simplify(lit(true).not_eq(lit(false))), lit(true),);
    }

    #[test]
    fn simplify_expr_not_eq_skip_nonboolean_type() {
        let schema = expr_test_schema();

        // when one of the operand is not of boolean type, folding the
        // other boolean constant will change return type of
        // expression to non-boolean.
        assert_eq!(col("c1").get_type(&schema).unwrap(), DataType::Utf8);

        assert_eq!(
            simplify(col("c1").not_eq(lit("foo"))),
            col("c1").not_eq(lit("foo")),
        );
    }

    #[test]
    fn simplify_literal_case_equality() {
        // CASE WHEN c2 != false THEN "ok" ELSE "not_ok"
        let simple_case = Expr::Case(Case::new(
            None,
            vec![(
                Box::new(col("c2_non_null").not_eq(lit(false))),
                Box::new(lit("ok")),
            )],
            Some(Box::new(lit("not_ok"))),
        ));

        // CASE WHEN c2 != false THEN "ok" ELSE "not_ok" == "ok"
        // -->
        // CASE WHEN c2 != false THEN "ok" == "ok" ELSE "not_ok" == "ok"
        // -->
        // CASE WHEN c2 != false THEN true ELSE false
        // -->
        // c2
        assert_eq!(
            simplify(binary_expr(simple_case.clone(), Operator::Eq, lit("ok"),)),
            col("c2_non_null"),
        );

        // CASE WHEN c2 != false THEN "ok" ELSE "not_ok" != "ok"
        // -->
        // NOT(CASE WHEN c2 != false THEN "ok" == "ok" ELSE "not_ok" == "ok")
        // -->
        // NOT(CASE WHEN c2 != false THEN true ELSE false)
        // -->
        // NOT(c2)
        assert_eq!(
            simplify(binary_expr(simple_case, Operator::NotEq, lit("ok"),)),
            not(col("c2_non_null")),
        );

        let complex_case = Expr::Case(Case::new(
            None,
            vec![
                (
                    Box::new(col("c1").eq(lit("inboxed"))),
                    Box::new(lit("pending")),
                ),
                (
                    Box::new(col("c1").eq(lit("scheduled"))),
                    Box::new(lit("pending")),
                ),
                (
                    Box::new(col("c1").eq(lit("completed"))),
                    Box::new(lit("completed")),
                ),
                (
                    Box::new(col("c1").eq(lit("paused"))),
                    Box::new(lit("paused")),
                ),
                (Box::new(col("c2")), Box::new(lit("running"))),
                (
                    Box::new(col("c1").eq(lit("invoked")).and(col("c3").gt(lit(0)))),
                    Box::new(lit("backing-off")),
                ),
            ],
            Some(Box::new(lit("ready"))),
        ));

        assert_eq!(
            simplify(binary_expr(
                complex_case.clone(),
                Operator::Eq,
                lit("completed"),
            )),
            not_distinct_from(col("c1").eq(lit("completed")), lit(true)).and(
                distinct_from(col("c1").eq(lit("inboxed")), lit(true))
                    .and(distinct_from(col("c1").eq(lit("scheduled")), lit(true)))
            )
        );

        assert_eq!(
            simplify(binary_expr(
                complex_case.clone(),
                Operator::NotEq,
                lit("completed"),
            )),
            distinct_from(col("c1").eq(lit("completed")), lit(true))
                .or(not_distinct_from(col("c1").eq(lit("inboxed")), lit(true))
                    .or(not_distinct_from(col("c1").eq(lit("scheduled")), lit(true))))
        );

        assert_eq!(
            simplify(binary_expr(
                complex_case.clone(),
                Operator::Eq,
                lit("running"),
            )),
            not_distinct_from(col("c2"), lit(true)).and(
                distinct_from(col("c1").eq(lit("inboxed")), lit(true))
                    .and(distinct_from(col("c1").eq(lit("scheduled")), lit(true)))
                    .and(distinct_from(col("c1").eq(lit("completed")), lit(true)))
                    .and(distinct_from(col("c1").eq(lit("paused")), lit(true)))
            )
        );

        assert_eq!(
            simplify(binary_expr(
                complex_case.clone(),
                Operator::Eq,
                lit("ready"),
            )),
            distinct_from(col("c1").eq(lit("inboxed")), lit(true))
                .and(distinct_from(col("c1").eq(lit("scheduled")), lit(true)))
                .and(distinct_from(col("c1").eq(lit("completed")), lit(true)))
                .and(distinct_from(col("c1").eq(lit("paused")), lit(true)))
                .and(distinct_from(col("c2"), lit(true)))
                .and(distinct_from(
                    col("c1").eq(lit("invoked")).and(col("c3").gt(lit(0))),
                    lit(true)
                ))
        );

        assert_eq!(
            simplify(binary_expr(
                complex_case.clone(),
                Operator::NotEq,
                lit("ready"),
            )),
            not_distinct_from(col("c1").eq(lit("inboxed")), lit(true))
                .or(not_distinct_from(col("c1").eq(lit("scheduled")), lit(true)))
                .or(not_distinct_from(col("c1").eq(lit("completed")), lit(true)))
                .or(not_distinct_from(col("c1").eq(lit("paused")), lit(true)))
                .or(not_distinct_from(col("c2"), lit(true)))
                .or(not_distinct_from(
                    col("c1").eq(lit("invoked")).and(col("c3").gt(lit(0))),
                    lit(true)
                ))
        );
    }

    #[test]
    fn simplify_expr_case_when_then_else() {
        // CASE WHEN c2 != false THEN "ok" == "not_ok" ELSE c2 == true
        // -->
        // CASE WHEN c2 THEN false ELSE c2
        // -->
        // false
        assert_eq!(
            simplify(Expr::Case(Case::new(
                None,
                vec![(
                    Box::new(col("c2_non_null").not_eq(lit(false))),
                    Box::new(lit("ok").eq(lit("not_ok"))),
                )],
                Some(Box::new(col("c2_non_null").eq(lit(true)))),
            ))),
            lit(false) // #1716
        );

        // CASE WHEN c2 != false THEN "ok" == "ok" ELSE c2
        // -->
        // CASE WHEN c2 THEN true ELSE c2
        // -->
        // c2
        //
        // Need to call simplify 2x due to
        // https://github.com/apache/datafusion/issues/1160
        assert_eq!(
            simplify(simplify(Expr::Case(Case::new(
                None,
                vec![(
                    Box::new(col("c2_non_null").not_eq(lit(false))),
                    Box::new(lit("ok").eq(lit("ok"))),
                )],
                Some(Box::new(col("c2_non_null").eq(lit(true)))),
            )))),
            col("c2_non_null")
        );

        // CASE WHEN ISNULL(c2) THEN true ELSE c2
        // -->
        // ISNULL(c2) OR c2
        //
        // Need to call simplify 2x due to
        // https://github.com/apache/datafusion/issues/1160
        assert_eq!(
            simplify(simplify(Expr::Case(Case::new(
                None,
                vec![(Box::new(col("c2").is_null()), Box::new(lit(true)),)],
                Some(Box::new(col("c2"))),
            )))),
            col("c2")
                .is_null()
                .or(col("c2").is_not_null().and(col("c2")))
        );

        // CASE WHEN c1 then true WHEN c2 then false ELSE true
        // --> c1 OR (NOT(c1) AND c2 AND FALSE) OR (NOT(c1 OR c2) AND TRUE)
        // --> c1 OR (NOT(c1) AND NOT(c2))
        // --> c1 OR NOT(c2)
        //
        // Need to call simplify 2x due to
        // https://github.com/apache/datafusion/issues/1160
        assert_eq!(
            simplify(simplify(Expr::Case(Case::new(
                None,
                vec![
                    (Box::new(col("c1_non_null")), Box::new(lit(true)),),
                    (Box::new(col("c2_non_null")), Box::new(lit(false)),),
                ],
                Some(Box::new(lit(true))),
            )))),
            col("c1_non_null").or(col("c1_non_null").not().and(col("c2_non_null").not()))
        );

        // CASE WHEN c1 then true WHEN c2 then true ELSE false
        // --> c1 OR (NOT(c1) AND c2 AND TRUE) OR (NOT(c1 OR c2) AND FALSE)
        // --> c1 OR (NOT(c1) AND c2)
        // --> c1 OR c2
        //
        // Need to call simplify 2x due to
        // https://github.com/apache/datafusion/issues/1160
        assert_eq!(
            simplify(simplify(Expr::Case(Case::new(
                None,
                vec![
                    (Box::new(col("c1_non_null")), Box::new(lit(true)),),
                    (Box::new(col("c2_non_null")), Box::new(lit(false)),),
                ],
                Some(Box::new(lit(true))),
            )))),
            col("c1_non_null").or(col("c1_non_null").not().and(col("c2_non_null").not()))
        );

        // CASE WHEN c > 0 THEN true END AS c1
        assert_eq!(
            simplify(simplify(Expr::Case(Case::new(
                None,
                vec![(Box::new(col("c3").gt(lit(0_i64))), Box::new(lit(true)))],
                None,
            )))),
            not_distinct_from(col("c3").gt(lit(0_i64)), lit(true)).or(distinct_from(
                col("c3").gt(lit(0_i64)),
                lit(true)
            )
            .and(lit_bool_null()))
        );

        // CASE WHEN c > 0 THEN true ELSE false END AS c1
        assert_eq!(
            simplify(simplify(Expr::Case(Case::new(
                None,
                vec![(Box::new(col("c3").gt(lit(0_i64))), Box::new(lit(true)))],
                Some(Box::new(lit(false))),
            )))),
            not_distinct_from(col("c3").gt(lit(0_i64)), lit(true))
        );
    }

    #[test]
    fn simplify_expr_case_when_first_true() {
        // CASE WHEN true THEN 1 ELSE c1 END --> 1
        assert_eq!(
            simplify(Expr::Case(Case::new(
                None,
                vec![(Box::new(lit(true)), Box::new(lit(1)),)],
                Some(Box::new(col("c1"))),
            ))),
            lit(1)
        );

        // CASE WHEN true THEN col('a') ELSE col('b') END --> col('a')
        assert_eq!(
            simplify(Expr::Case(Case::new(
                None,
                vec![(Box::new(lit(true)), Box::new(lit("a")),)],
                Some(Box::new(lit("b"))),
            ))),
            lit("a")
        );

        // CASE WHEN true THEN col('a') WHEN col('x') > 5 THEN col('b') ELSE col('c') END --> col('a')
        assert_eq!(
            simplify(Expr::Case(Case::new(
                None,
                vec![
                    (Box::new(lit(true)), Box::new(lit("a"))),
                    (Box::new(lit("x").gt(lit(5))), Box::new(lit("b"))),
                ],
                Some(Box::new(lit("c"))),
            ))),
            lit("a")
        );

        // CASE WHEN true THEN col('a') END --> col('a') (no else clause)
        assert_eq!(
            simplify(Expr::Case(Case::new(
                None,
                vec![(Box::new(lit(true)), Box::new(lit("a")),)],
                None,
            ))),
            lit("a")
        );

        // Negative test: CASE WHEN c2 THEN 1 ELSE 2 END should not be simplified
        let expr = Expr::Case(Case::new(
            None,
            vec![(Box::new(col("c2")), Box::new(lit(1)))],
            Some(Box::new(lit(2))),
        ));
        assert_eq!(simplify(expr.clone()), expr);

        // Negative test: CASE WHEN false THEN 1 ELSE 2 END should not use this rule
        let expr = Expr::Case(Case::new(
            None,
            vec![(Box::new(lit(false)), Box::new(lit(1)))],
            Some(Box::new(lit(2))),
        ));
        assert_ne!(simplify(expr), lit(1));

        // Negative test: CASE WHEN col('c1') > 5 THEN 1 ELSE 2 END should not be simplified
        let expr = Expr::Case(Case::new(
            None,
            vec![(Box::new(col("c1").gt(lit(5))), Box::new(lit(1)))],
            Some(Box::new(lit(2))),
        ));
        assert_eq!(simplify(expr.clone()), expr);
    }

    #[test]
    fn simplify_expr_case_when_any_true() {
        // CASE WHEN c3 > 0 THEN 'a' WHEN true THEN 'b' ELSE 'c' END --> CASE WHEN c3 > 0 THEN 'a' ELSE 'b' END
        assert_eq!(
            simplify(Expr::Case(Case::new(
                None,
                vec![
                    (Box::new(col("c3").gt(lit(0))), Box::new(lit("a"))),
                    (Box::new(lit(true)), Box::new(lit("b"))),
                ],
                Some(Box::new(lit("c"))),
            ))),
            Expr::Case(Case::new(
                None,
                vec![(Box::new(col("c3").gt(lit(0))), Box::new(lit("a")))],
                Some(Box::new(lit("b"))),
            ))
        );

        // CASE WHEN c3 > 0 THEN 'a' WHEN c4 < 0 THEN 'b' WHEN true THEN 'c' WHEN c3 = 0 THEN 'd' ELSE 'e' END
        // --> CASE WHEN c3 > 0 THEN 'a' WHEN c4 < 0 THEN 'b' ELSE 'c' END
        assert_eq!(
            simplify(Expr::Case(Case::new(
                None,
                vec![
                    (Box::new(col("c3").gt(lit(0))), Box::new(lit("a"))),
                    (Box::new(col("c4").lt(lit(0))), Box::new(lit("b"))),
                    (Box::new(lit(true)), Box::new(lit("c"))),
                    (Box::new(col("c3").eq(lit(0))), Box::new(lit("d"))),
                ],
                Some(Box::new(lit("e"))),
            ))),
            Expr::Case(Case::new(
                None,
                vec![
                    (Box::new(col("c3").gt(lit(0))), Box::new(lit("a"))),
                    (Box::new(col("c4").lt(lit(0))), Box::new(lit("b"))),
                ],
                Some(Box::new(lit("c"))),
            ))
        );

        // CASE WHEN c3 > 0 THEN 1 WHEN c4 < 0 THEN 2 WHEN true THEN 3 END (no else)
        // --> CASE WHEN c3 > 0 THEN 1 WHEN c4 < 0 THEN 2 ELSE 3 END
        assert_eq!(
            simplify(Expr::Case(Case::new(
                None,
                vec![
                    (Box::new(col("c3").gt(lit(0))), Box::new(lit(1))),
                    (Box::new(col("c4").lt(lit(0))), Box::new(lit(2))),
                    (Box::new(lit(true)), Box::new(lit(3))),
                ],
                None,
            ))),
            Expr::Case(Case::new(
                None,
                vec![
                    (Box::new(col("c3").gt(lit(0))), Box::new(lit(1))),
                    (Box::new(col("c4").lt(lit(0))), Box::new(lit(2))),
                ],
                Some(Box::new(lit(3))),
            ))
        );

        // Negative test: CASE WHEN c3 > 0 THEN c3 WHEN c4 < 0 THEN 2 ELSE 3 END should not be simplified
        let expr = Expr::Case(Case::new(
            None,
            vec![
                (Box::new(col("c3").gt(lit(0))), Box::new(col("c3"))),
                (Box::new(col("c4").lt(lit(0))), Box::new(lit(2))),
            ],
            Some(Box::new(lit(3))),
        ));
        assert_eq!(simplify(expr.clone()), expr);
    }

    #[test]
    fn simplify_expr_case_when_any_false() {
        // CASE WHEN false THEN 'a' END --> NULL
        assert_eq!(
            simplify(Expr::Case(Case::new(
                None,
                vec![(Box::new(lit(false)), Box::new(lit("a")))],
                None,
            ))),
            Expr::Literal(ScalarValue::Utf8(None), None)
        );

        // CASE WHEN false THEN 2 ELSE 1 END --> 1
        assert_eq!(
            simplify(Expr::Case(Case::new(
                None,
                vec![(Box::new(lit(false)), Box::new(lit(2)))],
                Some(Box::new(lit(1))),
            ))),
            lit(1),
        );

        // CASE WHEN c3 < 10 THEN 'b' WHEN false then c3 ELSE c4 END --> CASE WHEN c3 < 10 THEN b ELSE c4 END
        assert_eq!(
            simplify(Expr::Case(Case::new(
                None,
                vec![
                    (Box::new(col("c3").lt(lit(10))), Box::new(lit("b"))),
                    (Box::new(lit(false)), Box::new(col("c3"))),
                ],
                Some(Box::new(col("c4"))),
            ))),
            Expr::Case(Case::new(
                None,
                vec![(Box::new(col("c3").lt(lit(10))), Box::new(lit("b")))],
                Some(Box::new(col("c4"))),
            ))
        );

        // Negative test: CASE WHEN c3 = 4 THEN 1 ELSE 2 END should not be simplified
        let expr = Expr::Case(Case::new(
            None,
            vec![(Box::new(col("c3").eq(lit(4))), Box::new(lit(1)))],
            Some(Box::new(lit(2))),
        ));
        assert_eq!(simplify(expr.clone()), expr);
    }

    fn distinct_from(left: impl Into<Expr>, right: impl Into<Expr>) -> Expr {
        Expr::BinaryExpr(BinaryExpr {
            left: Box::new(left.into()),
            op: Operator::IsDistinctFrom,
            right: Box::new(right.into()),
        })
    }

    fn not_distinct_from(left: impl Into<Expr>, right: impl Into<Expr>) -> Expr {
        Expr::BinaryExpr(BinaryExpr {
            left: Box::new(left.into()),
            op: Operator::IsNotDistinctFrom,
            right: Box::new(right.into()),
        })
    }

    #[test]
    fn simplify_expr_bool_or() {
        // col || true is always true
        assert_eq!(simplify(col("c2").or(lit(true))), lit(true),);

        // col || false is always col
        assert_eq!(simplify(col("c2").or(lit(false))), col("c2"),);

        // true || null is always true
        assert_eq!(simplify(lit(true).or(lit_bool_null())), lit(true),);

        // null || true is always true
        assert_eq!(simplify(lit_bool_null().or(lit(true))), lit(true),);

        // false || null is always null
        assert_eq!(simplify(lit(false).or(lit_bool_null())), lit_bool_null(),);

        // null || false is always null
        assert_eq!(simplify(lit_bool_null().or(lit(false))), lit_bool_null(),);

        // ( c1 BETWEEN Int32(0) AND Int32(10) ) OR Boolean(NULL)
        // it can be either NULL or  TRUE depending on the value of `c1 BETWEEN Int32(0) AND Int32(10)`
        // and should not be rewritten
        let expr = col("c1").between(lit(0), lit(10));
        let expr = expr.or(lit_bool_null());
        let result = simplify(expr);

        let expected_expr = or(
            and(col("c1").gt_eq(lit(0)), col("c1").lt_eq(lit(10))),
            lit_bool_null(),
        );
        assert_eq!(expected_expr, result);
    }

    #[test]
    fn simplify_inlist() {
        assert_eq!(simplify(in_list(col("c1"), vec![], false)), lit(false));
        assert_eq!(simplify(in_list(col("c1"), vec![], true)), lit(true));

        // null in (...)  --> null
        assert_eq!(
            simplify(in_list(lit_bool_null(), vec![col("c1"), lit(1)], false)),
            lit_bool_null()
        );

        // null not in (...)  --> null
        assert_eq!(
            simplify(in_list(lit_bool_null(), vec![col("c1"), lit(1)], true)),
            lit_bool_null()
        );

        assert_eq!(
            simplify(in_list(col("c1"), vec![lit(1)], false)),
            col("c1").eq(lit(1))
        );
        assert_eq!(
            simplify(in_list(col("c1"), vec![lit(1)], true)),
            col("c1").not_eq(lit(1))
        );

        // more complex expressions can be simplified if list contains
        // one element only
        assert_eq!(
            simplify(in_list(col("c1") * lit(10), vec![lit(2)], false)),
            (col("c1") * lit(10)).eq(lit(2))
        );

        assert_eq!(
            simplify(in_list(col("c1"), vec![lit(1), lit(2)], false)),
            col("c1").eq(lit(1)).or(col("c1").eq(lit(2)))
        );
        assert_eq!(
            simplify(in_list(col("c1"), vec![lit(1), lit(2)], true)),
            col("c1").not_eq(lit(1)).and(col("c1").not_eq(lit(2)))
        );

        let subquery = Arc::new(test_table_scan_with_name("test").unwrap());
        assert_eq!(
            simplify(in_list(
                col("c1"),
                vec![scalar_subquery(Arc::clone(&subquery))],
                false
            )),
            in_subquery(col("c1"), Arc::clone(&subquery))
        );
        assert_eq!(
            simplify(in_list(
                col("c1"),
                vec![scalar_subquery(Arc::clone(&subquery))],
                true
            )),
            not_in_subquery(col("c1"), subquery)
        );

        let subquery1 =
            scalar_subquery(Arc::new(test_table_scan_with_name("test1").unwrap()));
        let subquery2 =
            scalar_subquery(Arc::new(test_table_scan_with_name("test2").unwrap()));

        // c1 NOT IN (<subquery1>, <subquery2>) -> c1 != <subquery1> AND c1 != <subquery2>
        assert_eq!(
            simplify(in_list(
                col("c1"),
                vec![subquery1.clone(), subquery2.clone()],
                true
            )),
            col("c1")
                .not_eq(subquery1.clone())
                .and(col("c1").not_eq(subquery2.clone()))
        );

        // c1 IN (<subquery1>, <subquery2>) -> c1 == <subquery1> OR c1 == <subquery2>
        assert_eq!(
            simplify(in_list(
                col("c1"),
                vec![subquery1.clone(), subquery2.clone()],
                false
            )),
            col("c1").eq(subquery1).or(col("c1").eq(subquery2))
        );

        // 1. c1 IN (1,2,3,4) AND c1 IN (5,6,7,8) -> false
        let expr = in_list(col("c1"), vec![lit(1), lit(2), lit(3), lit(4)], false).and(
            in_list(col("c1"), vec![lit(5), lit(6), lit(7), lit(8)], false),
        );
        assert_eq!(simplify(expr), lit(false));

        // 2. c1 IN (1,2,3,4) AND c1 IN (4,5,6,7) -> c1 = 4
        let expr = in_list(col("c1"), vec![lit(1), lit(2), lit(3), lit(4)], false).and(
            in_list(col("c1"), vec![lit(4), lit(5), lit(6), lit(7)], false),
        );
        assert_eq!(simplify(expr), col("c1").eq(lit(4)));

        // 3. c1 NOT IN (1, 2, 3, 4) OR c1 NOT IN (5, 6, 7, 8) -> true
        let expr = in_list(col("c1"), vec![lit(1), lit(2), lit(3), lit(4)], true).or(
            in_list(col("c1"), vec![lit(5), lit(6), lit(7), lit(8)], true),
        );
        assert_eq!(simplify(expr), lit(true));

        // 3.5 c1 NOT IN (1, 2, 3, 4) OR c1 NOT IN (4, 5, 6, 7) -> c1 != 4 (4 overlaps)
        let expr = in_list(col("c1"), vec![lit(1), lit(2), lit(3), lit(4)], true).or(
            in_list(col("c1"), vec![lit(4), lit(5), lit(6), lit(7)], true),
        );
        assert_eq!(simplify(expr), col("c1").not_eq(lit(4)));

        // 4. c1 NOT IN (1,2,3,4) AND c1 NOT IN (4,5,6,7) -> c1 NOT IN (1,2,3,4,5,6,7)
        let expr = in_list(col("c1"), vec![lit(1), lit(2), lit(3), lit(4)], true).and(
            in_list(col("c1"), vec![lit(4), lit(5), lit(6), lit(7)], true),
        );
        assert_eq!(
            simplify(expr),
            in_list(
                col("c1"),
                vec![lit(1), lit(2), lit(3), lit(4), lit(5), lit(6), lit(7)],
                true
            )
        );

        // 5. c1 IN (1,2,3,4) OR c1 IN (2,3,4,5) -> c1 IN (1,2,3,4,5)
        let expr = in_list(col("c1"), vec![lit(1), lit(2), lit(3), lit(4)], false).or(
            in_list(col("c1"), vec![lit(2), lit(3), lit(4), lit(5)], false),
        );
        assert_eq!(
            simplify(expr),
            in_list(
                col("c1"),
                vec![lit(1), lit(2), lit(3), lit(4), lit(5)],
                false
            )
        );

        // 6. c1 IN (1,2,3) AND c1 NOT INT (1,2,3,4,5) -> false
        let expr = in_list(col("c1"), vec![lit(1), lit(2), lit(3)], false).and(in_list(
            col("c1"),
            vec![lit(1), lit(2), lit(3), lit(4), lit(5)],
            true,
        ));
        assert_eq!(simplify(expr), lit(false));

        // 7. c1 NOT IN (1,2,3,4) AND c1 IN (1,2,3,4,5) -> c1 = 5
        let expr =
            in_list(col("c1"), vec![lit(1), lit(2), lit(3), lit(4)], true).and(in_list(
                col("c1"),
                vec![lit(1), lit(2), lit(3), lit(4), lit(5)],
                false,
            ));
        assert_eq!(simplify(expr), col("c1").eq(lit(5)));

        // 8. c1 IN (1,2,3,4) AND c1 NOT IN (5,6,7,8) -> c1 IN (1,2,3,4)
        let expr = in_list(col("c1"), vec![lit(1), lit(2), lit(3), lit(4)], false).and(
            in_list(col("c1"), vec![lit(5), lit(6), lit(7), lit(8)], true),
        );
        assert_eq!(
            simplify(expr),
            in_list(col("c1"), vec![lit(1), lit(2), lit(3), lit(4)], false)
        );

        // inlist with more than two expressions
        // c1 IN (1,2,3,4,5,6) AND c1 IN (1,3,5,6) AND c1 IN (3,6) -> c1 = 3 OR c1 = 6
        let expr = in_list(
            col("c1"),
            vec![lit(1), lit(2), lit(3), lit(4), lit(5), lit(6)],
            false,
        )
        .and(in_list(
            col("c1"),
            vec![lit(1), lit(3), lit(5), lit(6)],
            false,
        ))
        .and(in_list(col("c1"), vec![lit(3), lit(6)], false));
        assert_eq!(
            simplify(expr),
            col("c1").eq(lit(3)).or(col("c1").eq(lit(6)))
        );

        // c1 NOT IN (1,2,3,4) AND c1 IN (5,6,7,8) AND c1 NOT IN (3,4,5,6) AND c1 IN (8,9,10) -> c1 = 8
        let expr = in_list(col("c1"), vec![lit(1), lit(2), lit(3), lit(4)], true).and(
            in_list(col("c1"), vec![lit(5), lit(6), lit(7), lit(8)], false)
                .and(in_list(
                    col("c1"),
                    vec![lit(3), lit(4), lit(5), lit(6)],
                    true,
                ))
                .and(in_list(col("c1"), vec![lit(8), lit(9), lit(10)], false)),
        );
        assert_eq!(simplify(expr), col("c1").eq(lit(8)));

        // Contains non-InList expression
        // c1 NOT IN (1,2,3,4) OR c1 != 5 OR c1 NOT IN (6,7,8,9) -> c1 NOT IN (1,2,3,4) OR c1 != 5 OR c1 NOT IN (6,7,8,9)
        let expr =
            in_list(col("c1"), vec![lit(1), lit(2), lit(3), lit(4)], true).or(col("c1")
                .not_eq(lit(5))
                .or(in_list(
                    col("c1"),
                    vec![lit(6), lit(7), lit(8), lit(9)],
                    true,
                )));
        // TODO: Further simplify this expression
        // https://github.com/apache/datafusion/issues/8970
        // assert_eq!(simplify(expr.clone()), lit(true));
        assert_eq!(simplify(expr.clone()), expr);
    }

    #[test]
    fn simplify_null_in_empty_inlist() {
        // `NULL::boolean IN ()` == `NULL::boolean IN (SELECT foo FROM empty)` == false
        let expr = in_list(lit_bool_null(), vec![], false);
        assert_eq!(simplify(expr), lit(false));

        // `NULL::boolean NOT IN ()` == `NULL::boolean NOT IN (SELECT foo FROM empty)` == true
        let expr = in_list(lit_bool_null(), vec![], true);
        assert_eq!(simplify(expr), lit(true));

        // `NULL IN ()` == `NULL IN (SELECT foo FROM empty)` == false
        let null_null = || Expr::Literal(ScalarValue::Null, None);
        let expr = in_list(null_null(), vec![], false);
        assert_eq!(simplify(expr), lit(false));

        // `NULL NOT IN ()` == `NULL NOT IN (SELECT foo FROM empty)` == true
        let expr = in_list(null_null(), vec![], true);
        assert_eq!(simplify(expr), lit(true));
    }

    #[test]
    fn just_simplifier_simplify_null_in_empty_inlist() {
        let simplify = |expr: Expr| -> Expr {
            let schema = expr_test_schema();
            let execution_props = ExecutionProps::new();
            let info = SimplifyContext::new(&execution_props).with_schema(schema);
            let simplifier = &mut Simplifier::new(&info);
            expr.rewrite(simplifier)
                .expect("Failed to simplify expression")
                .data
        };

        // `NULL::boolean IN ()` == `NULL::boolean IN (SELECT foo FROM empty)` == false
        let expr = in_list(lit_bool_null(), vec![], false);
        assert_eq!(simplify(expr), lit(false));

        // `NULL::boolean NOT IN ()` == `NULL::boolean NOT IN (SELECT foo FROM empty)` == true
        let expr = in_list(lit_bool_null(), vec![], true);
        assert_eq!(simplify(expr), lit(true));

        // `NULL IN ()` == `NULL IN (SELECT foo FROM empty)` == false
        let null_null = || Expr::Literal(ScalarValue::Null, None);
        let expr = in_list(null_null(), vec![], false);
        assert_eq!(simplify(expr), lit(false));

        // `NULL NOT IN ()` == `NULL NOT IN (SELECT foo FROM empty)` == true
        let expr = in_list(null_null(), vec![], true);
        assert_eq!(simplify(expr), lit(true));
    }

    #[test]
    fn simplify_large_or() {
        let expr = (0..5)
            .map(|i| col("c1").eq(lit(i)))
            .fold(lit(false), |acc, e| acc.or(e));
        assert_eq!(
            simplify(expr),
            in_list(col("c1"), (0..5).map(lit).collect(), false),
        );
    }

    #[test]
    fn simplify_expr_bool_and() {
        // col & true is always col
        assert_eq!(simplify(col("c2").and(lit(true))), col("c2"),);
        // col & false is always false
        assert_eq!(simplify(col("c2").and(lit(false))), lit(false),);

        // true && null is always null
        assert_eq!(simplify(lit(true).and(lit_bool_null())), lit_bool_null(),);

        // null && true is always null
        assert_eq!(simplify(lit_bool_null().and(lit(true))), lit_bool_null(),);

        // false && null is always false
        assert_eq!(simplify(lit(false).and(lit_bool_null())), lit(false),);

        // null && false is always false
        assert_eq!(simplify(lit_bool_null().and(lit(false))), lit(false),);

        // c1 BETWEEN Int32(0) AND Int32(10) AND Boolean(NULL)
        // it can be either NULL or FALSE depending on the value of `c1 BETWEEN Int32(0) AND Int32(10)`
        // and the Boolean(NULL) should remain
        let expr = col("c1").between(lit(0), lit(10));
        let expr = expr.and(lit_bool_null());
        let result = simplify(expr);

        let expected_expr = and(
            and(col("c1").gt_eq(lit(0)), col("c1").lt_eq(lit(10))),
            lit_bool_null(),
        );
        assert_eq!(expected_expr, result);
    }

    #[test]
    fn simplify_expr_between() {
        // c2 between 3 and 4 is c2 >= 3 and c2 <= 4
        let expr = col("c2").between(lit(3), lit(4));
        assert_eq!(
            simplify(expr),
            and(col("c2").gt_eq(lit(3)), col("c2").lt_eq(lit(4)))
        );

        // c2 not between 3 and 4 is c2 < 3 or c2 > 4
        let expr = col("c2").not_between(lit(3), lit(4));
        assert_eq!(
            simplify(expr),
            or(col("c2").lt(lit(3)), col("c2").gt(lit(4)))
        );
    }

    #[test]
    fn test_like_and_ilike() {
        let null = lit(ScalarValue::Utf8(None));

        // expr [NOT] [I]LIKE NULL
        let expr = col("c1").like(null.clone());
        assert_eq!(simplify(expr), lit_bool_null());

        let expr = col("c1").not_like(null.clone());
        assert_eq!(simplify(expr), lit_bool_null());

        let expr = col("c1").ilike(null.clone());
        assert_eq!(simplify(expr), lit_bool_null());

        let expr = col("c1").not_ilike(null.clone());
        assert_eq!(simplify(expr), lit_bool_null());

        // expr [NOT] [I]LIKE '%'
        let expr = col("c1").like(lit("%"));
        assert_eq!(simplify(expr), if_not_null(col("c1"), true));

        let expr = col("c1").not_like(lit("%"));
        assert_eq!(simplify(expr), if_not_null(col("c1"), false));

        let expr = col("c1").ilike(lit("%"));
        assert_eq!(simplify(expr), if_not_null(col("c1"), true));

        let expr = col("c1").not_ilike(lit("%"));
        assert_eq!(simplify(expr), if_not_null(col("c1"), false));

        // expr [NOT] [I]LIKE '%%'
        let expr = col("c1").like(lit("%%"));
        assert_eq!(simplify(expr), if_not_null(col("c1"), true));

        let expr = col("c1").not_like(lit("%%"));
        assert_eq!(simplify(expr), if_not_null(col("c1"), false));

        let expr = col("c1").ilike(lit("%%"));
        assert_eq!(simplify(expr), if_not_null(col("c1"), true));

        let expr = col("c1").not_ilike(lit("%%"));
        assert_eq!(simplify(expr), if_not_null(col("c1"), false));

        // not_null_expr [NOT] [I]LIKE '%'
        let expr = col("c1_non_null").like(lit("%"));
        assert_eq!(simplify(expr), lit(true));

        let expr = col("c1_non_null").not_like(lit("%"));
        assert_eq!(simplify(expr), lit(false));

        let expr = col("c1_non_null").ilike(lit("%"));
        assert_eq!(simplify(expr), lit(true));

        let expr = col("c1_non_null").not_ilike(lit("%"));
        assert_eq!(simplify(expr), lit(false));

        // not_null_expr [NOT] [I]LIKE '%%'
        let expr = col("c1_non_null").like(lit("%%"));
        assert_eq!(simplify(expr), lit(true));

        let expr = col("c1_non_null").not_like(lit("%%"));
        assert_eq!(simplify(expr), lit(false));

        let expr = col("c1_non_null").ilike(lit("%%"));
        assert_eq!(simplify(expr), lit(true));

        let expr = col("c1_non_null").not_ilike(lit("%%"));
        assert_eq!(simplify(expr), lit(false));

        // null_constant [NOT] [I]LIKE '%'
        let expr = null.clone().like(lit("%"));
        assert_eq!(simplify(expr), lit_bool_null());

        let expr = null.clone().not_like(lit("%"));
        assert_eq!(simplify(expr), lit_bool_null());

        let expr = null.clone().ilike(lit("%"));
        assert_eq!(simplify(expr), lit_bool_null());

        let expr = null.clone().not_ilike(lit("%"));
        assert_eq!(simplify(expr), lit_bool_null());

        // null_constant [NOT] [I]LIKE '%%'
        let expr = null.clone().like(lit("%%"));
        assert_eq!(simplify(expr), lit_bool_null());

        let expr = null.clone().not_like(lit("%%"));
        assert_eq!(simplify(expr), lit_bool_null());

        let expr = null.clone().ilike(lit("%%"));
        assert_eq!(simplify(expr), lit_bool_null());

        let expr = null.clone().not_ilike(lit("%%"));
        assert_eq!(simplify(expr), lit_bool_null());

        // null_constant [NOT] [I]LIKE 'a%'
        let expr = null.clone().like(lit("a%"));
        assert_eq!(simplify(expr), lit_bool_null());

        let expr = null.clone().not_like(lit("a%"));
        assert_eq!(simplify(expr), lit_bool_null());

        let expr = null.clone().ilike(lit("a%"));
        assert_eq!(simplify(expr), lit_bool_null());

        let expr = null.clone().not_ilike(lit("a%"));
        assert_eq!(simplify(expr), lit_bool_null());

        // expr [NOT] [I]LIKE with pattern without wildcards
        let expr = col("c1").like(lit("a"));
        assert_eq!(simplify(expr), col("c1").eq(lit("a")));
        let expr = col("c1").not_like(lit("a"));
        assert_eq!(simplify(expr), col("c1").not_eq(lit("a")));
        let expr = col("c1").like(lit("a_"));
        assert_eq!(simplify(expr), col("c1").like(lit("a_")));
        let expr = col("c1").not_like(lit("a_"));
        assert_eq!(simplify(expr), col("c1").not_like(lit("a_")));

        let expr = col("c1").ilike(lit("a"));
        assert_eq!(simplify(expr), col("c1").ilike(lit("a")));
        let expr = col("c1").not_ilike(lit("a"));
        assert_eq!(simplify(expr), col("c1").not_ilike(lit("a")));
    }

    #[test]
    fn test_simplify_with_guarantee() {
        // (c3 >= 3) AND (c4 + 2 < 10 OR (c1 NOT IN ("a", "b")))
        let expr_x = col("c3").gt(lit(3_i64));
        let expr_y = (col("c4") + lit(2_u32)).lt(lit(10_u32));
        let expr_z = col("c1").in_list(vec![lit("a"), lit("b")], true);
        let expr = expr_x.clone().and(expr_y.or(expr_z));

        // All guaranteed null
        let guarantees = vec![
            (col("c3"), NullableInterval::from(ScalarValue::Int64(None))),
            (col("c4"), NullableInterval::from(ScalarValue::UInt32(None))),
            (col("c1"), NullableInterval::from(ScalarValue::Utf8(None))),
        ];

        let output = simplify_with_guarantee(expr.clone(), guarantees);
        assert_eq!(output, lit_bool_null());

        // All guaranteed false
        let guarantees = vec![
            (
                col("c3"),
                NullableInterval::NotNull {
                    values: Interval::make(Some(0_i64), Some(2_i64)).unwrap(),
                },
            ),
            (
                col("c4"),
                NullableInterval::from(ScalarValue::UInt32(Some(9))),
            ),
            (col("c1"), NullableInterval::from(ScalarValue::from("a"))),
        ];
        let output = simplify_with_guarantee(expr.clone(), guarantees);
        assert_eq!(output, lit(false));

        // Guaranteed false or null -> no change.
        let guarantees = vec![
            (
                col("c3"),
                NullableInterval::MaybeNull {
                    values: Interval::make(Some(0_i64), Some(2_i64)).unwrap(),
                },
            ),
            (
                col("c4"),
                NullableInterval::MaybeNull {
                    values: Interval::make(Some(9_u32), Some(9_u32)).unwrap(),
                },
            ),
            (
                col("c1"),
                NullableInterval::NotNull {
                    values: Interval::try_new(
                        ScalarValue::from("d"),
                        ScalarValue::from("f"),
                    )
                    .unwrap(),
                },
            ),
        ];
        let output = simplify_with_guarantee(expr.clone(), guarantees);
        assert_eq!(&output, &expr_x);

        // Sufficient true guarantees
        let guarantees = vec![
            (
                col("c3"),
                NullableInterval::from(ScalarValue::Int64(Some(9))),
            ),
            (
                col("c4"),
                NullableInterval::from(ScalarValue::UInt32(Some(3))),
            ),
        ];
        let output = simplify_with_guarantee(expr.clone(), guarantees);
        assert_eq!(output, lit(true));

        // Only partially simplify
        let guarantees = vec![(
            col("c4"),
            NullableInterval::from(ScalarValue::UInt32(Some(3))),
        )];
        let output = simplify_with_guarantee(expr, guarantees);
        assert_eq!(&output, &expr_x);
    }

    #[test]
    fn test_expression_partial_simplify_1() {
        // (1 + 2) + (4 / 0) -> 3 + (4 / 0)
        let expr = (lit(1) + lit(2)) + (lit(4) / lit(0));
        let expected = (lit(3)) + (lit(4) / lit(0));

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_expression_partial_simplify_2() {
        // (1 > 2) and (4 / 0) -> false
        let expr = (lit(1).gt(lit(2))).and(lit(4) / lit(0));
        let expected = lit(false);

        assert_eq!(simplify(expr), expected);
    }

    #[test]
    fn test_simplify_cycles() {
        // TRUE
        let expr = lit(true);
        let expected = lit(true);
        let (expr, num_iter) = simplify_with_cycle_count(expr);
        assert_eq!(expr, expected);
        assert_eq!(num_iter, 1);

        // (true != NULL) OR (5 > 10)
        let expr = lit(true).not_eq(lit_bool_null()).or(lit(5).gt(lit(10)));
        let expected = lit_bool_null();
        let (expr, num_iter) = simplify_with_cycle_count(expr);
        assert_eq!(expr, expected);
        assert_eq!(num_iter, 2);

        // NOTE: this currently does not simplify
        // (((c4 - 10) + 10) *100) / 100
        let expr = (((col("c4") - lit(10)) + lit(10)) * lit(100)) / lit(100);
        let expected = expr.clone();
        let (expr, num_iter) = simplify_with_cycle_count(expr);
        assert_eq!(expr, expected);
        assert_eq!(num_iter, 1);

        // ((c4<1 or c3<2) and c3_non_null<3) and false
        let expr = col("c4")
            .lt(lit(1))
            .or(col("c3").lt(lit(2)))
            .and(col("c3_non_null").lt(lit(3)))
            .and(lit(false));
        let expected = lit(false);
        let (expr, num_iter) = simplify_with_cycle_count(expr);
        assert_eq!(expr, expected);
        assert_eq!(num_iter, 2);
    }

    fn boolean_test_schema() -> DFSchemaRef {
        static BOOLEAN_TEST_SCHEMA: LazyLock<DFSchemaRef> = LazyLock::new(|| {
            Schema::new(vec![
                Field::new("A", DataType::Boolean, false),
                Field::new("B", DataType::Boolean, false),
                Field::new("C", DataType::Boolean, false),
                Field::new("D", DataType::Boolean, false),
            ])
            .to_dfschema_ref()
            .unwrap()
        });
        Arc::clone(&BOOLEAN_TEST_SCHEMA)
    }

    #[test]
    fn simplify_common_factor_conjunction_in_disjunction() {
        let props = ExecutionProps::new();
        let schema = boolean_test_schema();
        let simplifier =
            ExprSimplifier::new(SimplifyContext::new(&props).with_schema(schema));

        let a = || col("A");
        let b = || col("B");
        let c = || col("C");
        let d = || col("D");

        // (A AND B) OR (A AND C) -> A AND (B OR C)
        let expr = a().and(b()).or(a().and(c()));
        let expected = a().and(b().or(c()));

        assert_eq!(expected, simplifier.simplify(expr).unwrap());

        // (A AND B) OR (A AND C) OR (A AND D) -> A AND (B OR C OR D)
        let expr = a().and(b()).or(a().and(c())).or(a().and(d()));
        let expected = a().and(b().or(c()).or(d()));
        assert_eq!(expected, simplifier.simplify(expr).unwrap());

        // A OR (B AND C AND A) -> A
        let expr = a().or(b().and(c().and(a())));
        let expected = a();
        assert_eq!(expected, simplifier.simplify(expr).unwrap());
    }

    #[test]
    fn test_simplify_udaf() {
        let udaf = AggregateUDF::new_from_impl(SimplifyMockUdaf::new_with_simplify());
        let aggregate_function_expr =
            Expr::AggregateFunction(expr::AggregateFunction::new_udf(
                udaf.into(),
                vec![],
                false,
                None,
                vec![],
                None,
            ));

        let expected = col("result_column");
        assert_eq!(simplify(aggregate_function_expr), expected);

        let udaf = AggregateUDF::new_from_impl(SimplifyMockUdaf::new_without_simplify());
        let aggregate_function_expr =
            Expr::AggregateFunction(expr::AggregateFunction::new_udf(
                udaf.into(),
                vec![],
                false,
                None,
                vec![],
                None,
            ));

        let expected = aggregate_function_expr.clone();
        assert_eq!(simplify(aggregate_function_expr), expected);
    }

    /// A Mock UDAF which defines `simplify` to be used in tests
    /// related to UDAF simplification
    #[derive(Debug, Clone, PartialEq, Eq, Hash)]
    struct SimplifyMockUdaf {
        simplify: bool,
    }

    impl SimplifyMockUdaf {
        /// make simplify method return new expression
        fn new_with_simplify() -> Self {
            Self { simplify: true }
        }
        /// make simplify method return no change
        fn new_without_simplify() -> Self {
            Self { simplify: false }
        }
    }

    impl AggregateUDFImpl for SimplifyMockUdaf {
        fn as_any(&self) -> &dyn std::any::Any {
            self
        }

        fn name(&self) -> &str {
            "mock_simplify"
        }

        fn signature(&self) -> &Signature {
            unimplemented!()
        }

        fn return_type(&self, _arg_types: &[DataType]) -> Result<DataType> {
            unimplemented!("not needed for tests")
        }

        fn accumulator(
            &self,
            _acc_args: AccumulatorArgs,
        ) -> Result<Box<dyn Accumulator>> {
            unimplemented!("not needed for tests")
        }

        fn groups_accumulator_supported(&self, _args: AccumulatorArgs) -> bool {
            unimplemented!("not needed for testing")
        }

        fn create_groups_accumulator(
            &self,
            _args: AccumulatorArgs,
        ) -> Result<Box<dyn GroupsAccumulator>> {
            unimplemented!("not needed for testing")
        }

        fn simplify(&self) -> Option<AggregateFunctionSimplification> {
            if self.simplify {
                Some(Box::new(|_, _| Ok(col("result_column"))))
            } else {
                None
            }
        }
    }

    #[test]
    fn test_simplify_udwf() {
        let udwf = WindowFunctionDefinition::WindowUDF(
            WindowUDF::new_from_impl(SimplifyMockUdwf::new_with_simplify()).into(),
        );
        let window_function_expr = Expr::from(WindowFunction::new(udwf, vec![]));

        let expected = col("result_column");
        assert_eq!(simplify(window_function_expr), expected);

        let udwf = WindowFunctionDefinition::WindowUDF(
            WindowUDF::new_from_impl(SimplifyMockUdwf::new_without_simplify()).into(),
        );
        let window_function_expr = Expr::from(WindowFunction::new(udwf, vec![]));

        let expected = window_function_expr.clone();
        assert_eq!(simplify(window_function_expr), expected);
    }

    /// A Mock UDWF which defines `simplify` to be used in tests
    /// related to UDWF simplification
    #[derive(Debug, Clone, PartialEq, Eq, Hash)]
    struct SimplifyMockUdwf {
        simplify: bool,
    }

    impl SimplifyMockUdwf {
        /// make simplify method return new expression
        fn new_with_simplify() -> Self {
            Self { simplify: true }
        }
        /// make simplify method return no change
        fn new_without_simplify() -> Self {
            Self { simplify: false }
        }
    }

    impl WindowUDFImpl for SimplifyMockUdwf {
        fn as_any(&self) -> &dyn std::any::Any {
            self
        }

        fn name(&self) -> &str {
            "mock_simplify"
        }

        fn signature(&self) -> &Signature {
            unimplemented!()
        }

        fn simplify(&self) -> Option<WindowFunctionSimplification> {
            if self.simplify {
                Some(Box::new(|_, _| Ok(col("result_column"))))
            } else {
                None
            }
        }

        fn partition_evaluator(
            &self,
            _partition_evaluator_args: PartitionEvaluatorArgs,
        ) -> Result<Box<dyn PartitionEvaluator>> {
            unimplemented!("not needed for tests")
        }

        fn field(&self, _field_args: WindowUDFFieldArgs) -> Result<FieldRef> {
            unimplemented!("not needed for tests")
        }

        fn limit_effect(&self, _args: &[Arc<dyn PhysicalExpr>]) -> LimitEffect {
            LimitEffect::Unknown
        }
    }
    #[derive(Debug, PartialEq, Eq, Hash)]
    struct VolatileUdf {
        signature: Signature,
    }

    impl VolatileUdf {
        pub fn new() -> Self {
            Self {
                signature: Signature::exact(vec![], Volatility::Volatile),
            }
        }
    }
    impl ScalarUDFImpl for VolatileUdf {
        fn as_any(&self) -> &dyn std::any::Any {
            self
        }

        fn name(&self) -> &str {
            "VolatileUdf"
        }

        fn signature(&self) -> &Signature {
            &self.signature
        }

        fn return_type(&self, _arg_types: &[DataType]) -> Result<DataType> {
            Ok(DataType::Int16)
        }

        fn invoke_with_args(&self, _args: ScalarFunctionArgs) -> Result<ColumnarValue> {
            panic!("dummy - not implemented")
        }
    }

    #[test]
    fn test_optimize_volatile_conditions() {
        let fun = Arc::new(ScalarUDF::new_from_impl(VolatileUdf::new()));
        let rand = Expr::ScalarFunction(ScalarFunction::new_udf(fun, vec![]));
        {
            let expr = rand
                .clone()
                .eq(lit(0))
                .or(col("column1").eq(lit(2)).and(rand.clone().eq(lit(0))));

            assert_eq!(simplify(expr.clone()), expr);
        }

        {
            let expr = col("column1")
                .eq(lit(2))
                .or(col("column1").eq(lit(2)).and(rand.clone().eq(lit(0))));

            assert_eq!(simplify(expr), col("column1").eq(lit(2)));
        }

        {
            let expr = (col("column1").eq(lit(2)).and(rand.clone().eq(lit(0)))).or(col(
                "column1",
            )
            .eq(lit(2))
            .and(rand.clone().eq(lit(0))));

            assert_eq!(
                simplify(expr),
                col("column1")
                    .eq(lit(2))
                    .and((rand.clone().eq(lit(0))).or(rand.clone().eq(lit(0))))
            );
        }
    }

    #[test]
    fn simplify_fixed_size_binary_eq_lit() {
        let bytes = [1u8, 2, 3].as_slice();

        // The expression starts simple.
        let expr = col("c5").eq(lit(bytes));

        // The type coercer introduces a cast.
        let coerced = coerce(expr.clone());
        let schema = expr_test_schema();
        assert_eq!(
            coerced,
            col("c5")
                .cast_to(&DataType::Binary, schema.as_ref())
                .unwrap()
                .eq(lit(bytes))
        );

        // The simplifier removes the cast.
        assert_eq!(
            simplify(coerced),
            col("c5").eq(Expr::Literal(
                ScalarValue::FixedSizeBinary(3, Some(bytes.to_vec()),),
                None
            ))
        );
    }

    #[test]
    fn simplify_cast_literal() {
        // Test that CAST(literal) expressions are evaluated at plan time

        // CAST(123 AS Int64) should become 123i64
        let expr = Expr::Cast(Cast::new(Box::new(lit(123i32)), DataType::Int64));
        let expected = lit(123i64);
        assert_eq!(simplify(expr), expected);

        // CAST(1761630189642 AS Timestamp(Nanosecond, Some("+00:00")))
        // Integer to timestamp cast
        let expr = Expr::Cast(Cast::new(
            Box::new(lit(1761630189642i64)),
            DataType::Timestamp(
                arrow::datatypes::TimeUnit::Nanosecond,
                Some("+00:00".into()),
            ),
        ));
        // Should evaluate to a timestamp literal
        let result = simplify(expr);
        match result {
            Expr::Literal(ScalarValue::TimestampNanosecond(Some(val), tz), _) => {
                assert_eq!(val, 1761630189642i64);
                assert_eq!(tz.as_deref(), Some("+00:00"));
            }
            other => panic!("Expected TimestampNanosecond literal, got: {other:?}"),
        }

        // Test CAST of invalid string to timestamp - should return an error at plan time
        // This represents the case from the issue: CAST(Utf8("1761630189642") AS Timestamp)
        // "1761630189642" is NOT a valid timestamp string format
        let expr = Expr::Cast(Cast::new(
            Box::new(lit("1761630189642")),
            DataType::Timestamp(
                arrow::datatypes::TimeUnit::Nanosecond,
                Some("+00:00".into()),
            ),
        ));

        // The simplification should now fail with an error at plan time
        let schema = test_schema();
        let props = ExecutionProps::new();
        let simplifier =
            ExprSimplifier::new(SimplifyContext::new(&props).with_schema(schema));
        let result = simplifier.simplify(expr);
        assert!(result.is_err(), "Expected error for invalid cast");
        let err_msg = result.unwrap_err().to_string();
        assert_contains!(err_msg, "Error parsing timestamp");
    }

    fn if_not_null(expr: Expr, then: bool) -> Expr {
        Expr::Case(Case {
            expr: Some(expr.is_not_null().into()),
            when_then_expr: vec![(lit(true).into(), lit(then).into())],
            else_expr: None,
        })
    }
}