Crate symb_anafis 

Symbolic Differentiation Library

A fast, focused Rust library for symbolic differentiation.

Features

• Context-aware parsing with known symbols and custom functions
• Extensible simplification framework
• Support for built-in functions (sin, cos, ln, exp)
• Implicit function handling
• Partial derivative notation
• Type-safe expression building with operator overloading
• Builder pattern API for differentiation and simplification

Usage Examples

String-based API (original)

use symb_anafis::diff;
let result = diff("x^2", "x", &[], None).unwrap();
assert_eq!(result, "2*x");

Type-safe API (new)

use symb_anafis::{symb, Diff};
let x = symb("x");
let expr = x.pow(2.0) + x.sin();
let derivative = Diff::new().differentiate(&expr, &x).unwrap();
// derivative is: 2*x + cos(x)

Modules

visitor

Expression visitor pattern for AST traversal

Macros

rule

Macro to define a simplification rule with minimal boilerplate

rule_arc

Macro to define a simplification rule that returns Option<Arc<Expr>> directly. This avoids unnecessary wrapping when the result is already an Arc.

rule_with_helpers

Macro for rules with helpers that wrap result in Arc

rule_with_helpers_arc

Macro for rules with helpers that return Option<Arc<Expr>> directly

Structs

CompiledEvaluator

Compiled expression evaluator - thread-safe, reusable.

Context

Unified context for all symb_anafis operations.

CovarianceMatrix

Covariance matrix for uncertainty propagation

Diff

Builder for differentiation operations

Dual

Dual number for automatic differentiation

Expr

A symbolic mathematical expression.

Simplify

Builder for simplification operations

Span

Source location span for error reporting Represents a range of characters in the input string

Symbol

Symbol type and context for variable handling.

UserFunction

A user-defined function with optional body expression and partial derivatives.

Enums

CovEntry

Covariance matrix entry - can be numeric or symbolic

DiffError

Errors that can occur during parsing and differentiation

SymbolError

Errors that can occur during symbol operations

Constants

DEFAULT_MAX_DEPTH

Default maximum AST depth. This limit prevents stack overflow from deeply nested expressions.

DEFAULT_MAX_NODES

Default maximum AST node count. This limit prevents memory exhaustion from extremely large expressions.

Traits

ArcExprExt

Symbol type and context for variable handling.

MathScalar

A trait comprising all operations required for mathematical scalars in the SymbAnaFis library.

Functions

clear_symbols

Symbol type and context for variable handling.

diff

Main API function for symbolic differentiation

evaluate_str

Evaluate a formula string with given variable values Performs partial evaluation - returns simplified expression string

gradient

Compute the gradient of an expression with respect to multiple variables Returns a vector of partial derivatives [∂f/∂x₁, ∂f/∂x₂, …]

gradient_str

Compute gradient from a formula string

hessian

Compute the Hessian matrix of an expression Returns a 2D vector of second partial derivatives H[i][j] = ∂²f/∂xᵢ∂xⱼ

hessian_str

Compute Hessian matrix from a formula string

jacobian

Compute the Jacobian matrix of a vector of expressions Returns a 2D vector where J[i][j] = ∂fᵢ/∂xⱼ

jacobian_str

Compute Jacobian matrix from formula strings

parse

Parse a formula string into an expression AST

relative_uncertainty

Compute relative uncertainty expression: σ_f / |f|

remove_symbol

Symbol type and context for variable handling.

simplify

Simplify a mathematical expression

symb

Symbol type and context for variable handling.

symb_get

Symbol type and context for variable handling.

symb_new

Symbol type and context for variable handling.

symbol_count

Symbol type and context for variable handling.

symbol_exists

Symbol type and context for variable handling.

symbol_names

Symbol type and context for variable handling.

uncertainty_propagation

Compute the uncertainty propagation expression

Type Aliases

BodyFn

Thread-safe symbolic body function for user-defined functions. Takes argument expressions (as Arc<Expr>) and returns the function body as an expression.

PartialFn

Thread-safe partial derivative function. Takes argument expressions (as Arc<Expr>) and returns the partial derivative expression.