Module expr

evalexpr_jit

Module expr 

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Expression tree representation and symbolic differentiation Expression module for representing mathematical expressions.

This module defines the core expression types used to represent mathematical expressions in a form that supports both JIT compilation and automatic differentiation. The main types are:

  • Expr: An enum representing different kinds of mathematical expressions
  • VarRef: A struct containing metadata about variables in expressions

The expression tree is built recursively using Box<Expr> for nested expressions and can be:

  • JIT compiled into machine code using Cranelift
  • Symbolically differentiated to compute derivatives
  • Evaluated efficiently at runtime
  • Simplified using algebraic rules
  • Modified by inserting replacement expressions

Supported operations include:

  • Basic arithmetic (+, -, *, /)
  • Variables and constants
  • Absolute value
  • Integer exponentiation
  • Transcendental functions (exp, ln, sqrt)
  • Expression caching for optimization

§Expression Tree Structure

The expression tree is built recursively with each node being one of:

  • Leaf nodes: Constants and Variables
  • Unary operations: Abs, Neg, Exp, Ln, Sqrt
  • Binary operations: Add, Sub, Mul, Div
  • Special nodes: Pow (with integer exponent), Cached expressions

§Symbolic Differentiation

The derivative method implements symbolic differentiation by recursively applying calculus rules like:

  • Product rule
  • Quotient rule
  • Chain rule
  • Power rule
  • Special function derivatives (exp, ln, sqrt)

§Expression Simplification

The simplify method performs algebraic simplifications including:

  • Constant folding (e.g. 2 + 3 → 5)
  • Identity rules (e.g. x + 0 → x, x * 1 → x)
  • Exponent rules (e.g. x^0 → 1, x^1 → x)
  • Expression caching for repeated subexpressions
  • Special function simplifications

§Expression Modification

The insert method allows replacing parts of an expression tree by:

  • Matching nodes using a predicate function
  • Replacing matched nodes with a new expression
  • Recursively traversing and rebuilding the tree

Structs§

FlattenedExpr
Flattened expression representation for efficient evaluation
VarRef
Represents a reference to a variable in an expression.

Enums§

Expr
An expression tree node representing mathematical operations.
LinearOp
Linear operation for flattened expression evaluation