SymbAnaFis

High-performance symbolic mathematics library written in Rust with Python bindings.

SymbAnaFis provides a robust engine for symbolic differentiation, simplification, and evaluation, designed for performance-critical applications in physics, engineering, and machine learning.

Key Capabilities

• ∂ Symbolic Differentiation: Supports product, chain, and quotient rules for a vast array of mathematical functions.
• ✨ Algebraic Simplification: Intelligent simplification engine covering trigonometric identities, constant folding, and algebraic expansion.
• 📊 Uncertainty Propagation: Comprehensive support for calculating uncertainty propagation with full covariance matrix integration.
• ∇ Vector Calculus: Native symbolic computation of Gradients, Hessians, and Jacobian matrices.
• 🚀 Parallel Processing: Optional parallel evaluation engine using Rayon for massive batch operations.
• 📦 Python Bindings: Seamless Python integration via maturin, offering the speed of Rust with the ease of Python.

Visual Benchmarks

SymbAnaFis performance is validated against SymPy and SymEngine using complex physical simulations. Each benchmark features a Quad-View Dashboard comparing real-time simulations side-by-side.

Aizawa Attractor

Watch Video Simulates 500,000 particles flowing through the Aizawa field, comparing Euler integration throughput.

Clifford Attractor

Watch Video Visualizes 1,000,000 particles evolving in the Clifford map, testing discrete map evaluation speed.

Double Pendulum Matrix

Watch Video Simulates 50,000 chaotic double pendulums, verifying symbolic differentiation correctness and RK4 integration stability.

Gradient Descent Avalanche

Watch Video Massive particle descent on a complex terrain function, showcasing symbolic differentiation of compiled functions.

Installation

# Python
pip install symb-anafis

# Rust
cargo add symb_anafis

Quick Start

Python

import symb_anafis

# Differentiate complex expressions
result = symb_anafis.diff("x^3 + sin(x)", "x", [], None)
# → "3*x^2 + cos(x)"

# Algebraic Simplification
result = symb_anafis.simplify("sin(x)^2 + cos(x)^2", [], None)
# → "1"

# Handle constants automatically
result = symb_anafis.diff("a*x^2", "x", ["a"], None)
# → "2*a*x"

Rust

use symb_anafis::{diff, simplify, symb};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // String API for ease of use
    let result = diff("sin(x) * x", "x", &[], None)?;
    println!("{result}");  // cos(x)*x + sin(x)

    // Type-safe API (Symbol is Copy - no clone needed!)
    let x = symb("x");
    let expr = x.pow(2.0) + x.sin();  // x² + sin(x)
    
    // Export to LaTeX
    println!("{}", expr.to_latex());  // x^{2} + \sin(x)
    
    Ok(())
}

Advanced Features

🔍 Fine-Grained Control

Use the Builder pattern to configure safety limits and behavior.

use symb_anafis::{Diff, Simplify};

Diff::new()
    .domain_safe(true)     // Prevent unsafe simplifications (e.g., x/x != 1 if x=0)
    .max_depth(200)        // Prevent stack overflows on massive expressions
    .diff_str("sqrt(x^2)", "x", &[])?; // Result: abs(x)

📉 Uncertainty Propagation

Calculate error propagation symbolically, supporting correlated variables.

use symb_anafis::uncertainty_propagation;

// Calculate uncertainty formula for f = x + y with full covariance support
let sigma = uncertainty_propagation(&expr, &["x", "y"], None)?;
// → sqrt(sigma_x^2 + 2*sigma_x*sigma_y*rho_xy + sigma_y^2)

⚡ Parallel Evaluation

Evaluate expressions over large datasets in parallel (requires parallel feature).

// Requires: symb_anafis = { features = ["parallel"] }
use symb_anafis::{eval_parallel, symb};

let x = symb("x");
let expr = x.pow(2.0);

// Clean macro syntax for parallel evaluation
let results = eval_parallel!(
    exprs: ["x + y", expr],
    vars: [["x", "y"], ["x"]],
    values: [
        [[1.0, 2.0], [3.0, 4.0]],
        [[1.0, 2.0, 3.0]]
    ]
).unwrap();

🛠️ Custom Functions

Register custom functions with their own derivative rules.

use symb_anafis::{Diff, UserFunction};

Diff::new()
    .user_fn("f", UserFunction::new(1..=1).partial(0, |args| {
        // Define ∂f/∂u = 2u for f(u)
        // Clone the Arc (cheap), then multiply
        2.0 * args[0].clone()  
    }).unwrap())
    .diff_str("f(x^2)", "x", &[])?; // → 4*x^3

Supported Functions

SymbAnaFis supports over 50 built-in mathematical functions:

¹ exp_polar currently aliases exp (placeholder for future polar form support)

Documentation

• API Reference - Detailed guide to all functions and modules.
• docs.rs - Full Rust crate documentation.

License

Apache License 2.0 - see LICENSE

Citation

If you use SymbAnaFis in academic work, please cite:

@software{symbanafis,
  author       = {Martins, Pedro},
  title        = {SymbAnaFis: High-Performance Symbolic Mathematics Library},
  year         = {2026},
  url          = {https://github.com/CokieMiner/SymbAnaFis},
  version      = {0.8.0}
}

Built with ❤️ in Rust 🚀