Crate oxieml 

OxiEML — All elementary functions from a single binary operator.

This crate implements the EML operator eml(x, y) = exp(x) - ln(y) and builds uniform binary trees that represent all elementary functions using only this operator and the constant 1.

Based on the paper: “All elementary functions from a single binary operator” (arXiv:2603.21852).

Capabilities

1. Symbolic Regression: Discover closed-form formulas from data via gradient-based search over EML tree topologies.
2. Uniform Tree Representation: Express any elementary function using the grammar S → 1 | eml(S, S).

Example

use oxieml::{EmlTree, Canonical, EvalCtx};

// Build exp(x) = eml(x, 1)
let x = EmlTree::var(0);
let exp_x = Canonical::exp(&x);

// Evaluate at x = 1.0
let ctx = EvalCtx::new(&[1.0]);
let result = exp_x.eval_real(&ctx).unwrap();
assert!((result - std::f64::consts::E).abs() < 1e-10);

Re-exports

pub use canonical::Canonical;

pub use error::EmlError;

pub use eval::EvalCtx;

pub use integrate::IntegrateResult;

pub use limit::LimitPoint;

pub use limit::LimitResult;

pub use lower::LoweredOp;

pub use lower_interval::IntervalLO;

pub use named_const::NamedConst;

pub use numeric::QuadOpts;

pub use numeric::RootOpts;

pub use numeric::lambert_w0;

pub use numeric::lambert_wm1;

pub use numeric_verified::RootCertificate;

pub use numeric_verified::RootStatus;

pub use numeric_verified::VerifiedQuadOpts;

pub use ode::OdeForm;

pub use ode::OdeKind;

pub use ode::OdeSolution;

pub use ode::dsolve;

pub use parser::ParseError;

pub use parser::parse;

pub use poly::Factorization;

pub use poly::MultiPoly;

pub use poly::Poly;

pub use poly::PolyError;

pub use quadrature_nd::QuadNdMethod;

pub use quadrature_nd::QuadNdOpts;

pub use quadrature_nd::quadrature_nd;

pub use solve::SolveResult;

pub use solve::SystemSolveResult;

pub use solve::solve_for_all;

pub use solve::solve_linear_system;

pub use solve_poly::RootsResult;

pub use symreg::SymRegLoss;

pub use symreg::DiscoveredFormula;

pub use symreg::LmConfig;

pub use symreg::MultiOutputStrategy;

pub use symreg::OptimizerKind;

pub use symreg::PdeConfig;

pub use symreg::PdeResult;

pub use symreg::SelectionCriterion;

pub use symreg::SharedFormula;

pub use symreg::SymRegConfig;

pub use symreg::SymRegEngine;

pub use symreg::SymRegStrategy;

pub use symreg::discover_pde;

pub use symreg::pareto_front;

pub use symreg::LibraryTerm;

pub use symreg::SindyConfig;

pub use symreg::SindyEquation;

pub use symreg::SindyMode;

pub use symreg::SindyResult;

pub use symreg::discover_ode_sindy;

pub use system::SystemOpts;

pub use system::solve_system_newton;

pub use tree::EmlNode;

pub use tree::EmlTree;

pub use units::UnitError;

pub use units::Units;

Modules

autodiff

Automatic differentiation: forward-mode (JVP) and reverse-mode (VJP).

canonical

Canonical EML tree constructions for elementary functions.

compile

Compile EML trees to Rust source code.

error

Error types for the OxiEML crate.

eval

Numerical evaluation of EML trees.

grad

Automatic differentiation for EML trees.

integrate

Symbolic antidifferentiation and definite integration for LoweredOp.

limit

Limit computation for LoweredOp expression trees.

linalg

Pure-Rust dense linear algebra for the LM optimizer and PDE discovery.

lower

Lowering EML trees to standard mathematical operations.

lower_cse

Common-subexpression elimination (CSE) for LoweredOp trees.

lower_grad

Symbolic differentiation for the lowered IR.

lower_interval

Interval arithmetic for over-approximate evaluation of LoweredOp trees.

lower_simplify

Algebraic simplification for the lowered IR.

lower_units

Dimensional analysis extension for LoweredOp.

named_const

Named mathematical constants for the LoweredOp IR.

numeric

Numeric algorithms: root-finding, quadrature.

numeric_verified

Verified interval integration and Krawczyk root-finding.

ode

Symbolic ODE solving: dsolve.

parser

Parser for EML expression notation.

poly

Polynomial algebra over exact rational coefficients.

quadrature_nd

Multidimensional numerical quadrature.

series

Taylor and Maclaurin series expansion for LoweredOp expressions.

simplify

EML tree simplification and normalization.

solve

Symbolic equation solving for LoweredOp expression trees.

solve_poly

Polynomial and Lambert-W equation solving helpers for crate::solve::solve_for_all.

special

Special mathematical functions (erf, lgamma, digamma, Ei, Si, Ci). All implementations are pure Rust with no external dependencies.

symreg

Symbolic regression engine.

system

Multivariate Newton solver for systems of equations.

tree

EML tree data structures.

units

Dimensional analysis for unit-aware symbolic regression.