OxiEML 0.1.0 Released — Pure Rust EML Operator: All Elementary Functions from a Single Binary Operator

The mathematical foundation of the COOLJAPAN scientific computing ecosystem just achieved a theoretical breakthrough in practice.

Today we released OxiEML 0.1.0 — a complete, production-grade pure Rust crate that implements the revolutionary binary operator eml(x, y) = exp(x) − ln(y) and uses only this operator plus the constant 1 to construct uniform binary trees expressing all elementary mathematical functions.

No C. No Fortran. No external math libraries beyond the COOLJAPAN stack.
No unsafe code in hot paths. No FFI.
Just clean, memory-safe, auditable symbolic and numeric mathematics that compiles to a single static binary (or WASM) and runs everywhere — from laptops to browsers to edge devices to cloud.

Why OxiEML 0.1.0 is a game changer

For centuries, elementary functions (exp, ln, sin, cos, +, −, ×, ÷, ^, sqrt, trig, hyperbolic, etc.) have been treated as separate primitives. This fragmentation made symbolic regression, automatic formula discovery, and formal verification extremely difficult.

Existing tools are powerful but suffer from:

• Fragmented operator sets and complex expression trees
• Lack of a single unified representation for all functions
• Difficulty in symbolic regression over interpretable spaces
• Heavy dependencies and non-portable code generation

OxiEML 0.1.0 ends all of that.

It is based on the theoretical result from the paper “All elementary functions from a single binary operator” (arXiv:2603.21852) and delivers a practical, high-performance implementation that unifies all elementary mathematics into one elegant, uniform binary tree structure.

Technical Deep Dive: How We Built a Universal Mathematical Operator in Pure Rust

The architecture follows a clean separation of concerns built directly on the COOLJAPAN stack:

1. EML Tree Representation
   Uniform binary trees using the grammar S → 1 | eml(S, S). Canonical constructions for every elementary function (exp, ln, sin/cos/tan, arcsin/arccos/arctan, sinh/cosh/tanh, arithmetic, power, abs, sqrt, π, e, i, etc.).

2. Symbolic Regression Engine
   Gradient-based search (Adam optimizer) over EML tree topologies to discover closed-form formulas from data.

3. Lowering & Code Generation
   Algebraic simplification + common subexpression elimination (CSE) → lowered IR → efficient numeric evaluation or Rust source code emission (compile_to_rust).

4. Evaluation Engine
   Stack-machine evaluator (post-order traversal) with support for real, complex, and batch data. Optional SIMD (via oxiblas-core) and parallel (Rayon) acceleration.

5. Advanced Features
   CLI tool (oxieml), parser with round-trip guarantee, SMT solving via OxiZ (feature smt), constraint propagation.

Key Rust advantages:

• 100% Pure Rust, zero FFI by default
• Full integration with SciRS2 / NumRS2 and OxiBLAS
• Memory-safe tree manipulation and evaluation
• SIMD + parallel batch evaluation (up to 4.26× speedup)
• Type-safe symbolic regression and codegen

What’s inside 0.1.0 (released April 15)

• Full phylogenetic tree of elementary functions implemented
• Symbolic regression engine with Adam optimization
• Lowering pipeline with CSE and Rust code generation
• CLI tool for evaluation, constant discovery, and tree inspection
• Optional SMT solving (OxiZ backend) and SIMD batch evaluation (oxiblas-core)
• Production readiness confirmed through 173 passing tests (covering all canonical functions, parser round-trip, symbolic regression, lowering, SIMD/parallel correctness, and SMT)
• Zero Clippy warnings, fail0 enforced

This is the foundation

OxiEML is now the official mathematical unification layer for the entire COOLJAPAN stack (total ecosystem: 26M+ SLoC Rust, 660+ crates, 40+ production-grade libraries):

• SciRS2 / NumRS2 — all core numerical and symbolic operations
• OxiBLAS / OxiFFT — accelerated evaluation of lowered trees
• OptiRS — optimization inside symbolic regression
• OxiCUDA / OxiONNX — GPU-accelerated batch evaluation and model integration
• OxiMedia / VoiRS — signal processing and audio formula discovery
• Spintronics / OxiHuman — physics-informed and biomechanical symbolic math
• OxiLean — future formally verified EML trees

Repository: https://github.com/cool-japan/oxieml

Star the repo if you want a mathematically elegant, fully unified foundation for symbolic computation and automatic formula discovery.

The era of treating elementary functions as unrelated primitives is over.

Pure Rust EML — one operator to rule them all — is here, fast, safe, and sovereign.

— KitaSan at COOLJAPAN OÜ April 15, 2026