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Elementary functions, rebuilt from one operator.
This site documents a Python implementation of the EML construction from All elementary functions from a single binary operator. It focuses on a clean library API, compiler tooling, benchmark reporting, and publishable documentation.
eml(x, y) = exp(x) - log(y)
Acknowledgement
Andrzej Odrzywołek deserves full credit for the central idea. The paper is a genuinely elegant piece of mathematical engineering: compact in statement, surprising in conclusion, and unusually generous in reproducibility. It does not merely claim that a single operator works; it shows a constructive path from that operator to the repertoire of a scientific calculator.
The accompanying research code also reflects serious craftsmanship. It makes the result inspectable, testable, and portable across symbolic and numeric environments. That combination of conceptual clarity and implementation discipline is rare and worth stating plainly.
Why build this project?
Research code and engineering code serve different needs. The original work is the authoritative source for the mathematical idea. This repository exists to translate that idea into a Python package that is easier to install, test, benchmark, visualize, and publish.
Concretely, this project adds a library-style API, a compiler CLI, benchmark bundles, plot generation, GitHub Pages documentation, and a test suite that treats the EML construction as a reusable software component rather than only a proof-of-concept artifact.
Theory-first documentation
The theory page reconstructs exponentials, logarithms, arithmetic, powers, trigonometric functions, and inverse functions directly from EML.
Engineering-focused guide
The guide page explains installation, Python usage, the compiler CLI, benchmark commands, and what the project adds beyond the paper.
Implementation notes
A dedicated page now documents branch choices, complex-domain execution, stability tradeoffs, and why the library avoids shortcut calls to high-level NumPy functions.
Published benchmark artifacts
The benchmark page links to JSON and CSV outputs and embeds the generated PNG plots so the Pages site remains self-contained.
Static site by design
Everything lives under docs/, so the repository can be published through GitHub Pages without an extra build system.
What to read first
- Theory if you want the constructive derivation.
- Implementation if you want branch, stability, and engineering details.
- Guide if you want installation, commands, and API usage.
- Benchmarks if you want empirical accuracy and complexity data.
Primary reference
A. Odrzywołek, All elementary functions from a single binary operator, arXiv:2603.21852, 2026.