ries 2.0.1

Find algebraic equations given their solution - Rust implementation
Documentation

ries-rs

Rust inverse equation solver for turning a target number into compact algebraic equations.

CI Coverage Live Demo Crates.io PyPI DOI License: MIT

ries-rs is a Rust implementation of Robert P. Munafo's RIES inverse equation solver. Given a target number, it searches for algebraic equations that have that number as a solution.

The historical acronym is RIES, for "RILYBOT Inverse Equation Solver". This repository aims to be a modern, documented, reproducible reference implementation rather than a historical clone.

Name map: crates.io crate ries; installed CLI ries-rs; PyPI package ries-rs; Python import ries_rs.

Project page: maxwellsantoro.com/projects/ries-rs
Live demo: maxwellsantoro.com/projects/ries-rs/app/

RIES-RS web UI

Who It's For

  • Researchers who want reproducible constant-recognition runs with structured output and run manifests
  • Programmers who want equation search embedded in Rust, Python, or browser workflows
  • People comparing modern behavior against historical RIES baselines with explicit parity notes
  • Educators and demo authors who want the same engine behind a CLI, Python module, and live browser demo

Why Use ries-rs

  • Rust implementation with a cleaner architecture and broad regression coverage
  • Deterministic mode for reproducible output ordering
  • Structured JSON and manifests for automation and research workflows
  • Browser and library integrations in addition to the CLI
  • Public benchmark artifacts and explicit parity tracking against older versions

Install

CLI

Use cargo install ries --locked to install the ries-rs executable.

cargo install ries --locked

Prebuilt Linux, macOS, and Windows archives are attached to each GitHub release.

For unreleased development builds:

cargo install --git https://github.com/maxwellsantoro/ries-rs --locked

# Or, from a local checkout:
cargo install --path . --locked

Python Bindings

pip install ries-rs

For local source development of the bindings:

pip install maturin
cd ries-py
maturin develop --release

For Rust-side binding checks without building/loading the extension module:

./scripts/test_ries_py_rust.sh

For end-to-end Python import/search checks in an isolated virtualenv:

./scripts/test_ries_py_python.sh -q

Web App / WASM

GitHub releases include a ries-rs-wasm.tar.gz artifact with the generated WASM packages. To build the browser bundle locally, install the JS dependencies and the nightly Rust toolchain first:

npm install
rustup toolchain install nightly
npm run build:web:site

Deploy the contents of dist/web-site/ to a path such as https://example.com/projects/ries-rs/.

The current local WASM build scripts use nightly wasm-pack via -Z build-std.

For the public deployment, use the canonical landing page at https://maxwellsantoro.com/projects/ries-rs and the standalone app at https://maxwellsantoro.com/projects/ries-rs/app/.

Detailed setup guides:

Quick Start

Basic search:

ries-rs 3.141592653589793

Example output:

                       x = pi                       ('exact' match) {29}
                      -x = -pi                      ('exact' match) {43}
                     1/x = 1/pi                     ('exact' match) {43}

Classic-style output:

ries-rs --classic 2.5063

Deterministic machine-readable output:

ries-rs 3.141592653589793 --deterministic --json --emit-manifest run.json

Turbo mode (parallelize matching across all cores for maximum speed):

ries-rs 2.506314 -l3 --turbo

--turbo runs the match/Newton phase on every core. It returns the same single best match as the serial path but trades reproducibility and memory for speed — the lower-ranked tail may differ between runs and thread counts. Use --deterministic instead when you need reproducible output.

For the authoritative option list:

ries-rs --help

Project Scope

ries-rs is intended to be a disciplined, modern reference implementation:

  • Faithful reimplementation of the core RIES search model
  • Deterministic and documented execution modes
  • Memory-safe Rust implementation with optional parallel generation and a parallel --turbo match phase
  • Structured output for automation (--json, --emit-manifest)
  • CLI, Rust library, Python bindings, and WebAssembly builds
  • Modular presets, profiles, and extension points

Not primary goals of this repository:

  • Symbolic AI or conjecture systems
  • Turning the bundled PSLQ integer-relation mode into a separate research platform
  • Experimental search branches outside the core RIES model

Performance

Performance claims are tracked conservatively with separate benchmark artifacts for end-to-end CLI runs and generation-only scaling:

  • End-to-end CLI baseline: docs/benchmarks/2026-03-20-level3-baseline.md captures the current level-3 workload; after tightening the adaptive search radius and snapping exact default-scale trig singularities, the candidate scan set dropped to about 8.1M pairs. The default --parallel CLI path is near break-even on this workload because it parallelizes generation only, while the dominant matching/Newton phase stays serial to preserve byte-identical results.
  • --turbo parallelizes the matching/Newton phase itself, trading the byte-identical guarantee (and extra memory) for large end-to-end speedups on multi-core machines — measured 4x–35x over the serial path on level-3 targets (8 cores). It still returns the same single best match as serial; see docs/SEARCH_MODEL.md for the turbo contract.
  • Generation-only scaling: docs/benchmarks/2026-02-25-generation-parallel-scaling.md reports 3.18x median speedup for parallel generation.

Raw benchmark artifacts live under docs/benchmarks/artifacts/.

Compatibility

ries-rs tracks behavior against two historical baselines while keeping a Rust-native engine and build surface:

  1. The original RIES by Robert Munafo
  2. The clsn/ries fork with additional compatibility-oriented CLI behavior

Current status in brief:

  • Core equation search and classic-style output flow are implemented
  • Legacy CLI semantics and diagnostic channels are supported substantially more completely than in early versions
  • The Rust-native engine keeps modern build and integration advantages, while edge-case ordering or complexity scores can still differ from historical binaries on some targets

See docs/PARITY_STATUS.md for the detailed status and historical notes.

How It Works

  1. Enumerate valid postfix expressions up to the current complexity limit
  2. Check fast-path exact matches against well-known constants when possible
  3. Generate left-hand-side and right-hand-side expression candidates
  4. Use Newton refinement to solve LHS(x) = RHS
  5. Filter, deduplicate, and refine candidate equations
  6. Rank matches by exactness, then error (exact matches rank by simplicity, not sub-tolerance residual), then parity-style or complexity-style order

Documentation

Contributing

If you want to improve the engine, docs, packaging, or release surfaces, start with CONTRIBUTING.md for setup and verification expectations.

Additional Interfaces

Python

The Python bindings expose ries_rs.search() and typed match objects through PyO3. See docs/PYTHON_BINDINGS.md for PyPI install, source development, API details, and troubleshooting.

WebAssembly

The WASM build supports browser, Node.js, bundler, and static-site workflows. See docs/WASM_BINDINGS.md for the JS/TS API and web/README.md for the browser UI and static hosting flow.

PSLQ

The CLI includes PSLQ integer-relation detection via --pslq, --pslq-extended, and --pslq-max-coeff. This is part of the shipped tool, but it is not the primary focus of the repository.

How to Cite

If you use ries-rs in academic work, cite the project version you used. CITATION.cff is the canonical metadata source.

@software{ries-rs2026,
  author       = {Santoro, Maxwell},
  title        = {ries-rs: A Rust Implementation of the RIES Inverse Equation Solver},
  year         = {2026},
  version      = {2.0.1},
  url          = {https://maxwellsantoro.com/projects/ries-rs},
  license      = {MIT},
  note         = {Features parallel search, deterministic mode, and run manifest for reproducibility}
}

Zenodo concept DOI for the project and its archived releases: 10.5281/zenodo.19101924

The latest verified version DOI is for v1.1.1: 10.5281/zenodo.19101925

No version DOI is recorded for v2.0.1 until its Zenodo archive has completed.

Use the concept DOI when you want a stable project-level reference that resolves to the latest archived release. Use the version DOI when you need to cite the specific archived release you used.

For reproducible research runs, prefer --deterministic together with --emit-manifest.

License

MIT License. See LICENSE.

References