# Rewrite Rule Inference Using Equality Saturation

arXiv: https://arxiv.org/abs/2108.10436 · HTML: https://mlsanity.com/paper/2108.10436/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2021.

## Built on by (most cited first, 10 of 10)

- [QUITE: A Query Rewrite System Beyond Rules with LLM Agents](https://mlsanity.com/paper/2506.07675/) (2025)
- [NeuRI: Diversifying DNN Generation via Inductive Rule Inference](https://mlsanity.com/paper/2302.02261/) (2023)
- [Search-Based Regular Expression Inference on a GPU](https://mlsanity.com/paper/2305.18575/) (2023)
- [EGG-SR: Embedding Symbolic Equivalence into Symbolic Regression via Equality Graph](https://mlsanity.com/paper/2511.05849/) (2025)
- [SEER: Super-Optimization Explorer for HLS using E-graph Rewriting with MLIR](https://mlsanity.com/paper/2308.07654/) (2023)
- [Modelling Program Spaces in Program Synthesis with Constraints](https://mlsanity.com/paper/2508.00005/) (2025)
- [Saturating Scaling Laws for Equational Discovery: A Phenomenology of Growth Dynamics in Three Toy Substrates with Two Real-World Replications](https://mlsanity.com/paper/2605.23983/) (2026)
- [Abstract Interpretation on E-Graphs](https://mlsanity.com/paper/2203.09191/) (2022)
- [Verifying Computational Graphs in Production-Grade Distributed Machine Learning Frameworks](https://mlsanity.com/paper/2509.10694/) (2025)
- [LLM-Guided Strategy Synthesis for Scalable Equality Saturation](https://mlsanity.com/paper/2604.17364/) (2026)

## Abstract (arXiv)

Many compilers, synthesizers, and theorem provers rely on rewrite rules to simplify expressions or prove equivalences. Developing rewrite rules can be difficult: rules may be subtly incorrect, profitable rules are easy to miss, and rulesets must be rechecked or extended whenever semantics are tweaked. Large rulesets can also be challenging to apply: redundant rules slow down rule-based search and frustrate debugging. This paper explores how equality saturation, a promising technique that uses e-graphs to apply rewrite rules, can also be used to infer rewrite rules. E-graphs can compactly represent the exponentially large sets of enumerated terms and potential rewrite rules. We show that equality saturation efficiently shrinks both sets, leading to faster synthesis of smaller, more general rulesets. We prototyped these strategies in a tool dubbed ruler. Compared to a similar tool built on CVC4, ruler synthesizes 5.8X smaller rulesets 25X faster without compromising on proving power. In an end-to-end case study, we show ruler-synthesized rules which perform as well as those crafted by domain experts, and addressed a longstanding issue in a popular open source tool.