egg: e-graphs good

The egg project uses e-graphs to provide a new way to build program optimizers and synthesizers. egg is developed by Max Willsey and his friends on GitHub.

An e-graph compactly represents many equivalent programs. These four e-graphs represent more and more (even infinite!) ways to write (a × 2) / 2. egg makes e-graphs fast and flexible enough for use in program optimization and synthesis.

The core egg library provides high-performance, flexible e-graphs implemented in Rust. It is packaged on and documented on, including a tutorial that provides an introduction to e-graphs and their use cases.

  author = {Willsey, Max and Nandi, Chandrakana and Wang, Yisu Remy and Flatt, Oliver and Tatlock, Zachary and Panchekha, Pavel},
  title = {egg: Fast and Extensible Equality Saturation},
  year = {2021},
  issue_date = {January 2021},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  volume = {5},
  number = {POPL},
  url = {},
  doi = {10.1145/3434304},
  abstract = {An e-graph efficiently represents a congruence relation over many expressions. Although they were originally developed in the late 1970s for use in automated theorem provers, a more recent technique known as equality saturation repurposes e-graphs to implement state-of-the-art, rewrite-driven compiler optimizations and program synthesizers. However, e-graphs remain unspecialized for this newer use case. Equality saturation workloads exhibit distinct characteristics and often require ad-hoc e-graph extensions to incorporate transformations beyond purely syntactic rewrites.  This work contributes two techniques that make e-graphs fast and extensible, specializing them to equality saturation. A new amortized invariant restoration technique called rebuilding takes advantage of equality saturation's distinct workload, providing asymptotic speedups over current techniques in practice. A general mechanism called e-class analyses integrates domain-specific analyses into the e-graph, reducing the need for ad hoc manipulation.  We implemented these techniques in a new open-source library called egg. Our case studies on three previously published applications of equality saturation highlight how egg's performance and flexibility enable state-of-the-art results across diverse domains.},
  journal = {Proc. ACM Program. Lang.},
  month = jan,
  articleno = {23},
  numpages = {29},
  keywords = {equality saturation, e-graphs}


For updates on egg itself, see the changelog.

Projects using egg

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Projects inspired by egg