Growing E-Graph

Equality Saturation

key invariant to maintain: the equivalence relation is closed under congruence. (a = b implies f(a) = f(b))

deferred invariant maintenance

find all patterns

initial term

e-graph

apply all matches

restore all invariants

optimized term

comparison of pseducode

Evaluation

Overall, congruence is 88x faster, and equality saturation is 21x faster

Intuition of the speed-up

• Consider f1(x) ... fn(x) and y1 ... yn
• workload: merge(x, y1) ... merge(x, yn)
• traditional: O(n^2)
• deferred only does O(n)

egg: A Rust library

• An open source Rust library
• https://docs.rs/egg/

Case study

• Herbie: floating point
  • 3000x faster
• SPORES: linear algebra kernels
  • 1.5-2x better
• TASO(SOSP'19): superoptimization of ML Computational graph
  • substition of computational subgraphs
  • 23% better, 48x faster
• Szalinski: CAD synthesis
  • 1000x faster
• ..., TVM, Java testing, vectorization, hw/sw co-design, educational problems, ...