Synthesizing mathematical identities with e-graphs

Identities compactly describe properties of a mathematical expression and can be leveraged into faster and more accurate function implementations. However, identities must currently be discovered manually, which requires a lot of expertise. We propose a two-phase synthesis and deduplication pipeline that discovers these identities automatically. In the synthesis step, a set of rewrite rules is composed, using an e-graph, to discover candidate identities. However, most of these candidates are duplicates, which a secondary de-duplication step discards using integer linear programming and another e-graph. Applied to a set of 61 benchmarks, the synthesis phase generates 7215 candidate identities which the de-duplication phase then reduces down to 125 core identities.