egg: Fast and extensible equality saturation

An e-graph efficiently represents a congruence relation over many expressions. Although they were originally developed in the late 1970s for use automated theorem provers, more recent technique known as equality saturation repurposes e-graphs to implement state-of-the-art, rewrite-driven compiler optimizations and program synthesizers. However, remain unspecialized this newer case. Equality workloads exhibit distinct characteristics often require ad-hoc extensions incorporate transformations beyond purely syntactic rewrites. This work contributes two techniques that make fast extensible, specializing them saturation. A new amortized invariant restoration called rebuilding takes advantage of saturation's workload, providing asymptotic speedups current practice. general mechanism e-class analyses integrates domain-specific into e-graph, reducing need ad hoc manipulation. We implemented these open-source library egg. Our case studies on three previously published applications highlight how egg's performance flexibility enable state-of-the-art results across diverse domains.