Rewrite Rule Inference Using Equality Saturation

Abstract

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 5.8× smaller rulesets 25× 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.

Automated Code Optimization with E-Graphs

“…The equational nature of our framework is particularly adapt for prefixing the adjective "algebraic" to the name of these practices. Authors of egg [58] have recently published a paper introducing a technique that is using equality saturation to automatically infer new systems of rewrite rules [35]. Rewrite rules and systems can be treated as algebraic entities much like terms in symbolic mathematics.…”

Caviar: An E-graph Based TRS for Automatic Code Optimization

“…Since their first appearance [4], E-graphs have been used in different domains, although mainly focused on program optimization. E-graphs were initially proposed as a data structure that is capable of representing equivalence 3 The time limit used in this evaluation is 3s relation efficiently, before becoming an essential part of every SMT solver [13].…”

“…By exploiting E-Class Analysis, Constant Folding can be implemented as an e-class analysis that highlights the parallels with abstract interpretation. egg is being used in multiple projects in different domains, in the likes of Ruler [3] which uses equality saturation to automatically infer rewrite rules, Diospyros [11] which performs vectorization for digital signal processors via equality saturation, Tensat [14] which presents a novel technique for tensor graph superoptimization using equality saturation and e-graphs, Herbie [6] which improves the accuracy of floating point expressions , Szalinski [2] which is a tool that uses Equality Saturation with semantics-preserving CAD rewrites to efficiently search for more optimized equivalent programs, SPORES [12] which uses equality saturation to simplify linear algebra expressions, and Glenside [8] which performs term rewriting using equality saturation to map program fragments to hardware accelerator invocations and automatically discover classic data layout transformations.…”