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Generating high-performance code for diverse hardware and application domainsis challenging. Functional array programming languages with patterns like mapand reduce have been successfully combined with term rewriting to define andexplore optimization spaces. However, deciding what sequence of rewrites toapply is hard and has a huge impact on the performance of the rewrittenprogram. Equality saturation avoids the issue by exploring many possible waysto apply rewrites, efficiently representing many equivalent programs in ane-graph data structure.  Equality saturation has some limitations when rewriting functional languageterms, as currently naive encodings of the lambda calculus are used. We presentnew techniques for encoding polymorphically typed lambda calculi, and show thatthe efficient encoding reduces the runtime and memory consumption of equalitysaturation by orders of magnitude.  Moreover, equality saturation does not yet scale to complex compileroptimizations. These emerge from long rewrite sequences of thousands of rewritesteps, and may use pathological combinations of rewrite rules that cause thee-graph to quickly grow too large. This paper introduces \emph{sketch-guidedequality saturation}, a semi-automatic technique that allows programmers toprovide program sketches to guide rewriting. Sketch-guided equality saturationis evaluated for seven complex matrix multiplication optimizations, includingloop blocking, vectorization, and multi-threading. Even with efficient lambdacalculus encoding, unguided equality saturation can locate only the twosimplest of these optimizations, the remaining five are undiscovered even withan hour of compilation time and 60GB of RAM. By specifying three or fewersketch guides all seven optimizations are found in seconds of compilation time,using under 1GB of RAM, and generating high performance code.

Sketch-Guided Equality Saturation: Scaling Equality Saturation to Complex Optimizations of Functional Programs