Equality Saturation for Optimizing High-Level Julia IR

Compilers are indispensable for transforming code written in high-level languages into performant machine code, but their general-purpose optimizations sometimes fall short. Domain experts might be aware of certain optimizations that the compiler is unable to apply or that are only valid in a particular domain. We have developed a system that allows domain experts to express rewrite rules to optimize code in the Julia programming language. Our system builds on e-graphs and equality saturation. It can apply optimizations in the presence of control flow and side effects. As Julia uses multiple dispatch, we allow users to constrain rewrite rules by argument types, and propagate type information through the e-graph representation. We propose an ILP formulation for optimal e-graph extraction taking into account dominance properties for code reuse and introduce CFG skeleton relaxation to rewrite calls to pure functions as well as those with side effects. Use cases demonstrate that our system can perform rewrites on high-level, domain-specific code, as well as on lower-level code such as Julia's broadcasting mechanism. Finally, we analyze the required compilation time.