Russel Arbore, Alvin Cheung, Max Willsey
Equality saturation is a technique for program optimization based on non-destructive rewriting and a form of abstract interpretation called e-class analysis. Existing e-class analyses are pessimistic and therefore ineffective at analyzing cyclic programs, such as those in SSA form. We show that a straightforward optimistic variant of e-class analysis can result in unsoundness, due to a subtlety in how e-graphs represent programs. We propose an abstract interpretation algorithm that circumvents this issue and can optimistically analyze e-graphs during equality saturation. This results in a unified algorithm for optimistic analysis and non-destructive rewriting. To demonstrate the practicality of our approach, we implement a prototype abstract interpreter and equality saturation tool for SSA programs using a new semantics of SSA. Our tool exhibits precision improvements over pure abstract interpretation (without rewriting) and pessimistic e-class analysis on example programs. Additionally, its performance is comparable to existing abstract interpretation and e-class analysis techniques.