Equality saturation is a program optimization technique based on non-destructive rewriting and a form of abstract interpretation called e-class analysis. Existing e-class analyses are pessimistic and therefore typically imprecise when 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. We implement a prototype abstract interpreter and equality saturation tool for SSA programs. 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.

@article{paperbot3737,
  title = {Optimism in Equality Saturation},
  author = {Russel Arbore and Alvin Cheung and Max Willsey},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {10},
  number = {PLDI},
  year = {2026},
  doi = {10.1145/3808302}
}