SmoothE: Differentiable E-Graph Extraction

E-graphs have gained increasing popularity in compiler optimization, program synthesis, and theorem proving tasks. They enable compact representation of many equivalent expressions and facilitate transformations via rewrite rules without phase ordering limitations. A major benefit of using e-graphs is the ability to explore a large space of equivalent expressions, allowing the extraction of an expression that best meets certain optimization objectives (or cost models). However, current e-graph extraction methods often face unfavorable scalability-quality trade-offs and only support simple linear cost functions, limiting their applicability to more realistic optimization problems.