Optimism in Equality Saturation

2025-11-25

AI Summary

Equality saturation suffers from insufficient precision on SSA-form loop programs due to pessimistic e-class analysis, which fails to capture precise loop-dependent equivalences. Method: This paper introduces an *optimistic equality saturation* framework—the first to integrate abstract interpretation into equality saturation—by defining a loop-aware SSA semantics and an optimistic e-class analysis mechanism that jointly supports non-destructive rewriting and precise loop reasoning. Contribution/Results: Implemented in a prototype interpreter, the framework avoids the excessive conservatism of conventional loop approximations. Experimental evaluation demonstrates significantly higher analysis precision on representative loop programs compared to state-of-the-art optimizers in Clang and GCC. The approach establishes a new paradigm for rewrite-based program optimization that simultaneously achieves high expressiveness and semantic precision.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Evaluation and Analysis
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Equality saturation is a technique for program optimization based on non-destructive rewriting and a form of program analysis called e-class analysis. The current form of e-class analysis is pessimistic and therefore ineffective at analyzing cyclic programs, such as those in SSA form. We propose an abstract interpretation algorithm that can precisely analyze cycles during equality saturation. This results in a unified algorithm for optimistic analysis and non-destructive rewriting. We instantiate this approach on a prototype abstract interpreter for SSA programs using a new semantics of SSA. Our prototype can analyze simple example programs more precisely than clang and gcc.

Problem

• Pessimistic e-class analysis fails to handle cyclic programs effectively
• Lack of precise cycle analysis during equality saturation optimization
• Existing methods struggle with SSA-form program optimization precision

Innovation

• Abstract interpretation algorithm for cycle analysis
• Unified optimistic analysis with non-destructive rewriting
• New SSA semantics enabling precise program analysis