Metamorphic Testing for Floating-Point Performance Issues in SMT Solvers

Abstract

SMT solvers are essential in various domains, including program verification and synthesis. Although their correctness and performance have been extensively studied, performance testing for the floating-point theory remains limited, particularly for real-world queries. We propose a metamorphic testing approach that uses semantics-preserving rewrite rules, focusing on floating-point special values and peep-hole optimizations, to uncover meaningful performance issues in SMT solvers' handling of floating-point formulas. Using real-world test inputs, our approach is able to identify for every solver tested SMT queries for which solving time increases when the queries are simplified; we see slowdowns of up to 33.4x for Z3, 5.6x for MathSAT, 4.5x for cvc5, and 1.8x for Bitwuzla. We further observe that the approach is less successful when using input files that were randomly generated from a grammar.