Solving Floating-Point Constraints with Continuous Optimization

Abstract

The Satisfiability Modulo Theory (SMT) problem over floating-point operations presents a significant challenge. State-of-the-art SMT solvers often run into difficulties when dealing with large, complex floating-point constraints. Recently, a new approach to floating-point constraint solving emerges, utilizing mathematical optimization (MO) methods as an engine of their solving approach. Despite the novelty, these methods can fall short in both effectiveness and efficiency due to issues of the translated functions (e.g., discontinuity) and inherent limitations of their underlying MO method (e.g., imprecise search process, scalability issues). Driven by these weaknesses of prior solvers, this paper introduces a new MO-based approach that is shown highly potent in solving floating-point constraints. Specifically, on the benchmarks of JFS (a recent solver based on fuzzing), Grater, a realization of our approach, solves as many constraints as Bitwuzla and one more than CVC5 but runs over 10 times faster and over 40 times faster than Bitwuzla and CVC5 in median solving time across all benchmarks. It is worth mentioning that Bitwuzla and CVC5 are the strongest solvers for floating-point constraints according to results of the annual international SMT solver competition (SMT-COMP). Together, they have won all gold medals for QF_FPArith and FPArith divisions, which focus on floating-point constraints solving, over the past three years. To further evaluate Grater, we select over 100 most difficult benchmarks from the FP SMT-LIB, a logic regularly used in SMT-COMP. The difficulty is measured by the complexity of the composition (e.g., number of variables, clauses) and the interdependencies within constraints. Grater again solves the same number of constraints as Bitwuzla and CVC5 while running over 10 times faster than both solvers in average solving time, and over 50 times (resp. 30 times) faster than Bitwuzla (resp. CVC5) in median solving time. We release the source code of Grater, along with all evaluation data, including detailed comparisons of Grater against each baseline solver (i.e., Z3, CVC5, Bitwuzla, JFS, XSat, and CoverMe), at https://github.com/grater-exp/grater-experiment to facilitate reproducibility.