Formally Verified Roundoff Errors Using SMT-based Certificates and Subdivisions.

Summary

When compared to idealized, real-valued arithmetic, finite precision arithmetic introduces unavoidable errors, for which numerous tools compute sound upper bounds. To ensure soundness, providing formal guarantees on these complex tools is highly valuable. In this paper we extend one such formally verified tool, FloVer. First, we extend FloVer with an SMT-based domain using results from an external SMT solver as an oracle. Second, we implement interval subdivision on top of the existing analyses. Our evaluation shows that these extensions allow FloVer to efficiently certify more precise bounds for nonlinear expressions.