Formally Verified Roundoff Errors Using SMT-based Certificates and Subdivisions

  • Joachim Bard
  • Heiko BeckerEmail author
  • Eva Darulova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11800)


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.


Coq Roundoff error Finite-precision SMT Subdivision 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.MPI-SWS, Saarland Informatics CampusSaarbrückenGermany

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