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On Sound Relative Error Bounds for Floating-Point Arithmetic [article]

Anastasiia Izycheva, Eva Darulova
2017 arXiv   pre-print
State-of-the-art static analysis tools for verifying finite-precision code compute worst-case absolute error bounds on numerical errors. These are, however, often not a good estimate of accuracy as they do not take into account the magnitude of the computed values. Relative errors, which compute errors relative to the value's magnitude, are thus preferable. While today's tools do report relative error bounds, these are merely computed via absolute errors and thus not necessarily tight or more
more » ... formative. Furthermore, whenever the computed value is close to zero on part of the domain, the tools do not report any relative error estimate at all. Surprisingly, the quality of relative error bounds computed by today's tools has not been systematically studied or reported to date. In this paper, we investigate how state-of-the-art static techniques for computing sound absolute error bounds can be used, extended and combined for the computation of relative errors. Our experiments on a standard benchmark set show that computing relative errors directly, as opposed to via absolute errors, is often beneficial and can provide error estimates up to six orders of magnitude tighter, i.e. more accurate. We also show that interval subdivision, another commonly used technique to reduce over-approximations, has less benefit when computing relative errors directly, but it can help to alleviate the effects of the inherent issue of relative error estimates close to zero.
arXiv:1707.02121v2 fatcat:j3d26pjgdfe7fpnfx2cmokvffu

Counterexample- and Simulation-Guided Floating-Point Loop Invariant Synthesis [chapter]

Anastasiia Izycheva, Eva Darulova, Helmut Seidl
2020 Lecture Notes in Computer Science  
nearbyPts volume 100 1000 0 0.5 500 2.283 100 1000 0 0.5 100 2.297 100 10000 5 0.25 100 2.311 100 1000 2 0.25 100 2.314 100 10000 1 0.5 500 2.335 https://github.com/izycheva  ... 
doi:10.1007/978-3-030-65474-0_8 fatcat:g62rmena2ranrmrobp6jmwqhde

Daisy - Framework for Analysis and Optimization of Numerical Programs (Tool Paper) [chapter]

Eva Darulova, Anastasiia Izycheva, Fariha Nasir, Fabian Ritter, Heiko Becker, Robert Bastian
2018 Lecture Notes in Computer Science  
Automated techniques for analysis and optimization of finite-precision computations have recently garnered significant interest. Most of these were, however, developed independently. As a consequence, reuse and combination of the techniques is challenging and much of the underlying building blocks have been re-implemented several times, including in our own tools. This paper presents a new framework, called Daisy, which provides in a single tool the main building blocks for accuracy analysis of
more » ... floating-point and fixed-point computations which have emerged from recent related work. Together with its modular structure and optimization methods, Daisy allows developers to easily recombine, explore and develop new techniques. Daisy's input language, a subset of Scala, and its limited dependencies make it furthermore user-friendly and portable.
doi:10.1007/978-3-319-89960-2_15 fatcat:ktavggsosfh5zihqco7rtcolou

Approximate Systems (Dagstuhl Seminar 21302)

Eva Darulova, Babak Falsafi, Andreas Gerstlauer, Phillip Stanley-Marbell
2021
International license © Eva Darulova Joint work of Anastasia Volkova, Anastasiia Izycheva, Helmut Seidl, Heiko Becker, Magnus Myreen, Zachary Tatlock, Debasmita Lohar, Sylvie Putot, Eric Goubault Eva Darulova  ... 
doi:10.4230/dagrep.11.6.147 fatcat:pkgfs6cfsfhhpf6ys6sb6lyenq