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• W1915348541 abstract "The verification of floating-point mathematical libraries requires computing numerical bounds on approximation errors. Due to the tightness of these bounds and the peculiar structure of approximation errors, such a verification is out of the reach of generic tools such as computer algebra systems. In fact, the inherent difficulty of computing such bounds often mandates a formal proof of them. In this paper, we present a tactic for the Coq proof assistant that is designed to automatically and formally prove bounds on univariate expressions. It is based on a formalization of floating-point and interval arithmetic, associated with an on-the-fly computation of Taylor expansions. All the computations are performed inside Coq’s logic, in a reflexive setting. This paper also compares our tactic with various existing tools on a large set of examples." @default.
• W1915348541 created "2016-06-24" @default.
• W1915348541 creator A5042046844 @default.
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• W1915348541 date "2015-10-05" @default.
• W1915348541 modified "2023-10-10" @default.
• W1915348541 title "Proving Tight Bounds on Univariate Expressions with Elementary Functions in Coq" @default.
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• W1915348541 doi "https://doi.org/10.1007/s10817-015-9350-4" @default.
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