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Programs with floating-point computations are often derived from mathematicalmodels or designed with the semantics of the real numbers in mind. However, fora given input, the computed path with floating-point numbers may differ fromthe path corresponding to the same computation with real numbers. A commonpractice when validating such programs consists in estimating the accuracy offloating-point computations with respect to the same sequence of operations inan ide-alized semantics of real numbers. However, state-of-the-art toolscompute an over-approximation of the error introduced by floating-pointoperations. As a consequence, totally inappropriate behaviors of a program maybe dreaded but the developer does not know whether these behaviors willactually occur, or not. In this paper, we introduce a new constraint-basedapproach that searches for test cases in the part of the over-approximationwhere errors due to floating-point arithmetic would lead to inappropriatebehaviors.

Searching input values hitting suspicious Intervals in programs with floating-point operations