Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may significantly differ from the path corresponding to the same computation with real numbers. As a consequence, developers do not know whether the program can actually produce very unexpected outputs. We introduce here a new constraint-based approach that searches for test cases in the part of the over-approximation where errors due to floating-point arithmetic could lead to unexpected decisions.