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Interpretation-based value analysis is a classical approach for verifying programs with floating-point computations. However, state-of-the-art tools compute an over-approximation of the variable values that can be very coarse. Constraint solvers have recently been used to significantly refine the approximations computed by such tools. In this paper, we introduce a hybrid approach that combines abstract interpretation and constraint programming techniques in a single static and automatic analysis. First experiments showed that this approach can successfully analyze programs that could not be handled by abstract interpretation or constraint programming tools alone.