Static value analysis is a classical approach for verifying programs with floating-point computations. Value analysis mainly relies on abstract interpretation and over-approximates the possible values of program variables. State-of-the-art tools may however compute over-approximations that can be rather coarse for some very usual program expressions. In this paper, we show that constraint solvers can significantly refine approximations computed with abstract interpretation tools. More precisely, we introduce a hybrid approach that combines abstract interpretation and constraint programming techniques in a single static and automatic analysis. We compared the efficiency of the system we developed---named rAiCp---with state-of-the-art static analyzers: rAiCp produces substantially more precise approximations and is able to check program properties on both academic and industrial benchmarks.