Floating-point arithmetic differs from real arithmetic, which makes programming with floating-point numbers tricky. Estimating the precision of a floating-point computation in a program, i.e., estimat- ing the difference with the result of the same sequence of operations in an idealized real number semantics, is then necessary. Tools like Fluc- tuat, based on abstract interpretation, have been designed to address this problem. However, these tools compute an over-approximation of the domains of the floating-point variables that may be very coarse on some tricky programs. In this paper, we use a constraint solver over floating- point numbers to refine the over-approximation computed by Fluctuat and reduce the domains of floating-point variables. Our approach could be successfully applied to C programs that are difficult for abstract in- terpretation techniques as implemented in Fluctuat.