Solving constraints over floating-point numbers is a critical issue in numerous applications notably in program verification. Capabilities of filtering algorithms for constraints over the floating-point numbers have been so far limited to 2b-consistency and its derivatives. Though safe, such filtering techniques suffer from the well known pathological problems of local consistencies, e.g., inability to efficiently handle mul- tiple occurrences of the variables. These limitations also take roots in the strongly restricted floating-point arithmetic. To circumvent the poor properties of floating-point arithmetic, we propose in this paper to build various relaxations over the reals of the problem over the floats. We show that using linear programming (LP) to shrink the domains with safe linearisations of such relaxations can be very effective for boosting filtering techniques for constraints over the floats. Preliminary experiments on a limited but relevant set of benchmarks are very promising.