The disclosure generally describes methods, software, and systems for defining a constraint satisfaction problem including floating point variables. Floating-point domains are described using a notation that allows arbitrarily many ranges denoted by at least one of intervals with boundary information or singleton values comprising fully discrete domains. Mathematically correct results are computed using closures combined with interval arithmetic. A new consistency level for constraint propagation is provided, including multi-bounds consistency, over floating point variables, where the multi-bounds consistency achieves domain consistency over monotonic functions.