I'm not sure how a "spec with floats" differs from a spec with networks, RAM, 64-bit integers, multi-level cache, or any computing concept, none of which exists as a primitive in mathematics. A floating point number is a pair of integers, or sometimes we think about it as a real number plus some error, and TLAPS can check theorems about specifications that describe floating-point operations.

Of course, things can become more involved if you want to account for overflow, but overflow can get complicated even with integers.