For IEEE, the single representation is 1-bit sign, 8-bit exponent and 23-bit mantissa. This means that at each exponent value, you can test all 2^23-1 (roughly 9mil cases) possible combination of binary representation (give or take). Then you do it for all exponent value (255 values), and you can basically cover all floating points represented by IEEE.
However, for double precision, such approach is not really viable. With 52-bit mantissa, at each value of exponent you would need to test 2^52-1 binary combinations (which is roughly 4 million bilion, ~E15).
This seems to suggest that you need some randomizing scheme to test that your arithmetic implementation is bounded with high probability. But do we know which scheme to use? Would it also be beneficial to consider how floating point numbers are distributed (i.e. more collocated around certain value/zero)?