Rather than stripping bits, you can just compare if the bit-casted numbers are less than N apart (choose an appropriate N that works for your data; a good starting point is 4).

This breaks down across the positive/negative boundary, but honestly, that's probably a good property. -0.00001 is not all that similar to +0.00001 despite being close on the number line.

It also requires that the inputs are finite (no INF/NAN), unless you are okay saying that FLT_MAX is roughly equal to infinity.