From a cursory look at the code, I don't see any use of fused-multiply-add (FMA) which would likely help with precision issues in a number of places with the float version. The "problem in more detail"[1] readme specifically calls out computation of `x^2 - y^2` as a source for error, and that has methods that dramatically reduce error with FMAs[2].
[1] https://github.com/ProfJski/FloatCompMandelbrot/blob/master/... [2] https://pharr.org/matt/blog/2019/11/03/difference-of-floats