> Again, with the mental model, you'll be in a better position to state what you expect by "exactly".

I'm long in the tooth, if I want exactly I'll use a symbolic algebra program (such as Cayley|Magma).

I don't expect exactly when using floats (or doubles, etc) and my mental model includes the image of the "fine teeth of coverage" having uneven spacing, that the float graticule across the reals is uneven and at best semi quasi regular has largely been my greatest issue (in geophysical computation engine development).