Huh, what? Floating point numbers have a standard, you know. They aren't non-deterministic YOLO numbers.

By default, the compiler has to stick to what the standard requires, and can't just say add arbitrary imprecision.

Your epsilon is what you get when you try to analyse floating point numbers as approximations of real numbers. But they also have an independent life as bit patterns, and the compiler can't just willy-nilly muck around with these bit patterns.

Look at the link. Floating point has limited precision and the complete inability to exactly represent some numbers.

Example, this equality check is false:

0.1 + 0.2 == 0.3

Because the last bits of a floating point number, after any practical chain of operations, is practically random, do to errors from limited precision.