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This is wrong code. It only works somewhat correctly when a and b around 1.

Yeah, should be scaled like |x - y| <= ε * max(|x|, |y|)

Will do.

If both terms are infinites and of same sign, subtraction will give NaN and it will fail.

How is that a problem? infinities shouldn't be considered equal

For IEEE 754, and in Java for example, they are. Only NaN is not equal to itself (and different from itself).