As I understand it, it's more that the mathematical functions aren't specified by the standard.
There is no sqrt instruction. So you stard with a taylor approximation, then maybe do a few rounds of Newton's method to refine the answer. But what degree is the taylor series? Where did you centre it (can't be around 0)? How many Newton's methods did you do? IEEE 754 might dictate what multiplication looks like, but for sqrt, sin, cos, tan you need to come up with a method of calculation, and that's in the standard library which usually comes from the compiler. You could make your own implementations but...
Floats are not associative: (a+b)+c != a+(b+c). So even something like reordering fundamental operations can cause divergence.
There is no sqrt instruction. So you stard with a taylor approximation, then maybe do a few rounds of Newton's method to refine the answer. But what degree is the taylor series? Where did you centre it (can't be around 0)? How many Newton's methods did you do? IEEE 754 might dictate what multiplication looks like, but for sqrt, sin, cos, tan you need to come up with a method of calculation, and that's in the standard library which usually comes from the compiler. You could make your own implementations but...
Floats are not associative: (a+b)+c != a+(b+c). So even something like reordering fundamental operations can cause divergence.