The approx is very interesting, but how good is it? Of course with interval arithmetic you can easily get proven bounds, but they are only rarely optimal, can y

The approx is very interesting, but how good is it? Of course with interval arithmetic you can easily get proven bounds, but they are only rarely optimal, can you do better? What if you can mathematically prove the bounds, but the type check fails? And to be honest, I pretty much fail to see the point (although that might be ignorance on my part), even the motivation seems incredibly weak. Sure, implementing numerical algorithms is hard, but finding out that you wrote "-" instead of "+", is one of the easiest things in the world to spot. In almost every situation it is impossible not to notice as your algorithm will give extremely inaccurate answers, which is something even the most novice of programmers could write a test for. And even if that weren't the case writing a good test suit to test numerical algorithms for standard functions seems far simpler.