[enriquto]

> If you really think this is all correct behavior and IA is going to make your life better, start using it in production and you'll learn it the hard way.

Even if this may come out as a bit snarky, this is a very good, honest, and helpful answer. At least, it would be helpful to extremely skeptical people like me. I'm a bit like crazygringo, and I cannot be convinced of anything until I have tried it myself and dirtied my hands with it.

To crazygringo: for a concrete, real-world example, try to implement a Kalman filter (a very simple numerical algorithm) using interval arithmetic. It simply doesn't work. You'll see that you cannot extract any useful result from the output of the computation. The implementation of an "interval Kalman filtering" is a (niche) subject of current research, where various very complicated algorithms are being invented to try to reproduce the nice properties of Kalman filtering--even when using something obviously inappropriate like interval arithmetic. For an intuitive understanding, assume that the input data are quantized to integer values, so that the starting intervals are of length 1.