Uncertain<T>

This concept has been done many times in the past, under the name "interval arithmetic." Boost has it [1] as does flint [2]

What is really curious is why, after being reinvented so many times, it is not more mainstream. I would love to talk to people who have tried using it in production and then decided it was a bad idea (if they exist).

[1]: https://www.boost.org/doc/libs/1_89_0/libs/numeric/interval/... [2]: https://arblib.org/

Interval arithmetic is only a constant factor slower but may simplify at every step. For every operation over numbers there is a unique most precise equivalent op over intervals, because there's a Galois connection. But just because there is a most precise way to represent a set of numbers as an interval doesn't mean the representation is precise.

A computation graph which gets sampled like here is much slower but can be accurate. You don't need an abstract domain which loses precision at every step.