Time Loop Software (2013)

I think one implementation could possibly be a probabilistic Turing machine [1]. You could have it produce some random output within an expected range and then do lots of fast probabilistic computations to resolve the answer.

It would come up with the correct answer before the computation is complete some percentage of the time, the other times you would need to wait for it to resolve. You can't be sure until it's finished, but some possibly correct answer might even be useful whilst you wait for it to complete.

[1] https://en.wikipedia.org/wiki/Probabilistic_Turing_machine

It reminds me of this playful talk on similar topics by Damian Conway using Raku: https://www.youtube.com/watch?v=ORjyXcLDd9M

If your computation is pure, this can be modeled in Haskell with the Tardis monad.

I may be mistaken but I believe this method of computation is referenced in Harry Potter and the Methods of Rationality