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For some reason the first thing that popped into my head when I read this was fuzzers like American Fuzzy Lopp. I wonder if you could use the same sort of stochastic exploration to explore the space of possible programs satisfying a set of tests rather than explore the space of possible inputs given a program?

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That's called program synthesis which is a hot research area. Specifically, what you mention is called "programming by example". I can't remember many examples on top of my head but some people from Microsoft Research are working on it for example: https://microsoft.github.io/prose/

I can't Google the name right now, but this does exist as an optimization technique. Just start with any program, create random permutations, score them for correctness and performance, keep the best ones, repeat.

The problem is that this is incredibly computation intense, since the number of possible programs is huge. Right now it's viable for improving small code parts with a know-correct starting point. Maybe some day computers become fast enough to make more viable.

Stochastic optimization? STOKE [1] from Stanford is trying to that if I understood it correctly.

[1]: https://github.com/StanfordPL/stoke

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