In my side-projects I use simpler solutions as oracles to more complex solutions if I'm fuzzing. E.g. if I implemented some sophisticated `fac` implementation w

In my side-projects I use simpler solutions as oracles to more complex solutions if I'm fuzzing. E.g. if I implemented some sophisticated `fac` implementation with secret sauce and mathematical yada yada, I use `def fac(n): return 1 if n==0 else n * fac(n-1)` as oracle, which works but is slow. I never used something like this for work, so I don't know what's the industry standard way to write an oracle, but this works fairly well. Another examples: I implemented polynomial multiplication with FFT and then tested it with canonical O(N^2) algorithm. I implemented Strassen algorithm, tested it with canonical O(N^3) algorithm. You can even have multiple levels of oracles: If canonical polynomial mul is too slow, use FFT PM to test a more sophisticated polynomial multiplication algorithm. In college, in my OS class my professor said something like in the space missions algorithms were implemented bunch of times by bunch of different teams and then in runtime they voted on output. You can do something like this to orchestrate an oracle too. Implement the same function 5 times, they vote on an output, their agreed upon output is the oracle's output and then now use this to test your real function. It goes without saying, if the problem is NP, then you can build a function that tests the output. Of course, now you need to test this function...