[jrm4]

I would be very comfortable with - re-run 100 times with different seeds. If the outcome is the same every time, you're reliably good to go.

[SpaceNoodled]

Even when it's wrong each time?

[onion2k]

If it's wrong then it's not provably correct (for any value of 'proof').

How you define your proof is up to you. It might be a simple test, or an exhaustive suite of tests, or a formal proof. It doesn't matter. If the output of the code is correct by your definition, then it doesn't matter what the underlying code actually is.