Years ago, in a similar situation, I wrote a tool to capture parameters and results for the algorithm while QA ran their full application test suite. Ended up

Years ago, in a similar situation, I wrote a tool to capture parameters and results for the algorithm while QA ran their full application test suite. Ended up with a few thousand cases and expected results; results where QA had verified the software worked as expected. Used that to create a test suite that we could then maintain normally. Much better than random.