They know what the actual details required for the inputs and outputs are, along with all the means to do the computations. Once they give you something that works (no matter how slow or kludgy), you have an executable specification to refactor, or rewrite, and you can A/B test to make sure your code works correctly compared to their reference/spec.
You spend some valuable time on the part of the experts, but you more than make up for it in saved time doing the wrong thing across possibly years.