There is no way to completely check a program. It may be possible to compare results to manual calcs for a few simple cases, but the only way to be sure a program calculates everything correctly is to completely review the program code. Impossible of course, since the vendor doesn't provide the program code. So, whenever we use someone else's software, we're hoping (and praying) that the program is correct.
I trusted a program once after checking some cases against hand calcs. Turned out, the program didn't check some section of the code that rarely governed. I didn't pick up the error in my comparisons, and neither did anyone else using the software, apparently. The structure needed to be reinforced. We paid. The software vendor, who admitted the error, was liable for the cost of the software, a tiny fraction of the cost of repair. Many software vendors include verbiage in the contract that limits their liability in this way.