HP PPL and Statistical distributions

[compaqdrew]

This might be better answered by somebody who knows the calculator better. Part of the issue is that for a function like Integrate, it tries a lot of different methods. I believe that Prime, Giac/Xcas, and some HP48 routines can take a crack at integration, and each of those codebases have many methods inside them. I think some of these methods do look at CAS or Home precision, but I'm not sure all of them do. Based on the errors I get running your program, it seems a lot of time is spent trying different methods, and so that may be an issue regardless of accuracy.

You might have better luck using a specific method. There is a builtin romberg function, I don't know if it can handle your integrals but it's worth a try to replace them with romberg calls and see how it performs. There's also some numerical methods for the Prime written by Jhonatan Peretz that you can try, in particular he has a Legendere quadrature that might work well.

Back to your question, there are specific integration methods that trade off time for accuracy. Monte carlo integration is the first that comes to mind, since you can reduce the iteration count. There is a double integral version for PPL by Eddie Shore, but it's probably simple enough you can port the simpler single algorithm from anywhere. The trick will be the infinite integration limits. Usually you can just use large/small values if the contribution outside the range will be small.