On Monday, July 22, 2013 9:28:14 PM UTC-4, Albert Rich wrote: > On Monday, July 22, 2013 11:53:11 AM UTC-10, da...@axiom-developer.org wrote: > > > > > On Sunday, July 21, 2013 8:04:31 PM UTC-4, Albert Rich wrote: > > > > >> Sorry, I don't want to wade through megabytes of raw Axiom test results. What I, and I think others, want to know is what percentage of the problems did Axiom get the optimal antiderivative, what percentage did it get valid but non-optimal antiderivatives, and what percentage is it unable to integrate. > > > > > Perfectly reasonable. However, it takes a while to create and process > > > 40,000+ integrals. I'll make a second pass when I have created the test > > > suite to evaluate the results. So far it takes about 3-4 days to create > > > one of the test suites and you appear to have posted 80 files. The raw > > > numbers you seek probably won't exist until the end of the year at this > > > rate. > > > > > > Rather than the raw numbers I'm more interested in the classes of problems > > > that Axiom does not handle. My long term plan for this test suite is to > > > use your patterns to form these classes and then use your patterns to write > > > pattern-based integration routines to handle them. > > > > Glad to hear Rubi and its test-suite will be of use in your efforts to improve Axiom's symbolic integrator. Since you have apparently written a program to run the test-suite, seems like extending it to compare the results with the optimal antiderivatives and assign a grade should be relatively easy... > > > > Albert
On a per-file basis this information is readily available. Every integral is a 5 step process where the 5th step compares the derivative of the difference between your "optimal integral" and Axiom's answer. If the 5th step is 0 then they have the same answer. If they differ by a non-constant value then one of us has the wrong answer. This could be decided by taking the derivative of the "optimal integral". If that is non-constant then the supplied result is wrong.
There were a couple of examples where Rubi's answer did not differentiate to a constant value. These are mentioned in a previous post.
To make life easier I'll update the abstract at the start of the file to include these statistics (on a per-file basis).