Nasser M. Abbasi  wrote:   
   >   
   > But I am getting lots of time-outs from sympy. I have 3 minute time   
   > out set.  So sympy so far, is not doing too well. But I used 3 long   
   > minutes on all other CAS's so to be fair I have to keep it 3 minutes   
   > for sympy also.   
   >   
   > I figured, if CAS can't solve it in 3 minutes on fast PC, there is   
   > good chance more time will not help too much?   
      
   Depends on meaning of 'good chance' and 'too much'.  Main   
   Sympy method is parallel Risch-Norman integrator.  This method   
   builds system of linear equations of size depending   
   on your input.  For simple inputs you get relatively small   
   systems.  Sligthly larger systems still can be solved quite   
   fast, which led to claims that parallel integrators are fast.   
   But with complicated integrals systems may easily get so big   
   that it will take quite a lot of time.  When I looked at   
   Sympy I found another problem: its solver for linear   
   equations was quite slow.  Of course, it may happen that   
   you will eventually run out of memory.  But expect non-negigible   
   fraction of integrals to take between 3 minutes and say 12 hours.   
   Disclaimer: I looked at sympy few years ago, so it could   
   improve.  But what you wrote suggests that my observations   
   still hold.   
      
   To some degree similar things happens with FriCAS.  Large part   
   of old Rubi testsute can be done quite quickly (10 ms or less   
   per integral).  But some integrals need complex processing   
   and may take hours, days or even months to do.  For FriCAS   
   limiting time to 3 minutes would probably have resonably   
   small effect on counts of solved integrals, but large part   
   of those exceeding time limit can be done given enough time.   
      
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