From: nma@12000.org   
      
   On 10/9/2022 12:12 PM, clicliclic@freenet.de wrote:   
      
   >   
   > Interesting indeed.   
   >   
   > The performance of Mathematica, Maple, and FriCAS in dependence on the   
   > number of distinct rules used by Rubi exhibits a plateau or even a rise   
   > over the range from 4 to 7 rules. May this be caused by some   
   > peculiarity in the construction of the Rubi test suite in particular,   
   > rather than by features of the integration algorithms fielded by the   
   > three competitors? The other four systems show a fairly steady decrease   
   > with the number of rules.   
   >   
   > The performance in dependence on the total number of steps used by Rubi   
   > also shows a diffrence between the behavior of Mathematica, Maple, and   
   > FriCAS, and that of Giac, Maxima, Mupad, and Sympy: a gradual decrease   
   > for the first three systems, versus a small increase at two steps that   
   > changes to a relatively fast decrease up to 8 or 10 steps that is   
   > followed by a plateau for the last four systems. Again, two groups of   
   > algorithms appear to react differently to the overall testsuite.   
   >   
   > In the histograms of the number of integrals solved versus leaf size of   
   > the antiderivative, Rubi is exceptional in that the first bin (of sizes   
   > below 40 leaves) does not hold significantly more integrals than the   
   > next one (from 40 to 80 leaves) contains, whereas all bins for all   
   > other systems conform to a general decrease with leaf count. Could this   
   > be caused specifically by Rubi's poor performance on Waldek's integrals   
   > based on 10'000 random antiderivatives?   
   >   
   > Martin.   
      
      
   If anyone has suggestions of other useful statistics to generate, feel   
   free to let me know.   
      
   With SQL, it is much much easier to generate all sorts of statistics   
   than before because I can just do SQL command to obtain any sort   
   of information I want now. Before, I had to code all these things   
   manually.   
      
   I just do not now what other useful stats I could ask. But If   
   I think of other things, will add them.   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)