From: hebisch@math.uni.wroc.pl   
      
   clicliclic@freenet.de wrote:   
   >   
   > Albert Rich schrieb:   
   > >   
   > > In your executive summary the "total leaf size" means problems having   
   > > large antiderivatives totally overwhelm problems having small ones.   
   > > Instead each problem should be given the same weight.  This can be   
   > > accomplished by comparing the leaf count size of a result with the   
   > > leaf count size of the optimal antiderivative.  Then for each system   
   > > tested, the average of these ratios could be included in your   
   > > executive summary.   
   > >   
   > > [...]   
   > >   
   >   
   > A more objective way may be to calculate geometric instead of arithmetic   
   > mean values of the run-time and leaf-count data. This may be achieved   
   > simply by averaging LOG(data) and diplaying EXP(mean). Am I right in   
   > supposing that neither huge nor tiny values then dominate the results?   
   >   
      
   What kind of statistic to you depends on your goal.  If you   
   want ot estimate time to do a batch of integrals, than   
   artithmetic mean is OK.  Geometric mean may severly underestimate   
   time because small valus cancel effect of large ones.  If you want   
   to estimate how much time "average" integral takes, then madian is   
   better.  Sometimes you want "warranted response time", then   
   maximal time is more apropriate.  To beter estimate distribution   
   quantiles are useful.  In different setting I used histogram   
   with geometrically sized bins.   
      
   FYI I run FriCAS trough old version af Rubi testsute and median   
   was of 10ms.  I did not compute average, but there were few integrals   
   taking each more than 1000s, so clearly average were dominated   
   by long running integrals.   
      
   --   
                                 Waldek Hebisch   
   hebisch@math.uni.wroc.pl   
      
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