From: nma@12000.org   
      
   On 3/31/2017 11:53 AM, acer wrote:   
      
   > But it is important that your grading scheme measures the size of   
   >the "optimal" anti-derivative using the same system as for the measurement of   
   the result.   
   >   
   > For example, if you use Maple's own `LeafCount` to measure the size of   
   >an integration result, then you should very much also be formulating the   
   >optimal result in Maple as well, and then comparing by computing the size   
   >of that optimal result it Maple. You must never compare against the   
   >optimal size as measured by any other system.   
   >   
   > I suspect that Albert's has made the same point. I'd like to stress it.   
   >If that is already your approach then apologies for mentioning it.   
   >   
      
   Hello Acer;   
      
   Each CAS has it own set of test files at Rubi's web site. The optimal   
   result is the 4th field for each integral record. Written in CAS   
   own synatx.   
      
   For example, Timofeev  #1 has this   
      
       [1/(a^2-b^2*x^2),x,1,arctanh(b*x/a)/(a*b)]   
      
   The 4th field above, is the optimal result. This is the one   
   used to compare its leaf count with the leaf count of the   
   result produced by Maple. Both is done using Maple own LeafCount()   
   function. For example, Maple gives anti-derivative for this as   
      
   {-1/2/a/b*ln(b*x-a)+1/2*ln(b*x+a)/a/b}   
      
   Therefore   
      
   MmaTranslator[Mma][LeafCount]({-1/2/a/b*ln(b*x-a)+1/2*ln(b*x+a)/a/b});   
         32   
      
   MmaTranslator[Mma][LeafCount](arctanh(b*x/a)/(a*b));   
        14   
      
   Hence the ratio is   
      
   32/14.;   
                              2.285714286   
      
   So this for, Maple got "B" grade, since its passed, but its leaf count is   
   more than 2 times the optimal leaf count.   
      
   regards,   
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
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