Diff for "AverageNormalizedExecutionTime"

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Normalize: Given a reference execution time A, take the execution time you have (B) and divide it by the reference execution time. What you get is a normalized execution time of B with respect to A.

                    Excution time of B
Normalized(B) = ----------------------------
                 Reference Execution Time A 

Given several programs P1, P2, ..., Pn, the average (GeometricMean) normalized execution time is

 For (i=1; i++, <= n) {
   P *= Normalized(Pi) 
 }
 return P^(1/n)

or
       _____________
      / n
   n / __
    /  ||  Normalized(Pi)
  \/   i=1

Using the geometric mean gives a consistent ranking no matter which machine you normalize to, as in: Computer A is faster than computer B. The Arithmetic mean (average) does not give a consistent ranking when we normalize to different machines. However, the arithmetic mean does give you an execution time average while the geometric mean does not! Instead, it gives you a composite measure.

We note that the geometric mean violates our fundamental principle of performance measurement - it does not predict execution time.

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