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The geometric mean of P1,..,Pn is
<<latex($$Geometric~Mean = \sqrt[n]{\prod_{i=1}^{n} Normalized(P_i)}$$)>>
where <<latex($$Normalized(P_i) = \frac{P_i}{Pn}$$)>> where n is the referenced execution time. Obviously the geometic mean of the referenced machine is 1.
One of the nice features of Geometric means is that the following property holds:
<<latex($$GeometricMean\left(\frac{X_i}{Y_i}\right) = \frac{GeometricMean(X_i)}{GeometricMean(Y_i)}$$)>>
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