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$$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$$

See SpeedUp

Notice that we are talking about the entire task here and that performance (speedup) is defined in terms of execution time! So we have to define the following:

$$$Speedup Overall = \frac{Old~Execution~Time}{New~Execution~Time}$$$

This gives a new Execution time of

$$$New~Exec~Time = Old~Exec~Time( 1 - Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced})$$$

So we have

$$$Speedup Overall=\left(\frac{1}{1-Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced}}\right)$$$

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