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← Revision 32 as of 2020-01-23 23:15:20 ⇥
Size: 676
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| Deletions are marked like this. | Additions are marked like this. |
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| {{{ Performance for entire task using the enhancement when possible Speedup = ----------------------------------------------------------------- Performance for entire taks without using the enhancement }}} |
$$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$$ |
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| {{{ Old Execution Time SpeedupOverall = -------------------- New Execution Time |
$$$Speedup Overall = \frac{Old~Execution~Time}{New~Execution~Time}$$$ |
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| FractionEnhanced New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ ) SpeedupEnhanced |
This gives a new Execution time of |
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| --> 1 SpeedupOverall = -------------------------------------------- FractionEnhanced (1 - FractionEnhanced) + ------------------ ) SpeedupEnhanced |
$$$New~Exec~Time = Old~Exec~Time( 1 - Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced})$$$ |
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| }}} | So we have $$$Speedup Overall=\left(\frac{1}{1-Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced}}\right)$$$ |
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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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