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← Revision 32 as of 2020-01-23 23:15:20 ⇥
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| Deletions are marked like this. | Additions are marked like this. |
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| {{{#!latex2 $$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$ }}} |
$$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$$ |
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| [[latex($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)]] (1) | $$$Speedup Overall = \frac{Old~Execution~Time}{New~Execution~Time}$$$ |
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| {{{#!latex2 $$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$ }}} |
This gives a new Execution time of |
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| {{{ or Execution Time affected by Improvement New Execution Time = -------------------------------------- + Execution Time unaffected Amount of Improvement (x times) |
$$$New~Exec~Time = Old~Exec~Time( 1 - Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced})$$$ |
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| 1 SpeedupOverall = -------------------------------------------- FractionEnhanced (1 - FractionEnhanced) + ------------------ ) SpeedupEnhanced |
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| }}} | $$$Speedup Overall=\left(\frac{1}{1-Fraction Enhanced + \frac{Fraction Enhanced}{Speedup Enhanced}}\right)$$$ |
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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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