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| {{{#!latex2 \begin{equation} Speedup = \frac{Performance~for~entire~task~using~the~enhancement~when~possible}{Performance~for~entire~task~without~enhancement} \end(equation} }}} Hello {{{ Performance for entire task using the enhancement when possible Speedup = ----------------------------------------------------------------- Performance for entire taks without using the enhancement }}} |
[[latex2($$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$)]] |
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| {{{ Old Execution Time SpeedupOverall = -------------------- New Execution Time |
[[latex2($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)]] |
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| FractionEnhanced New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ ) SpeedupEnhanced or Execution Time affected by Improvement New Execution Time = -------------------------------------- + Execution Time unaffected Amount of Improvement (x times) |
This gives a new Execution time of [[latex2($$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$)]] |
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| 1 SpeedupOverall = -------------------------------------------- FractionEnhanced (1 - FractionEnhanced) + ------------------ ) SpeedupEnhanced }}} |
[[latex2($$SpeedupOverall=\frac{1}{1-FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}}$$)]] |
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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:
latex2($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)
This gives a new Execution time of latex2($$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$)
So we have latex2($$SpeedupOverall=\frac{1}{1-FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}}$$)
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