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| [[latex2($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)]] (1) and more stuff over here. | |
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| \begin{equation} SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time} \end{equation} \begin{equation} New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right) \end{equation} | $$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$ | 
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| FractionEnhanced New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ ) SpeedupEnhanced | 
Back to ComputerTerms
$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$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:
latex2($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$) (1) and more stuff over here.
$$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$or
                       Execution Time affected by Improvement
New Execution Time =   --------------------------------------  + Execution Time unaffected
                            Amount of Improvement (x times) 
So we have
                                     1
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhancedBack to ComputerTerms
