AmdahlsLaw

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\begin{equation} \label{eq:speedup}
   Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}
\end{equation}

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:

\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}

                                                                    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) 

So we have
                                     1
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced

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