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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:
$$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$
$$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$
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) + ------------------ ) SpeedupEnhanced
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