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Say a program runs and results in $T_{1} = 157s$ then is modified and runs in $T_{2} = 16s$.

What is the correct way to display (in %):

  • How much faster is $T_{2}$ than $T_{1}$?
  • How much of an increase is the completion time of $T_{2}$ than $T_{1}$?

I imagine them to be read as:

  • $T_{2}$ is __% faster than $T_{1}$
  • $T_{2}$ was an increase of __% in completion time

With the latter being something along the lines of "... $4000$% ..." or "... 32x ..." or so.

pstatix
  • 239

1 Answers1

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A way is use, with reference to time, the ratio

$$p_T=\frac{T_1-T_2}{T_1}=\frac{141}{157}\approx 0.898=89.8\%$$

or as an alternative with reference to speed

$$p_S=\frac{\frac1{T_2}}{\frac1{T_2}}=\frac{T_1}{T_2}\approx 9.81=981\%$$

user
  • 154,566
  • So that says $T_{2}$ is approximately $89.9%$ faster than $T_{1}$ since it is relative to $T_{1}$ right? How would I say "$T_{2}$ is a __% increase in completion time"? – pstatix Aug 03 '18 at 17:31
  • @pstatix $p_T$ is a mesure of the time saved by $T_2$ with respect to $T_1$ (we save 90% of the time while $p_S$ is a mesur of how mach $T_2$ is faster ($T_2$ is about 10 times faster than $T_1$). – user Aug 03 '18 at 17:38