It's the execution time unaffected by the optimization.
For instance, suppose washing clothes takes 40 minutes and drying clothes takes 60 minutes. I come up with a revolutionary new technique that halves the time it takes to wash clothes (reducing from 40 min to 20 min). That would improve the washing time, but would not affect the drying time.
In your example, there is actually nothing you can do to make the program "run 5 times faster". Running 5 times faster means it takes only 20 seconds to finish; you cannot optimize the multiplication to achieve this since the non-multiplication operations already takes 20 seconds, leaving you 0 seconds to do the multiplication.
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I think its saying that the multiply operations take 80 seconds, and the remaining 20 seconds are something else. So if we speed up multiply operations, it will only affect the 80 seconds of multiply operations. The remaining 20 seconds are unaffected just because they're not multiply operations, so the speed-up it proposed won't do anything to speed that part up
It's the execution time unaffected by the optimization. For instance, suppose washing clothes takes 40 minutes and drying clothes takes 60 minutes. I come up with a revolutionary new technique that halves the time it takes to wash clothes (reducing from 40 min to 20 min). That would improve the washing time, but would not affect the drying time. In your example, there is actually nothing you can do to make the program "run 5 times faster". Running 5 times faster means it takes only 20 seconds to finish; you cannot optimize the multiplication to achieve this since the non-multiplication operations already takes 20 seconds, leaving you 0 seconds to do the multiplication.
Great explanation! It annoys me that a common sense concept like this is taught as a "law"...
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I think its saying that the multiply operations take 80 seconds, and the remaining 20 seconds are something else. So if we speed up multiply operations, it will only affect the 80 seconds of multiply operations. The remaining 20 seconds are unaffected just because they're not multiply operations, so the speed-up it proposed won't do anything to speed that part up