[regularfry]

> you say "10 5% improvements of state S0" in that sentence and then later on you use 10 5% improvements of state S0, S1... S9.

No, I don't.

Here's a very simplistic example. Say I've got a complicated computation with 10 nested loops, and there's a potential for a 5% speedup tweak at every nesting level, each of which takes about the same amount of effort to find; or, for the same overall effort I can speed up the whole thing by 50% by replacing the whole algorithm with a faster one.

The former case gives you a better outcome than the latter, and it doesn't matter what order you do the tweaks in, or whether you do them all at once. The point is that they can compound without caring about the previous or latter state of anything other than their own level.

[emiljbs]

Yes but the point is that the (at least I assumed so) 5% increase in speed was based on the initial performance of the system and that it didn't scale. Isn't that basically what you're talking about?

[regularfry]

If you take two speed-ups which individually would be 5% over the initial performance and apply them both, you get 10.25%, not 10%. The point is that it can scale.

[sitkack]

A number of discrete improvements is also more resilient. If a single perf improvement needs to be removed, only a 5% gain is removed. If the big 50% gain is monolithic it is much more susceptible to disruption.

[cowsandmilk]

you're statement needs a lot of qualifications. It is in only very specialized cases where this is true.

Let's say my program takes time 1.0 and is made up of part A taking 0.5 and part B taking 0.5

Defining 5% speedup is weird in the first place, but let's say 5% speedup is taking 0.95 for the program and 10% speedup is taking 0.9 for the program.

5% speedup by improving part A => 0.45 + 0.5 => 0.95 runtime 5% speedup by improving part B => 0.5 + 0.45 => 0.95 runtime

making both improvements: 0.45 + 0.45 => 0.9

So, two speed-ups which individually would be 5% over the initial performance gives us a 10% speed up.

percentage speed ups do not necessarily compound. And in practice, usually they do not.