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

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.