[vouwfietsman]

There's a lot more than big O, like data layout, simd, parallelism, cache efficiency, caching, allocation, data architecture, IO efficiency etc etc. And these are just the ones I know about, I bet there's many more.

For improving performance of larger pieces of code often times it's not really important to talk about big O, but much more about how the data is transformed through the system, how lookups are done in memory, how operations are composed together. Then look at what would be possible in an ideal version of the code, and work towards that in steps. This approach can have orders of magnitude improvements, without changing big O.

If you're starting from scratch, this is much easier. Simply never make your code slow :-)