> where that 1% is worth any hassle
Let's say you have a process that takes 100hrs to run and costs $1k/hr. You save an hour and $1k every time you run the process. You're going to save quite a bit. You don't just save the time to run the process, you save literal time and everything that that costs (customers, engineering time, support time, etc).
Let's say you have a process that takes 100ns and similarly costs $1k/hr. You now run in 99ns. Running the process 36 million times is going to be insignificant. In this setting even a 50% optimization probably isn't worthwhile (unless you're a high frequency trader or something)
This is where the saying "premature optimization is the root of all evil" comes from! The "premature" part is often disregarded and the rest of the context goes with it. Here's more context to Knuth's quote[0].
There is no doubt that the holy grail of efficiency leads to abuse. Programmers waste enormous amounts of time thinking about, or worrying about, the speed of noncritical parts of their programs, and these attempts at efficiency actually have a strong negative impact when debugging and maintenance are considered. We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil.
Yet we should not pass up our opportunities in that critical 3%. A good programmer will not be lulled into complacency by such reasoning, he will be wise to look carefully at the critical code; but only after that code has been identified.
So yes, there are plenty of times where that optimization will be worthwhile. The percentages don't mean anything without the context. Your job as a programmer is to determine that context. And not just in the scope of your program, but in the scope of the environment you expect a user to be running on. (i.e. their computer probably isn't entirely dedicated to your program)
[0] https://dl.acm.org/doi/10.1145/356635.356640 (alt) https://sci-hub.se/10.1145/356635.356640