Programmers are creative, compilers are well-tuned machines. Sometimes it's tough to beat a compiler's code, but I'm not sure that 'impossible' is meaningful.
Monkeys with typewriters could function as a highly parallel superoptimiser, after all.
Architecture, data structures, batching operations, memory locality, and a bunch of other metrics are all concepts the compiler can't really help you with whatsoever and they have a much larger impact on performance than the 10% the compiler is actually able to optimize.
The problem is that either programmers don't care, or they can't make the distinction between premature optimizations and architecture planning.
From a quick google: compiler optimisation can accelerate CPU-bound code to over 5x the unoptimised performance. https://www.phoronix.com/scan.php?page=article&item=clang-gc...
I forgot exactly where I got that number, but it's been a pretty good metric so far.
In a nutshell; the compiler is great a micro-optimizations and absolutely terrible at macro-optimizations. The former will get you a few percent of perf boosts while the later usually results in orders of magnitudes of performance gains.
Its near impossible to apply macro-optimizations at the end of a project without massive refactors.
Compilers are clever, but humans can also be really clever: They know how to think - You can change the algorithm entirely.
For practical reasons however (Premature optimisation also), trust your compiler.