> reminder that the biggest compiler optimizations often come from changing the algorithm, not optimizing the hot loop itself.

Isn't this true for most optimizations, not just in compilers? My usual goto process for optimizing is "Find stuff we're doing that we don't have to do, re-evaluate what data structures we use and then re-evaluate what algorithms we use" basically, with minor changes depending on the results. Served me well so far, and haven't (intentionally) written any compilers.