@CohenCyril mentioned that integral should probably be locked. I tried something but did not observe any time save on the slow lines a was looking at (the set of which is obviously not empty), so I gave up.
EDIT: I think I am misremembering and it is funpos and funneg that I was supposed to lock, otherwise the unification of \int[mu]_(x in D) f1^\+ x with \int[mu]_(x in D) f1^\- x obviously goes under the lock.

I am not convinced that we want all the changes, I can add the time saved be each change if this helps the decision making.

Fun fact: ~16% of the total compilation time is spent on HB commands and ~27% is spent importing things.