Slow is smooth, smooth is fast
Slow is smooth, smooth is fast is a neat phrase, but it is usually explained incompletely. People say: go slow, avoid mistakes, save time overall. That is true, but it misses why we rush in the first place.
The rush is mostly self-imposed. You feel embarrassed spending longer than expected, as if the time reflects on you rather than on the problem. You imagine a faster version of yourself who would have finished by now. Time estimates make this worse, reinforcing the idea that how long you spend is a measure of your ability rather than a fact about the problem’s difficulty.
So when you feel yourself rushing, ask whether it is necessary or self-imposed. Usually it is self-imposed. Enjoy the problem.