Let's say your program takes 100 seconds, of which 99% is spent in f(). Then if you optimize f() such that only 98% of the total time spent in f, then: ori

Let's say your program takes 100 seconds, of which 99% is spent in f(). Then if you optimize f() such that only 98% of the total time spent in f, then: orig_time = 100 orig_not_f = 0.01 * orig_time = 1 new_f = 0.98 * new_total new_total = new_f + orig_not_f new_total = 0.98 * new_total + orig_not_f new_total - 0.98 * new_total = orig_not_f 0.02 * new_total = 1 new_total = 1 / 0.02 = 50