...Except, of course, that even the exact solution won't always produce the correct answer, due to the wonders of computers not being perfect. Maybe 99.9% accu

...Except, of course, that even the exact solution won't always produce the correct answer, due to the wonders of computers not being perfect. Maybe 99.9% accurate isn't good enough, but there is always a level of inaccuracy from the algorithm where your random silent computer hardware errors dominate. And that may be still faster than the exact algorithm.