You'd think so, but check out the 'smooth surprise' in Kahan's great writeup: https://people.eecs.berkeley.edu/~wkahan/Mindless.pdf https://people.eecs.berkeley

You'd think so, but check out the 'smooth surprise' in Kahan's great writeup: https://people.eecs.berkeley.edu/~wkahan/Mindless.pdf https://people.eecs.berkeley.edu/~wkahan/Mindless.pdf We can approximate quite a bit, but ultimately further analysis is required to show that there are no such surprises on any particular root-finding problem.