Counterexample: adaptive quadrature. It's pretty simple to reason about, but it would be a bit of a mess to try to do iteratively. Adaptive quadrature is num

Counterexample: adaptive quadrature. It's pretty simple to reason about, but it would be a bit of a mess to try to do iteratively. Adaptive quadrature is numeric integration, with an accuracy that is better than an error bound. It uses a three-point and a five-point approximation of the integral value on a region. From the difference between the two, it makes an estimate of the error. If the error is above the error bound, it splits the interval in half, and recursively calls itself twice with the two halves of the interval (and both times with half the error bound). I mean, you could iteratively do that with a queue of intervals and error bounds, and a running total of the ones that met their error bound, but that seems messier than the recursive version.