There are even more improvements (in some regard) to this, e.g. Affine Arithmetic[0, 1]. Here, error terms from different operations are accumulated symbolically so that in the case where they would cancel out (as could be useful for numerical algorithms), tighter bounds can be obtained.
There are several research groups working on improving such analyses.
And the problem with it is that it can lead to [-inf;+inf] intervals on sane computation such as Newton's method (refinements have been introduced but nothing that fully solves the problem).
