People have devised methods for evaluation of polynomials with interval arithmetic, too (google it). Not sure how his method compares. It is well known that you can often work around the dependency problem for very specific expressions.
However, is not practical to tell people that they need to solve a new numerical-analysis research problem every time they have a new program in which a variable is used more than once (used more than once => dependency problem). And if you don't solve the dependency problem, your error bounds are useless for general-purpose tasks. And without accurate error bounds, adaptive precision is a non-starter.
