> a powerful language construct that enables evaluation of a function or algorithm for arbitrarily small margin of error, using automatically revised accuracy i

> a powerful language construct that enables evaluation of a function or algorithm for arbitrarily small margin of error, using automatically revised accuracy in the intermediate steps. AIUI, this is what "constructive (or 'exact') real numbers" give you, and it's quite computationally-intensive. Error arithmetic/interval arithmetic/etc. are only approximations to it. In many cases people don't even bother with the real deal because they're computing way more than one single result, so roundoff errors can be thought of as just one additional source of noise that is going to be averaged out over many 'steps'.