PS if you're a scientist and your accuracy estimate is on the same order as your rounding error, your are doing pretty well :-) At least in my field...
True enough, but in the case of interval arithmetic I like to be able to preserve the invariant that if I am working with intervals (even if only to collect accumulated rounding error in a Taylor model) that the answer lies within the interval, and doesn't escape due to some tight boundary condition or accumulated rounding error from when I was working too close to a pole.
In the case of Taylor models we try to keep the size of the intervals as small as possible by using the first k terms of a Taylor polynomial and only catching the slop in an interval.This is important because of course adding and multiplying intervals will cause the size of the intervals to baloon very quickly. Since the intervals in question are very close to the scale of floating point rounding error as possible, and we often have to conservatively slop the rounding error over from the Taylor coefficients into the interval, accurate handling of tight corner cases is critical.
-Edward
So I'm feeling a bit elated that I've sparked my first theoretical discussion in cafe, though I don't have much to contribute. :\ However in the interests of the original question, I guess I should clarify. What we do in our physics class seems to be what is being called "interval analysis" in this discussion. We have experimental values with absolute uncertainties, and we need to propagate those uncertainties in a deterministic way through formulas. I don't think my professor would take kindly to a random sampling approach. The intervals library seemed a bit like what I'm looking for, except that it appears to be broken for the later ghc 6 versions and ghc 7. -- Edward Amsden Student Computer Science Rochester Institute of Technology www.edwardamsden.com