  Interval arithmetic is a simple way to compute a mathematical expression to
an arbitrary accuracy, widely used for verifying floating-point computations.
Yet this simplicity belies challenges. Some inputs violate preconditions or
cause domain errors. Others cause the algorithm to enter an infinite loop and
fail to compute a ground truth. Plus, finding valid inputs is itself a
challenge when invalid and unsamplable points make up the vast majority of the
input space. These issues can make interval arithmetic brittle and
temperamental.
  This paper introduces three extensions to interval arithmetic to address
these challenges. Error intervals express rich notions of input validity and
indicate whether all or some points in an interval violate implicit or explicit
preconditions. Movability flags detect futile recomputations and prevent
timeouts by indicating whether a higher-precision recomputation will yield a
more accurate result. Andinput search restricts sampling to valid, samplable
points, so they are easier to find. We compare these extensions to the
state-of-the-art technical computing software Mathematica, and demonstrate that
our extensions are able to resolve 60.3% more challenging inputs, return 10.2x
fewer completely indeterminate results, and avoid 64 cases of fatal error.
