  We study the temperature regimes of the 1d interacting gas to determine when
the matter wave (c-field) theory is, in fact, correct and usable. The judgment
is made by investigating the level of discrepancy in many observables at once
in comparison to the exact Yang-Yang theory. We also determine what cutoff
maximizes the accuracy of such an approach. Results are given in terms of a
bound on accuracy, as well as an optimal cutoff prescription. For a wide range
of temperatures the optimal cutoff is independent of density or interaction
strength and so its temperature dependent form is suitable for many cloud
shapes and, possibly, basis choices. However, this best global choice is higher
in energy than most prior determinations. The high value is needed to obtain
the correct kinetic energy, but does not detrimentally affect other
observables.
