A limitation for underestimation via twin arithmetic (Q5935459)

Computing an enclosure for the range of a rational function over an interval is one of the main goals of interval analysis. One way to obtain such an enclosure is to use interval arithmetic evaluation of a formula for the function. Often one would like to check how close the overestimation is to correct range. \textit{V. Kreinovich, V. M. Nesterov} and \textit{N. A. Zheludeva} [ibid. 2, No. 2, 119-124 (1996; Zbl 0853.65050)] suggested a new kind of twin arithmetic which produces a twin of intervals at the same time: the usual enclosure, i.e. an interval which is an overestimation for the range, and an interval which is contained in the range, i.e. an interval which is an underestimation for the range. It is shown that in certain cases the computed inner interval is much smaller than the correct range. For example, if the function has the same value in the two endpoints of the interval then the inner interval is either empty or contains only one point.