This procedure uses a third order Taylor extension of an equation and an interval evaluation of the remainder. This leads to a second order equation in each of the variables, whose coefficients is computed. The analytic solution of this second order equation is used to improve the variable range. This filter is very efficient for non algebraic equations and if the width of the range for the variable is not too large.
The syntax is:
An optional fourth argument may be used. It consists in a list of one or two number. If this argument is [0.1,0.01], then the filter will be used only if the maximal width for the ranges is less than 0.1 and the filter will be used again if the gain in a range if larger than 0.01. If only one number is given in the list, then it will indicate the maximal width for the ranges.