This procedure uses a second order Taylor extension of an equation and an interval evaluation of the remainder. The equation system is transformed into a linear part and an interval remainder and an interval linear system solver is used to determine the bounds for the solutions. Hence this filter is global (i.e. it takes into account all equations of a system) while most of the other filter are local (i.e. they deal only with one equation at a time). This filter is usually 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.