An interval will be considered as a solution for a function of the system in the following cases:

- for equations the maximal diameter of the intervals is less than
a given threshold
`epsilon`and the corresponding interval evaluation of the function contains 0**or**the corresponding interval evaluation of the function has a diameter less than a given threshold`epsilonf`and the interval contains 0 - for inequalities : the upper bound of
the interval evaluation of the
function is negative
**or**the maximal diameter of the intervals is less than a given threshold`epsilon`and the corresponding interval evaluation of the function has at least a negative lower bound**or**the corresponding interval evaluation of the function has a diameter less than a given threshold`epsilonf`and the interval contains 0 - for inequalities : the lower bound of
the interval evaluation of the
function is positive
**or**the maximal diameter of the intervals is less than a given threshold`epsilon`and the corresponding interval evaluation of the function has at least a positive upper bound**or**the corresponding interval evaluation of the function has a diameter less than a given threshold`epsilonf`and the interval contains 0

Assume that two solutions have been found with the algorithm. We will first consider the case where we have to solve a system of equations in unknowns, possible with additional inequality constraints. First we will check with the Miranda theorem (see section 3.1.5) if include one (or more) solution(s). If both solutions are Miranda, then they will kept as solutions. If one of them is Miranda and other one is not Miranda we will consider the distance between the mid-point of : if this distance is lower than a given threshold we will keep as solution only the Miranda's one. If none of is Miranda we keep these solutions, provided that their distance is greater than the threshold. Note that in that case these solutions may disappear if a Miranda solution is found later on such that the distance between these solutions and the Miranda's one is lower than the threshold.

In the other case the solution will be ranked according the chosen order and if a solution is at a distance from a solution with a better ranking lower than the threshold, then this solution will be discarded.