Is it possible to have a feasible enclosure-computing method which is independent of the equivalent form?

The problem of computing the range y of a gven function f(x₁; : : : ; x_n) over given intervals xi - often called the main problem of interval com-putations - is, in general, NP-hard. This means that unless P = NP, it is not possible to have a feasible (= polynomial time) algorithm that always computes the desired range. Instead, interval computations al-gorithms compute an enclosure Y ⊇ y for the desired range. For all known feasible enclosure-computing methods - starting with straightfor-ward interval computations - there exist two expressions f(x₁; : : : ; x _n) and g(x₁; : : : ; x_N) for computing the same function that lead to different enclosures. We prove that, unless P = N, this is inevitable: it is not pos-sible to have a feasible enclosure-computing method which is independent of the equivalent form.