Figure shows the bottom-up algorithm applied to the same set of (H 2 O) 20 clusters that were used to test the top-down method. Energy screening is applied only to the three-body terms, retaining all one-and two-body terms (as in the top-down example). In this case, fourbody terms are accepted or rejected based strictly on parentage (M = 0, 1, or 2), rather than using a fourbody threshold τ 4 .