To put this into perspective, and to contrast the efficiency of the bottom-up approach, Fig. presents average timing data to construct the PIE-DAG for (H 2 O) 20 , for the calculations reported in Figs. and. Cached GFN2-xTB screening data were used to eliminate variations in run times, such that the only cost associated with energy screening is that of a hash lookup for the appropriate energy. When τ 3 is small, both algorithms exhibit a relatively large fragmentation cost because the PIE-DAG is quite dense, however, top-down screening has a high fixed cost even when the screening is more aggressive (larger τ 3 ). Bottom-up screening is more efficient even when τ 3 is small because it does not attempt to screen fourth-order and higher fragments whose parentage is incomplete. The present implementation can perform a single ∆E low IJKL calculation (using GFN2-xTB) in 0.02 s, and for top-down screening this equates to 4 h just to generate and screen the 679,120 unique subsystems required to apply MBE(4) to (H 2 O) 64 . Bottom-up screening can fragment the same system in less than 5 min.