Because the bottom-up algorithm propagates the screening procedure from low orders to high orders, it allows the energy-screened MBE(n) to be extended to arbitrarily high orders. Note that each n-body node in the PIE-DAG has n parents, each of which is a (n -1)body subsystem. Since higher-order subsystems have more parents than lower-order ones, fewer terms need to be considered as n increases, even prior to evalu- In both cases, cached data from GFN2-xTB were used for screening, so these timings simply reflection the lookup cost and the cost to construct the PIE-DAG. The top-down method requires data for every tetramer whereas the bottom-up approach does not. The steep cost increase for small values of τ 3 results from construction of a dense PIE-DAG. Benchmarks were performed on a laptop with a 2.6 GHz dual-core Intel Core i5 processor and 16 Gb of memory.