We show the accuracy for each reduction level and an increasing search space in Tbl. III. Level zero corresponds to single molecule fits, and we see that near 100% accuracy is achieved for all molecules fit. As the level increases the accuracy decreases but still remains above 98%. The SMARTS patterns for the b = 1 d = 3 model corresponding to a 95.4% accuracy is listed in SI Sec. 3.1. Looking into the failures, we found that some molecules were labeled in confusing ways. For example, symmetric hydrogen atoms were labeled differently; SMARTS patterns can never distinguish such cases. We found that if the molecules are reasonably labeled then the BESMARTS method can replicate the assignments with perfect accuracy. Finally, we note that we did not apply the resulting hierarchies to a validation set. Such a test would only serve to test how general the hierarchies are. Rather, we aimed to determine if the BESMARTS approach was able to find SMARTS patterns that were able to uniquely identify a single GAFF atom type. In this result, we were able to accurately identify all GAFF types except for some cases where SMARTS was insufficient to describe the difference between types. This is an interesting result because several of the GAFF types are explicitly redundant, and only matter when considering bonds, angles, and torsions. Given that this approach was able to uniquely identify all GAFF types, even redundant ones, it presumably will be able to capture most extended valence assignments as well.