The analysis so far has focused on the original SMARTY algorithm, which samples over all elements simultaneously. This approach is comprehensive, but leads to a combinatorial sampling problem. Imagine we want to find the hydrogen atom types in AlkEthOH. The most complex of these is H3, which requires specifying one atom in the alpha position and three atoms in the beta position (Figure ). When adding either an alpha or beta substituent, the probability of choosing a specific base type (i.e. correct element) is approximately 0.15. This means it could potentially take SMARTY more than 0.15 -4 ≈ 1, 000 moves to find H3 when starting with a hydrogen parent type. Including the necessity of choosing the correct parent element decreases the probability of each move to 0.015, meaning it could take SMARTY on the order of 10,000,000 moves to generate the correct SMARTS pattern for H3. The elemental SMARTY method, SMARTY , speeds the search by sampling only one element (base type) at a time. Thus, fewer iterations are required to first discover a SMARTS with a total score of 100%, as shown for AlkEthOH in Figure .