It is worth repeating that accuracies on this task are artificially low since in many cases a single word can be translated to many different words with the same meaning.
this definition is quite noisy: a word b i might have been aligned with a arbitrarily; or, b i might be a word that itself corresponds to a multiword translation in S. Thus, we also align the sentences in the T → S direction, and require that each b i in the phrase aligns either with a or with nothing.