1. A Boolean search formula generation apparatus comprising: a Boolean search formula generation unit that generates Boolean search formulas for searching a base set including one or more documents from a document set as a search target; and a search result acquisition unit that uses an arbitrary Boolean search formula to acquire results of searching the search target and that outputs the results to the Boolean search formula generation unit, wherein the Boolean search formula generation unit acquires search results, which are obtained when the search target is searched using products including one or more search terms as a Boolean search formula, from the search result acquisition unit to calculate a recall indicating a proportion, to the base set, of the documents included in the base set among the search results and a precision indicating a proportion, to the search results, of the documents included in the base set among the search results, evaluates the products by an evaluation formula established using the recall and the precision, and repeats connecting the products with maximum evaluation values based on the evaluation formula by a sum to generate the Boolean search formula expressed by a standard sum of products form.