1. A Boolean search formula generation apparatus comprising: a processor; a memory coupled with said processor; a Boolean search formula generation unit that generates one or more Boolean search formulas for searching a base set including one or more documents from a document set as a search target and stores the Boolean search formulas in the memory, where the base set is a first search result generated from a first search formula and each of the Boolean search formulas consists of search products including one or more search terms; and a search result acquisition unit that uses each of the Boolean search formulas to acquire second search results of searching the search target and that outputs the second search results of searching the search target to the Boolean search formula generation unit, wherein the processor controls the Boolean search formula generation unit to: acquire the second search results, which are obtained when the search target is searched using each of the Boolean search formulas, from the search result acquisition unit to calculate, for each of the Boolean search formulas, a recall indicating a proportion, to the base set, of the documents included in the base set among the second search results and a precision indicating a proportion, to the second search results, of the documents included in the base set among the second search results, evaluate each of the Boolean search formulas by an evaluation formula established using the respective recall and the respective precision, and combine the Boolean search formulas with maximum evaluation values based on the evaluation formula to generate a combined Boolean search formula expressed by a standard sum of products of the Boolean search formulas with maximum evaluation values, where the combined Boolean search formula approximates the base set generated by the first search formula, wherein: the search result acquisition unit acquires a number of hits of each search term in the search products from the number of hits of each search term recorded in a search index of the search target when the Boolean search formula generation unit calculates the precision of the search products, and the Boolean search formula generation unit uses the number of hits to approximate the precision.