Given a two-sided market where each agent ranks those on the other side by preference, the stable marriage problem calls for finding a perfect matching such that no pair of agents prefer each other to their matches. Recent studies show that the number of stable solutions can be large in practice. Yet the classical solution to the problem, the Gale-Shapley (GS) algorithm, assigns an optimal match to each agent on one side, and a pessimal one to each on the other side; such a solution may fare well in terms of equity only in highly asymmetric markets. Finding a stable matching that minimizes the sex equality cost, an equity measure expressing the discrepancy of mean happiness among the two sides, is strongly NP-hard. Extant heuristics either (a) oblige some agents to involuntarily abandon their matches, or (b) bias the outcome in favor of some agents, or (c) need high-polynomial or unbounded time.