And so far, for the hard problems, the solutions have required on the order of formula_6 computations. For any particular problem, people have found ways to reduce the number of computations needed. One might figure out that a way to do just 1% of the worst-case number of computation and that saves a "lot" of computing, but that is still formula_9 computations. And every extra rock still doubles the number of computations needed to solve the problem. There are insights that can produce methods to do even fewer computations producing variations of the model: e.g. formula_10. But the exponential function still dominates as formula_5 grows.