Many modern computations (such as video and audio encoders, Monte Carlo simulations, and machine learning algorithms) are designed to trade off accuracy in return for increased performance. To date, such computations typically use ad-hoc, domain-specific techniques developed specifically for the computation at hand. Loop perforation provides a general technique to trade accuracy for performance by transforming loops to execute a subset of their iterations. A criticality testing phase filters out critical loops (whose perforation produces unacceptable behavior) to identify tunable loops (whose perforation produces more efficient and still acceptably accurate computations). A perforation space exploration algorithm perforates combinations of tunable loops to find Pareto-optimal perforation policies. Our results indicate that, for a range of applications, this approach typically delivers performance increases of over a factor of two (and up to a factor of seven) while changing the result that the application produces by less than 10%.