Approximate computing, where computation quality is traded off for better performance and/or energy savings, has gained significant tractions from both academia and industry. With approximate computing, we expect to obtain acceptable results, but how do we make sure the quality of the final results are acceptable? This challenging problem remains largely unexplored. In this paper, we propose an effective and efficient quality management framework to achieve controlled quality-efficiency tradeoffs. To be specific, at the offline stage, our solution automatically selects an appropriate approximator configuration considering rollback recovery for large occasional errors with minimum cost under the target quality requirement. Then during the online execution, our framework judiciously determines when and how to rollback, which is achieved with cost-effective yet accurate quality predictors that synergistically combine the outputs of several basic light-weight predictors. Experimental results demonstrate that our proposed solution can achieve 11% to 23% energy savings compared to existing solutions under the target quality requirement.