Parallel applications are often based on numerical algorithms which compute an approximation solution for a discretized scientific problem. Such an approximation solution has a specific accuracy, which denotes how well the approximation fits to the true solution. The accuracy can be controlled by parameters given to the solution process by the application programmer. Parameters include the tolerance value in time-stepping methods or the truncation of a series expansion of the unknown solution. However, the parameter selection does not only influence the numerical quality but also the time needed for computing the approximation solution. The associated energy consumption may also increase but may exhibit a different growth behavior. Each parameter setting leads to a different execution variant of the approximation algorithm with a different numerical accuracy property of the solution and different execution time and energy behavior of the computation process. This article considers the interaction between the parameter settings and the solution quality and examines the possibilities to select time- and energy-efficient execution variants with a desired accuracy. In particular, a selection process is proposed that determines a Pareto-optimal execution variant of the approximation algorithm.