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Mixed-precision computing has the potential to significantly reduce the cost of exascale computations, but determining when and how to implement it in programs can be challenging. In this article, we consider Nekbone, a mini-application for the Computational Fluid Dynamics (CFD) solver Nek5000, as a case study, and propose a methodology for enabling mixed-precision with the help of computer arithmetic tools and roofline model. We evaluate the derived mixed-precision program by combining metrics in three dimensions: accuracy, time-to-solution, and energy-to-solution. Notably, the introduction of mixed-precision in Nekbone, reducing time-to-solution by 40.7% and energy-to-solution by 47% on 128 MPI ranks without sacrificing the accuracy.