Phase-Aware Optimization. For many iterative computa- tions, the outer loop controls the precision of the final solution. Here, the iterations of the outer loop naturally segment the overall application execution into multiple phases. We define a phase as a segment of execution that has distinct speedup or error characteristics. For example, a numerical solver execu- tion can go through an initialization phase, a maturity phase, and a convergence phase. Our experimental results show that two different phases of the computation may generate different amounts of error for the same level of approximation. This exposes a new opportunity for optimization algorithms – they can select not just how much to approximate, but also in which phase to approximate. We find empirically that for some applications (such as LULESH[ 3 ]), approximating one phase may induce almost 8X less error than applying the same approximation in another phase of the executio