OPPROX operates in four conceptual steps. First, OPPROX identifies different computation phases. Second, OPPROX models the speedup and error generated due to different levels of approximation in the individual ABs and in different com- putation phases using representative inputs. Third, OPPROX compares the benefits of various approximation settings in dif- ferent phases and splits the overall error budget e b into phase- specific error budgets in proportion to the predicted benefits. Finally, OPPROX formulates phase-specific trade-off space exploration as a numerical optimization problem and finds the most profitable approximation settings for each phase using the phase-specific error budgets as the constraints. We show that for many applications, both the approxima- tion level and the phase in which approximation is performed, have significant contributions towards the final error. Hence, phase-specific optimal approximation settings can provide good speedup (which we express here using the number of instructions executed) even under constrained error budget. When compared to an oracle but phase-agnostic version from prior works[ 43 , 44 ], our approach on average provides 42% speedup compared to 37% from the oracle version for an error budget of 20% and for a small error budget of 5% provides on average 14% speedup compared to only 2% achieved by the phase-agnostic oracle version.