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Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued implementation and specification language that explicitly includes different types of uncertainties. We then present a compilation algorithm that generates a conventional implementation that is guaranteed to meet the desired precision with respect to real numbers.arXiv:1309.2511v1 fatcat:riq4wqszj5emvmb7vlrqkbvlse