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We consider synthesis of arithmetic DSP circuits with finite precision fixed-point operations. The aim is to choose the lowest cost implementation that matches a real-valued specification within the allowed imprecision. Starting from Taylor series or real-valued polynomials, we demonstrate first a method to obtain satisfying implementations that uses intermediate arithmetic transform polynomials as an analytical apparatus suitable to precision analysis for both the quantization (bit-width) and approximation sources of imprecision. We then derive the precision optimization algorithm that explores multiple precision parameters in a branch-and-bound search.