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Arithmetic circuits in general do not match specifications exactly, leading to different implementations within allowed imprecision. We present a technique to search for the least expensive fixed-point implementations for a given error bound. The method is practical in real applications and overcomes traditional precision analysis pessimism, as it allows simultaneous selection of multiple word lengths and even some function approximation, primarily based on Taylor series. Starting from real-valued representation, such as Taylor series, we rely on arithmetic transform to explore maximum imprecision by a branch-and-bound search algorithm to investigate imprecision. We also adopt a new tight-bound interval scheme, and derive a precision optimization algorithm that explores multiple precision parameters to get an implementation with smallest area cost.