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In this paper we present a tool, LengthFinder, for optimizing word-lengths of hardware designs with fixed-point arithmetic based on analytical error models that guarantee accuracy. LengthFinder adopts a multi-stage approach, with four novel features. First, the code analysis stage selects loops to instrument, such that information about the number of iterations can be extracted to generate more accurate results. Second, aggressive heuristics are used to produce non-uniform word-lengths rapidly while meeting requirements from the guaranteed error functions. Third, a method capable of reducing the search space has been developed for data-partitioning with a variable word-length reduction. Fourth, a genetic algorithm with selective-crossover and high mutation probability is applied to obtain near-optimal results. The benefits of LengthFinder are illustrated with various case studies. We show that LengthFinder can run over 200 times faster than previous techniques (Lee et al., 2006), while producing more accurate results, relative to values obtained from integer linear programming.