In an embodiment, hardware implementing a transcendental or other non-linear function is based on a series expansion of the function. For example, a Taylor series expansion may be used as the basis. One or more of the initial terms of the Taylor series may be used, and may be implemented in hardware. In some embodiments, modifications to the Taylor series expansion may be used to increase the accuracy of the result. In one embodiment, a variety of bit widths for the function operands may be acceptable for use in a given implementation. A methodology for building a library of series-approximated components for use in integrated circuit design is provided which synthesizes the acceptable implementations and tests the results for accuracy. A smallest (area-wise) implementation which produces a desired level of accuracy may be selected as the library element.