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The design of highly non-linear circuits is a challenging and time-consuming task both for designers and design-automation tools. This paper presents a method for automated design of such circuits. By combining equations and heuristics with simulation-corrections, it allows to achieve the accuracy of optimization-based sizing with the speed of knowledge-based sizing one. The correction scheme is also used to reduce the number of independent variables. Sizing, speed and accuracy allow it to be used in the design and technology migration of digital libraries, full-custom cells as well as dynamically during timing analysis to compensate long critical paths. Applications are also appealing for highly non-linear analog functions. A prototype tool has been implemented in MATLAB.