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This paper presents a method that offers a uniform treatment for bit-width optimisation of both fixed-point and floating-point designs. Our work utilises automatic differentiation to compute the sensitivities of outputs to the bit-width of the various operands in the design. This sensitivity analysis enables us to explore and compare fixed-point and floating-point implementation for a particular design. As a result, we can automate the selection of the optimal number representation for each variable in a design to optimize area and performance. We implement our method in the BitSize tool targeting reconfigurable architectures, which takes user-defined constraints to direct the optimisation procedure. We illustrate our approach using applications such as ray-tracing and function approximation.