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We used evolutionary computation to approximate the nuclear binding energy B of stable nuclei with atomic mass number A = Z + N. Our symbolic regression approximation outperformed the Liquid Drop Model (LDM) for lighter nuclides, and is less complex. We also used evolutionary computation to obtain upper and lower bounds for the binding energy of 3535 experimentally found nuclei, the large majority of which are unstable. Our bounds can be well-approximated by an analytic continued fraction dependent only on A, which we found via a memetic algorithm. Our data-driven fitting with analytic continued fractions suggest the possibility of other nuclides between the obtained lower bound and known nuclides, up to A = 338 a value close to where the bounds meet.