If you know one differential in a spectral sequence, then others can often be deduced using the Leibniz rule and other techniques. To organize this effectively on a large scale, we frame spectral sequence computation as a constraint satisfaction problem: unknown differentials are variables which satisfy constraints coming from the Leibniz rule. In the stable and unstable Adams spectral sequences, this determines a surprising percentage of the differentials. This talk discusses work by Joey Beauvais-Feisthauer and in collaboration with Francis Baer and Dan Isaksen.