We have developed an efficient and accurate set of mostly analytic formulae, that describe the evolution of stars in a wide range of mass and metallicity from the zero-age main sequence to the tip of the AGB. These formulae are based on interpolation between full detailed stellar models. A particular advantage of this kind of algorithm, compared for instance to interpolation in tables, is the ease with which we can change from one mass-loss prescription to another, particularly during the FGB and AGB where the evolution of the core is effectively decoupled from that of the envelope. We model populations of AGB stars for various mass loss prescriptions and metallicities, and describe their distribution in the H-R diagram and the properties of the remnants that they leave behind. By comparing these models to observations we may constrain the evolution of AGB stars and the associated mass-loss rates.