The paper presents a rapid binary-evolution algorithm that models complex binary systems, including mass transfer, accretion, common-envelope evolution, collisions, supernova kicks, and angular momentum loss mechanisms. The algorithm calculates tidal interactions for convective, radiative, and degenerate damping mechanisms, focusing on circularization and synchronization of orbits. The authors use this algorithm to study various binary systems and investigate the impact of tidal friction on binary evolution. They generate large binary populations and evaluate the formation rates of specific species and events, comparing results with and without tidal friction to quantify the systematic effect of tides. The study highlights that tidal synchronism is important but that orbits generally circularize before Roche lobe overflow, making eccentricity distribution less critical in population synthesis of interacting binaries. The initial separations should be distributed according to the observed distribution of semilatus recta rather than periods or semimajor axes. The paper also discusses wind accretion, orbital changes due to mass variations, tidal evolution, gravitational radiation, magnetic braking, and Roche lobe overflow, providing detailed equations and models for each process.The paper presents a rapid binary-evolution algorithm that models complex binary systems, including mass transfer, accretion, common-envelope evolution, collisions, supernova kicks, and angular momentum loss mechanisms. The algorithm calculates tidal interactions for convective, radiative, and degenerate damping mechanisms, focusing on circularization and synchronization of orbits. The authors use this algorithm to study various binary systems and investigate the impact of tidal friction on binary evolution. They generate large binary populations and evaluate the formation rates of specific species and events, comparing results with and without tidal friction to quantify the systematic effect of tides. The study highlights that tidal synchronism is important but that orbits generally circularize before Roche lobe overflow, making eccentricity distribution less critical in population synthesis of interacting binaries. The initial separations should be distributed according to the observed distribution of semilatus recta rather than periods or semimajor axes. The paper also discusses wind accretion, orbital changes due to mass variations, tidal evolution, gravitational radiation, magnetic braking, and Roche lobe overflow, providing detailed equations and models for each process.