The beam-spin asymmetries in the hard exclusive electroproduction of photons on the proton (e p-->epgamma) were measured over a wide kinematic range and with high statistical accuracy. These asymmetries result from the interference of the Bethe-Heitler process and of deeply virtual Compton scattering. Over the whole kinematic range (x(B) from 0.11 to 0.58, Q2 from 1 to 4.8 GeV2, -t from 0.09 to 1.8 GeV2), the azimuthal dependence of the asymmetries is compatible with expectations from leading-twist dominance, A approximately a sinphi/(1+c cosphi). This extensive set of data can thus be used to constrain significantly the generalized parton distributions of the nucleon in the valence quark sector.