The beam-spin asymmetries in the hard exclusive electroproduction of photons on the proton ($\stackrel{\ensuremath{\rightarrow}}{e}p\ensuremath{\rightarrow}ep\ensuremath{\gamma}$) 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, ${Q}^{2}$ from 1 to $4.8\text{ }\text{ }{\mathrm{GeV}}^{2}$, $\ensuremath{-}t$ from 0.09 to $1.8\text{ }\text{ }{\mathrm{GeV}}^{2}$), the azimuthal dependence of the asymmetries is compatible with expectations from leading-twist dominance, $A\ensuremath{\simeq}a\mathrm{sin}\ensuremath{\phi}/(1+c\mathrm{cos}\ensuremath{\phi})$. This extensive set of data can thus be used to constrain significantly the generalized parton distributions of the nucleon in the valence quark sector.