  The detection of gravitational waves from inspiraling compact binaries using
matched filtering depends crucially on the availability of accurate template
waveforms. We determine whether the accuracy of the templates' phasing can be
improved by solving the post-Newtonian energy balance equation numerically,
rather than (as is normally done) analytically within the post-Newtonian
perturbative expansion. By specializing to the limit of a small mass ratio, we
find evidence that there is no gain in accuracy.
