  We present a framework for estimating exoplanet occurrence rates by
synthesizing constraints from radial velocity and transit surveys
simultaneously. We employ approximate Bayesian computation and various
mass-radius (M-R) relations to explore the population models describing these
surveys, both separately and in a joint fit. Using this approach, we fit a
planet distribution function of the form $d^{2} N/d\log{P}d\log{M} \propto
P^{\beta} M^{\alpha}$, with a break in the power law in mass at $M_{b}$, to
planets orbiting FGK stars with periods $P = [25, 200]$ days and masses $M =
[2, 50] M_{\oplus}$. We find that the M-R relation from Otegi et al. (2020),
which lets rocky and volatile-rich populations overlap in mass, allows us to
find a model that is consistent with both types of surveys. Our joint fit gives
$M_{b} = 21.6_{-3.2}^{+2.5} M_{\oplus}$ (errors reflect 68.3% credible
interval). This is nearly a factor of three higher than the break from
transit-only considerations and an M-R relation without such an overlap. The
corresponding planet-star mass ratio break $q_{b} \sim 7\times10^{-5}$ may be
consistent with microlensing studies ($q_b \sim 6\times10^{-5} -
2\times10^{-4}$). The joint fit also requires that a fraction of
$F_{\text{rocky}} = 0.63_{-0.04}^{+0.04}$ planets in the overlap region belong
to the rocky population. Our results strongly suggest that future M-R relations
should account for a mixture of distinct types of planets in order to describe
the observed planet population.
