  We report a measurement of $e^+e^-$ pairs from semileptonic heavy-flavor
decays in $p$+$p$ collisions at $\sqrt{s_{NN}}=200$~GeV. The $e^+e^-$ pair
yield from $b\bar{b}$ and $c\bar{c}$ is separated by exploiting a double
differential fit done simultaneously in dielectron invariant mass and $p_T$. We
used three different event generators, {\sc pythia}, {\sc mc@nlo}, and {\sc
powheg}, to simulate the $e^+e^-$ spectra from $c\bar{c}$ and $b\bar{b}$
production. The data can be well described by all three generators within the
detector acceptance. However, when using the generators to extrapolate to
$4\pi$, significant differences are observed for the total cross section. These
difference are less pronounced for $b\bar{b}$ than for $c\bar{c}$. The same
model dependence was observed in already published $d$+$A$ data. The $p$+$p$
data are also directly compared with $d$+$A$ data in mass and $p_T$, and within
the statistical accuracy no nuclear modification is seen.
