  The equation of state of dilute Bose gases, in which the energy only depends
on the $s$-wave scattering length, is rather unknown beyond the universal
limit. We have carried out a bunch of diffusion Monte Carlo calculations up to
gas parameters of $10^{-2}$ to explore how the departure from the universality
emerges. Using different model potentials, we calculate the energies of the gas
in an exact way, within some statistical noise, and report the results as a
function of the three relevant scattering parameters: the $s$-wave scattering
length $a_0$, the $s$-wave effective range $r_0$, and the $p$-wave scattering
length $a_1$. If the effective range is not large we observe universality in
terms of $a_0$ and $r_0$ up to gas parameters of $10^{-2}$. If $r_0$ grows the
regime of universality in these two parameters is reduced and effects of $a_1$
start to be observed. In the $(a_0,r_0)$ universal regime we propose an
analytical law that reproduces fairly well the exact energies.
