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We use the Voids-within-Voids-within-Voids (VVV) simulations, a suite ofsuccessive nested N-body simulations with extremely high resolution (denoted,from low to high resolution, by L0 to L7), to test the Press-Schechter (PS),Sheth-Tormen (ST), and extended Press-Schechter (EPS) formulae for the haloabundance over the entire mass range, from mini-haloes of $10^{-6}\\mathrm{M_\odot}$, to rich cluster haloes of $10^{15}\ \mathrm{M_\odot}$, atdifferent redshifts, from $z=30$ to the present. We find that at $z=0$ and$z=2$, ST gives the best prediction for the results of L0, which has the meancosmic density (i.e. overdensity $\delta=0$), at $10^{11-15}~\mathrm{M_\odot}$. The higher resolution levels (L1-L7) are biased regions atvarious underdensities ($\delta<-0.6$). The EPS formalism takes this intoaccount since it gives the mass function of a region conditioned, in this case,on having a given underdensity. The EPS gives good predictions for these higherlevels, with deviations $\lesssim 20\%$, at $10^{-6-12.5} ~\mathrm{M_\odot}$.At $z \sim 7-15$, the ST predictions for L0 and the EPS predictions for L1-L7show somewhat larger deviations from the simulation results. However, at evenhigher redshifts, $z \sim 30$, the EPS prediction fits the simulations wellagain. We further confirm our results by picking more subvolumes from the fullL0 simulation, finding that our conclusions depend only weakly on the size andoverdensity of the chosen region. Since at mean density the EPS reduces to thePS mass function, its good agreement with the higher-level simulations impliesthat the PS (or, even better, the ST) formula gives an accurate description ofthe total halo mass function in representative regions of the universe.

The abundance of dark matter haloes down to Earth mass