Ratio of the FoF (b = 0.2) HMF with the better mass resolution M10 to the one with the standard mass resolution Mil as a function of the number of standard resolution particles per halo N_part,M11, in wCDM (left) and f(R)CDM (right), at z = 0 and z = 1. This quantity has been computed using the matching in terms of initial conditions between the L656_M11 and the L328_M10 simulation sets. Each coloured line corresponds to one of the 80 cosmological models of the emulator training set. The black solid line gives the mean over all cosmological models, with the standard deviation among them as error bars. The grey band attached to the mean is an estimation of the typical expected error for the individual HMF ratio. The dashed line corresponds to the fit to the mean using the fitting function given in Eq. (7).