Ratio of the L164_M9 HMF, for the cosmological models P18, F5, and F6, and the L164_M8 HMF, for the model P18, with respect to the L164_M10 HMF, in the case of SO haloes with ∆ = 200c at z = 1 and z = 0. For visual clarity, the x coordinates have been slightly displaced. The dashed lines correspond to the fit performed in Sect. 3.2, which is used to correct the training data of the emulator from the L328_M10 simulations. We do not detect any statistically significant deviations from this fit, due to the effect of f (R) gravity or the higher M8 resolution.