Comparison of the emulator HMF predictions at z = 0 in wCDM (left) and f(R)CDM (right) to the HMF of L328_M10_wl2 (left) and L328_M10_F5 (right). The HMFs are normalized by the L328_M10_P18 simulation data. Top panels: ratio of the wCDM (left) HMF or f(R)CDM (right) HMF to the ΛCDM one measured from the simulation (solid circles) and from emulator predictions (dashed lines). The error bars correspond to the HMF simulation measurement errors (not always visible for small errors), while the shaded area around the lines correspond to the uncertainties of HMF emulator predictions. Bottom panels: relative difference between the HMF simulation measurements and the emulator predictions. The shaded area correspond to the 1σ confidence interval combining both the simulation noise and the emulator accuracy. There is a good agreement with differences of the order of a few percent level, and within the expected error bars.