Top: Comparison between the HMF predicted by the model of Euclid Collaboration: Castro et al. (2023) (curves) and the HMF measured for the extended large simulations (points). Error bars associated with each simulation point correspond to the Poisson uncertainty. Bottom: Relative difference between the model and the simulations. Different panels indicate different redshifts; from left to right, z = 0.00, 1.18, and 1.98.