We investigate the evolution of the Star Formation Rate Function (SFRF), star formation rate−stellar mass relation (SFR−M⋆) and Galaxy Stellar Mass Function (GSMF) of z ∼ 4-7 galaxies using high-resolution and large box size cosmological Smoothed Particle Hydrodynamics (SPH) simulations run with the new code P-GADGET3(XXL). We explore the effects of different feedback prescriptions (galactic winds and AGN feedback) and different initial stellar mass functions and metal cooling. We show that our fiducial model, with strong winds and efficient AGN feedback, is able to reproduce the observed SFRF at redshift z ∼ 4-7 and the observed GSMF obtained from UV selected samples at redshift 6 ≤ z ≤ 7, while at z ∼ 4 we are more consistent with recent results from IR selected samples. However, a tension between the simulated SFR−M⋆ realtion and GSMF with the ones observed exists. By combining the simulated SFR−M⋆ relation with the observed star formation rate functions, we argue that this disagreement may be the result of the uncertainty in the assumed observational Luv−M⋆ conversion and, especially, in the normalization of the observed SFR−M⋆ relation.