We numerically study the three-dimensional generalization of the kinetically constrained east model, the north-or-east-or-front (NEF) model. We characterize the equilibrium behavior of the NEF model in detail, measuring the temperature dependence of several quantities: alpha-relaxation time, distributions of relaxation times, dynamic susceptibility, dynamic correlation length, and four-point susceptibility. We show that the NEF model describes quantitatively experimental observations over an exceptionally wide range of time scales. We illustrate this by fitting experimental data obtained both in the mildly supercooled regime by optical Kerr effect and close to the glass transition by dielectric spectroscopy.