The focusing Nonlinear Schrodinger equation (NSL) is treated an one of the basic integrable models describing the rogue (anomalous) waves in nonlinear media including the ocean and nonlinear optics. The corresponding Cauchy data for NLS is the sum of the constant solution and a small perturbation. For the spatially periodic setting we show that the finite-gap formulas admits a good elementary approximation. In particular, in the case of one unstable mode we obtain simple approximate formulas for the first appearance of the anomalous wave and the recurrence law. These results were used in recent experiments in photorefractive crystals.