A grazing incidence fast atom diffraction (GIFAD or FAD) setup, installed on a molecular beam epitaxy chamber, has been used to characterize the beta(2)(2x4) reconstruction of a GaAs(001) surface at 530 degrees C under an As-4 overpressure. Using a 400-eV He-4 beam, high-resolution diffraction patterns with up to eighty well-resolved diffraction orders are observed simultaneously, providing a detailed fingerprint of the surface structure. Experimental diffraction data are in good agreement with results from quantum scattering calculations based on an ab initio projectile-surface interaction potential. Along with exact calculations, we show that a straightforward semiclassical analysis allows the features of the diffraction chart to be linked to the main characteristics of the surface reconstruction topography. Our results demonstrate that GIFAD is a technique suitable for measuring in situ the subtle details of complex surface reconstructions. We have performed measurements at very small incidence angles, where the kinetic energy of the projectile motion perpendicular to the surface can be reduced to less than 1 meV. This allowed the depth of the attractive van der Waals potential well to be estimated as -8.7 meV in very good agreement with results reported in literature.