  We obtain the planar correlation function of four half-BPS operators of
arbitrary weights, up to three loops. Our method exploits only elementary
properties of the integrand of the planar correlator, such as its symmetries
and singularity structure. This allows us to write down a general ansatz for
the integrand. The coefficients in the ansatz are fixed by means of a powerful
light-cone OPE relation between correlators with different weights. Our result
is formulated in terms of a limited number of functions built from known one-,
two- and three-loop conformal integrals. These results are useful for checking
recent integrability predictions for the OPE structure constants.
