In this work we present the first results from a new ray-tracing tool to calculate
cosmological distances in the context of fully nonlinear general relativity. We use this tool to
study the ability of the general cosmographic representation of luminosity distance, as truncated
at third order in redshift, to accurately capture anisotropies in the “true” luminosity
distance. We use numerical relativity simulations of cosmological large-scale structure formation
which are free from common simplifying assumptions in cosmology. We find the general, third-order
cosmography is accurate to within 1% for redshifts to ^{-1} Mpc, which is in agreement with an earlier prediction. We find the
inclusion of small-scale structure generally spoils the ability of the third-order cosmography to
accurately reproduce the full luminosity distance for wide redshift intervals, as might be
expected. For a simulation sampling small-scale structures, we find a ∼ ±5% variance in
the monopole of the ray-traced luminosity distance at