  This paper presents a comparison of the predictions for the 2 and 3-point
correlation functions of density fluctuations, xi_2 and xi_3, in gravitational
perturbation theory (PT) against large Cold Dark Matter (CDM) simulations. This
comparison is made possible for the first time on large weakly non-linear
scales (>10 Mpc/h) thanks to the development of a new algorithm to estimate
correlation functions for millions of points in only a few minutes. Previous
studies in the literature comparing the PT predictions of the 3-point
statistics to simulations have focused mostly on Fourier space, angular space
or smoothed fields. Results in configuration space, such as the ones presented
here, were limited to small scales were leading order PT gives a poor
approximation. Here we also propose and apply a method for separating the first
and subsequent orders contributions to PT by combining different output times
from the evolved simulations. We find that in all cases there is a regime were
simulations do reproduce the leading order (tree-level) predictions of PT for
the reduced 3-point function Q_3 ~ xi_3/ xi_2^2. For steeply decreasing
correlations (such as the standard CDM model) deviations from the tree-level
results are important even at relatively large scales, ~ 20 Mpc/h. On larger
scales xi_2 goes to zero and the results are dominated by sampling errors. In
more realistic models (like the Lambda CDM cosmology) deviations from the
leading order PT become important at smaller scales ~ 10 Mpc/h, although this
depends on the particular 3-point configuration. (abridge)
