We revisit the question of how to calculate correlations of the curvature perturbation, $zeta$, using the $delta N$ formalism when one cannot employ a truncated Taylor expansion of $N$. This problem arises when one uses lattice simulations to probe the effects of isocurvature modes on models of reheating. Working in real space, we use an expansion in the cross-correlation between fields at different positions, and present simple expressions for observables such as the power spectrum and the reduced bispectrum, $f_{rm NL}$. These take the same form as those of the usual $delta N$ expressions, but with the derivatives of $N$ replaced by non-perturbative $delta N$ coefficients. We test the validity of this expansion and argue that our expressions are particularly well suited for use with simulations.
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