Comparison of CRPropa simulations and analytic distributions for a serial cascade involving nuclear species {⁴⁰Ca→³⁹K→³⁸Ar→³⁷Ar→³⁶Ar→³⁵Cl}. The four top panels show the probability distributions as a function of distance for cases with 2-5 nucleon losses. The bottom panel shows the relative differences between CRPropa and the analytic distributions. There is a row for each case, including the one-nucleon-loss distributions. Each case simulated 10⁵ nuclei with γ = 3.5 ⋅ 10⁹. The interaction length for ⁴⁰Ca is the reference scale 1/λ.