Errors in ray tracing two neutron stars with R_e = 12 km, M = 1.6 M_⊙, ν = 400 Hz or R_e = 15 km, M = 1.4 M_⊙, ν = 600 Hz, and with observer inclinations i = 15°, 45° and 75°, solving the full geodesic equation vs. the split Hamilton-Jacobi equation. The leftmost panels show the maximum variation in the Hamiltonian H of the geodesic, while the two center panels show the maximum variation in the Jacobi constant, computed either with the left side (C₁) or the right side (C₂) of Eq. (20). Rightmost panels: relative error in the redshift computed by solving the split Hamilton-Jacobi equation compared with the redshift computed by solving the full geodesic equation.