Relative integration errors in the energy (top row of panels) and eccentricity (bottom row) for one orbit using the regularized Hermite integrator for Newton’s equations of motion for initial eccentricities e₀ ∈ {0.1, 0.5, 0.9} (left to right panels, respectively), for various time step parameters η ∈ {0.03, 0.01, 0.003, 0.001} (in colour: blue, green, red and orange, respectively).