Evolution of the relative error in the conserved angular momentum (top panels) and the Carter constant (bottom panels) for orbit B (left panels) and D (right panels) simulated with Δt = 0.01 until t = 500. The Hamiltonian scheme (green line) conserves both quantities, together with the energy, to machine precision. The RK4 (red line), IMR (blue line), and modified Hamiltonian (magenta lines) schemes instead introduce errors that are larger by several orders of magnitude.