Maximum relative variation in the Hamiltonian as a function of the integration time step over the radial period (top row) and as a function of the CPU integration time (bottom row). Each column corresponds to a different orbit (orange, red, and green points in Figs. 5 and 6), integrated over two radial periods with 𝒮𝒜ℬ𝒜₁. The blue curve and the black curve show the results obtained when using kinetic splitting and Kepler splitting. The orange, green, and pink curves correspond to the isochrone splitting with parametrisation points q = r_p, q = r_a, and q = r_⋆, respectively.