Error in the conservation of phase-space volume for the four non-symplectic integrators in galpy. The Jacobian of the volume transformation is computed by integrating (dx, dv) for an orbit with energy −1.25 and angular momentum 0.6 in the mid-plane of the MWPotential2014. All integrators except for odeint use a constant time step determined at the initial condition to provide a relative and absolute accuracy equal to or less than 10⁻⁸. The scipy integrator odeint leads to large errors in the volume integration, even for moderate numbers of orbital periods (note the different range on the y axis for odeint). The rk4_c and rk6_c solvers have small volume errors, even for hundreds of orbital periods; they are also the fastest for this particular orbit.