Fractional energy error as a function of the length of the integration for the orbit on the right in Figure 10 in MWPotential2014 for the eight orbit integrators contained in galpy. The top two integrators are pure python implementations: odeint is scipy's ordinary-differential-equation solver and leapfrog is a python implementation of the leapfrog integrator. The other six integrators are written in C: second-(leapfrog_c), fourth-(symplec4_c), and sixth-(symplec6_c) order symplectic integrators; fourth-, fifth-, and sixth-order Runge–Kutta solvers (rk4_c, dopr54_c, and rk6_c). The length of the integration is specified in units of the rotational period T_ϕ of the orbit. The energy error remains constant for the symplectic integrators while it increases in time for the other integrators.