as 5$\times10^{-15}$ after 0.4 Myr. The relative error of the total angular momentum is several orders of magnitude smaller. In Figs. \[ssevol0\] and \[ssevol1\] the evolution of the semi-major axes, eccentricities and inclinations of the eight major planets are shown for 1 Myr centred on the epoch JD2456000.5. The output time-step for these plots is 10$^3$ yr and no filtering or smoothing was applied to the data. This output cadence is not expected to introduce any aliasing.

The evolution of the semi-major axes, eccentricities and inclinations of the inner planets (Mercury to Mars) from -0.5 to +0.5 Myr are plotted in Fig. \[ssevol0\]. These results are similar to those in Laskar (1988, 1990), Quinn, Tremaine & Duncan (1991), Laskar, Joutel & Boudin (1993) or Ito & Tanikawa (2002). Major differences appear for Mercury but only prior to -250,000 yr and after 400,000 yr. The impact of these deviations on our results is expected to be negligible. The corresponding orbital evolution for the outer planets (Jupiter to Neptune) is displayed in Fig. \[ssevol1\]. Eccentricities in de Pater & Lissauer (2010), Fig. 2.14, match our results very well.

We have carried out a more detailed comparison between our results and those from 