Exponential divergence in the Pythagorean problem. In the top two panels and the lower left panel, Brutus is compared with Brutus with increasing precision. The yellow curves (curves at the top) compare a tolerance of 10−2 with 10−4, the orange curves (second curve from the top) compare 10−4 with 10−6 and so on. The word-length is a function of the tolerance as in equation (4). In the top left panel we show the distance in position-space, in the top right panel in velocity-space and in the bottom left panel in the full phase-space (all normalized by the number of stars and coordinates). The lower right panel compares the converged solution (black and lowest curve in the other plots), with Hermite solutions with time-step parameters η = 2−3, 2−5, 2−7 up to 2−13, with a color sequence similar as in the other panels.