Acceleration errors from the GPU. Distribution of acceleration errors for (blue) and (black) particles drawn from a Plummer sphere when using the state-of-the-art GPU-based direct-summation library sapporo (version 1.6) as compared to direct summation in double (64-bit) precision. The top, middle, and bottom panel refer to, respectively, the normalised (by the mean acceleration ), relative, and scaled (by f defined in equation (4)) acceleration errors. The thin vertical lines indicate the rms error (dashed) as well as the median and the 99 and 99.9 percentiles (solid). Bins are 0.1 dex wide.