Comparison of the matter power spectrum (boost) obtained from FML using the COLA method on a uniform grid and RAMSES using the standard N-body method on an adaptive grid, in the fiducial cosmology in Table 2 (equivalent to the transformation in Fig. 5a). To compensate for small code differences, we have rescaled all spectra to match the linear HI_CLASS spectrum at their smallest common k. We cut RAMSES’ spectra at increasingly higher k ≤ {1/2, 1, 2}⋅k_Nyquist as the mesh refinement increases for z = {3, 1.5, 0}. Although P from FML and RAMSES disagree, that error largely cancels in their boosts B = P_BD/P_GR, which agree to 1% up to k ≲ 5 h/Mpc.