Updated 3dcorr accuracy
$C_\ell$ weak lensing & (\ref{eq:cls}),(\ref{eq:transfer_lensing})& CCL6 &$10 \leq \ell\leq 3000$ & $10^{-3}$ & Fig. \ref{fig:cls_limber}\\
$C_\ell$ CMB lensing &(\ref{eq:cls}),(\ref{eq:cmblens}) & CCL6 & $10 \leq \ell\leq 3000$& $5\times 10^{-4}$ & Fig. \ref{fig:cls_cmblens}\\
$\xi_+,\xi_-,\xi_{gg}$ & (\ref{eq:xi22flat}),(\ref{eq:xi00flat}) & CCL6 & $0.01< \theta/{\rm deg}< 5$& $0.5\sigma_{\rm LSST}$ & Fig. \ref{fig:corrval}\\
- 3D correlation, $\xi$ & (\ref{eq:xi3d}) & CCL1-5 & $1<r/{\rm Mpc}<200$ \& $0 \leq z \leq 5$& $3\times 10^{-2}$ & Figs. \ref{fig:benchmark_xi} and \ref{fig:analytic_xi} \\
+ 3D correlation, $\xi$ & (\ref{eq:xi3d}) & CCL1-3 & $0.1<r/{\rm Mpc}<250$ \& $0 \leq z \leq 5$& $4\times 10^{-2}$ & Figs. \ref{fig:benchmark_xi} and \ref{fig:analytic_xi} \\
$C_\ell$ clustering {\tt non-Limber} & (\ref{eq:cls}),(\ref{eq:transfer_nc}),(\ref{eq:transfer_rsd}) & CCL1 & $500 \leq \ell < 1000$ & $2\times 10^{-2}$ & - \\
$C_\ell$ clustering {\tt Angpow} & (\ref{eq:cls}),(\ref{eq:transfer_nc}),(\ref{eq:transfer_rsd}) & CCL1 & $2 \leq \ell < 1000$ & $3\times 10^{-3}$ & Fig. \ref{fig:angpow} (right panel)\\
\hline
