Based on $(106.41 pm 0.86)times 10^{6}$ $psi(3686)$ events collected with the BESIII detector at the BEPCII collider, the branching fractions of $psi(3686) to pi^+pi^- J/psi$, $J/psi to e^+e^- $, and $J/psi to mu^+mu^-$ are measured. We obtain ${cal B}[psi(3686) to pi^+pi^-J/psi]=(34.98pm 0.02pm 0.45)%$, ${cal B}[J/psi to e^+e^-] = (5.983 pm 0.007 pm 0.037)%$ and ${cal B}[J/psi to mu^+mu^-] = (5.973 pm 0.007 pm 0.038)%$. The measurement of ${cal B}[psi(3686) to pi^{+}pi^{-}J/psi]$ confirms the CLEO-c measurement, and is apparently larger than the others. The measured $J/psi$ leptonic decay branching fractions agree with previous experiments within one standard deviation. These results lead to ${cal B}[J/psi to l^+l^-] = (5.978 pm 0.005 pm 0.040)%$ by averaging over the $e^{+}e^{-}$ and $mu^{+}mu^{-}$ channels and a ratio of ${cal B}[J/psi to e^+e^-] / {cal B}[J/psi to mu^+mu^-] = 1.0017 pm 0.0017 pm 0.0033$, which tests $e$-$mu$ universality at the four tenths of a percent level. All the measurements presented in this paper are the most precise in the world to date.
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