  We report a search for nonstandard neutrino interactions (NSI) using eight
years of TeV-scale atmospheric muon neutrino data from the IceCube Neutrino
Observatory. By reconstructing incident energies and zenith angles for
atmospheric neutrino events, this analysis presents unified confidence
intervals for the NSI parameter $\epsilon_{\mu \tau}$. The best-fit value is
consistent with no NSI at a p-value of 25.2%. With a 90% confidence interval of
$-0.0041 \leq \epsilon_{\mu \tau} \leq 0.0031$ along the real axis and similar
strength in the complex plane, this result is the strongest constraint on any
NSI parameter from any oscillation channel to date.
