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A diffuse flux of astrophysical neutrinos above $100\,\mathrm{TeV}$ has beenobserved at the IceCube Neutrino Observatory. Here we extend this analysis toprobe the astrophysical flux down to $35\,\mathrm{TeV}$ and analyze its flavorcomposition by classifying events as showers or tracks. Taking advantage oflower atmospheric backgrounds for shower-like events, we obtain a shower-biasedsample containing 129 showers and 8 tracks collected in three years from 2010to 2013. We demonstrate consistency with the$(f_e:f_{\mu}:f_\tau)_\oplus\approx(1:1:1)_\oplus$ flavor ratio at Earthcommonly expected from the averaged oscillations of neutrinos produced by piondecay in distant astrophysical sources. Limits are placed on non-standardflavor compositions that cannot be produced by averaged neutrino oscillationsbut could arise in exotic physics scenarios. A maximally track-like compositionof $(0:1:0)_\oplus$ is excluded at $3.3\sigma$, and a purely shower-likecomposition of $(1:0:0)_\oplus$ is excluded at $2.3\sigma$.

Flavor Ratio of Astrophysical Neutrinos above 35 TeV in IceCube