  Hydrodynamic calculations of ultra-relativistic heavy ion collisions are
performed using the iEBE-VISHNU 2+1D code with fluctuating initial conditions
and three different parameterizations of the Lattice QCD equations of state:
continuum extrapolations for stout and HISQ/tree actions, as well as the
s95p-v1 parameterization based upon calculations using the p4 action. All
parameterizations are matched to a hadron resonance gas equation of state at T
= 155 MeV, at which point the calculations are continued using the UrQMD
hadronic cascade. Calculations for $\sqrt{s_{NN}}=200$ GeV Au+Au collisions in
three centrality classes are compared to experimental data for final state
particle spectra and anisotropic flow coefficients $v_2$ and $v_3$ as well as
for pion HBT radii. Experimental observables for the stout and HISQ/tree
equations of state are observed to differ by less than a few percent for all
observables, while the s95p-v1 equation of state generates spectra and flow
coefficients which differ by ~10-20%. Calculations in which the HISQ/tree
equation of state is sampled from the published error distribution are also
observed to differ by less than a few percent.
