We update the pressure, energy density and entropy density calculations
at non-zero checmial potentials based on Taylor expansion up to 6th order
performed by the HotQCD Collaboration in 2017.
The HotQCD collaboration has now accumulated an order of magnitude larger
statistics for lattices with temporal extent
Nt=8 and 12 and added results for Nt=16 that were not available previously.
For Nt=8 we also calculated the 8th order expansion coefficients.
Furthermore, we showed that the straightforward Taylor series expansion
for the pressure provides a well controlled description of the pressure
upto $\mu_B / T \leq 2.5$.
In this talk, we will use the high statistics results on Taylor expansion
coefficients, calculated with HISQ fermions and extrapolated to the continuum
limit, for a determination of the QCD equation of state under conditions
relevant for the description of hot and dense matter created in heavy
ion collisions. We determine energy density and pressure along lines of
constant entropy per net baryon-number.
We furthermore use the eighth order Taylor series for the pressure to construct
Pade-resummed thermodynamic observables along lines of fixed entropy per
baryon number-density and comment on the location of
singularities in the complex chemical potential plane that influence
the convergence of the Taylor series for bulk thermodynamic observables.
At low temperature we compare our results with hadron resonance
gas (HRG) model calculations based on the recently constructed QMHRG2020
hadron list, which in addition to the hadronic resonances listed by the
Particle Data Group, also includes resonances calculated in relativistic