  An accurate expression for the exchange-correlation free energy f_{xc} of
homogeneous electron fluids at finite temperatures is presented on the basis of
Singwi-Tosi-Land-Sjolander (STLS) approximation. In addition to the derivation
for the paramagnetic state, that for the ferromagnetic state is newly carried
out in which a correction in the strong Coulomb coupling regime is incorporated
into the construction of analytic expression as a function of the coupling
constant and the Fermi degeneracy. The fitting formula for f_{xc} is then
extended over any degree of spin polarization with the aid of available
interpolation scheme. The proposed equation of state, called iSTLS formula,
shows reasonable agreements with the existing quantum Monte Carlo evaluations
at finite temperatures in the paramagnetic state, thus giving a consensus for
the thermodynamic functions between many-body theories and computer
simulations. On the other hand, the current status for the agreement among
various evaluations of f_{xc} is relatively unsatisfactory in the ferromagnetic
state, suggesting the necessity of further investigations.
