`CheckRhoSieFromPT` is a bit weird

The subroutine in question is:

template <typename EOS, typename Indexer_t = Real *>
PORTABLE_INLINE_FUNCTION bool
CheckRhoSieFromPT(EOS eos, Real rho, Real T,
                  Indexer_t &&lambda = static_cast<Real *>(nullptr)) {
  const Real P = eos.PressureFromDensityTemperature(rho, T, lambda);
  const Real sie = eos.InternalEnergyFromDensityTemperature(rho, T, lambda);
  Real rtest = 12; // set these to something
  Real etest = 1;
  eos.DensityEnergyFromPressureTemperature(P, T, lambda, rtest, etest);
  Real P_test = eos.PressureFromDensityTemperature(rtest, T, lambda);
  Real residual = P_test - P;
  Real frac_residual =
      std::min(std::abs(singularity::robust::ratio(residual, P)), std::abs(residual));
  bool results_good = (isClose(rho, rtest, 1e-8) && isClose(sie, etest, 1e-8))
                      // This is as good as it will get sometimes.
                      || (std::abs(frac_residual) <= 1e-8);
  if (!results_good) {
    printf("RhoSie of PT failure!\n"
           "\trho_true = %.14e\n"
           "\tsie_true = %.14e\n"
           "\tP        = %.14e\n"
           "\tT        = %.14e\n"
           "\trho      = %.14e\n"
           "\tsie      = %.14e\n"
           "\tP_test   = %.14e\n"
           "\tresidual = %.14e\n"
           "\tfracres  = %.14e\n",
           rho, sie, P, T, rtest, etest, P_test, residual, frac_residual);
  }
  return results_good;
}

As I understand it, is seems like this subroutine want to do the following. Initialize a state $(P_0, T_0)$, then to compute $\rho_0 := \rho(P_0,T_0)$ and $e_0 := e(P_0, T_0)$, and then check that the inversion is consistent $P(\rho_0, e_0) = P_0$ and $T(\rho_0, e_0) = T_0$. Basically, just check that inversion is consistent and there are no mistakes in the formula. I guess you could also start with $(\rho_0, e_0)$ and then do the reverse process.

I'm assuming the reason this might be happening this way is because certain EOS member function calls aren't available? What do we think?

Start by tracing CheckRhoSieFromPT and the EOS member functions it calls. Determine which forward and inverse state conversions are available and how existing validation tests exercise them. Done means agreeing on a consistent inversion check and updating the subroutine and its tests accordingly.