No benchmark covers the six-equation model, so the pressure-relaxation path has no performance coverage

[sbryngelson]

Every case in benchmarks/ runs model_eqns = 2:

benchmark	model_eqns
5eq_rk3_weno3_hll	2
5eq_rk3_weno3_hllc	2
5eq_rk3_weno3_lf	2
hypo_hll	2
ibm	2
igr	2
viscous_weno5_sgb_acoustic	2

So s_pressure_relaxation_procedure — which for a six-equation case runs over the whole domain every step, including a Newton iteration per cell and the equation-of-state chain beneath it — is never benchmarked. The correctness side is well covered (16 model_eqns = 3 entries in toolchain/mfc/test/cases.py), but nothing measures what it costs.

Two consequences:

1. A change that regresses six-equation throughput cannot be caught by CI. Nothing would move.
2. A change that improves it cannot be demonstrated either, which is the position Stop NVHPC IPO silently miscompiling the six-equation relaxation kernel #1878 was in: the NVHPC IPO exclusion it adds lands on exactly this path, and the existing suite could not say whether that was free or expensive. Measuring it needed a purpose-built case.

For what it is worth, that measurement came out at roughly 0.2% either way on a 3D 128^3 two-fluid case with a state-dependent EOS, 100 steps — well inside run-to-run noise, so the exclusion is free. But that number came from a throwaway case rather than anything the repository keeps.

A six-equation entry in benchmarks/ would close the gap. A Mie-Gruneisen or JWL fluid paired with a stiffened-gas one exercises the state-dependent branch of s_phase_coefficients, which is the part with the deepest call chain and the one most sensitive to inlining decisions; a two-fluid sphere-collapse or shock-interface setup reaches relaxation in most cells rather than a handful.

Noting the sizing honestly: the benchmark suite already runs on Frontier and Phoenix for every PR, so an eighth case is not free, and whether it earns its wall-clock is a judgement call for whoever owns that budget.