  Recently, $O(\alpha^3)$ corrections to the muon decay rate and
$O(\alpha_s^3)$ to heavy quark decays have been determined by Fael,
Sch\"onwald, and Steinhauser. This is the first such perturbative improvement
of these important quantities in more than two decades. We reveal and explain a
symmetry pattern in these new corrections, and confirm the most technically
difficult parts of their evaluation.
