  We derive an effective dimensionally reduced theory for the Standard Model
augmented by a real singlet scalar. We treat the singlet as a superheavy field
and integrate it out, leaving an effective theory involving only the Higgs and
$\mathrm{SU}(2)_\mathrm{L} \times \mathrm{U}(1)_Y$ gauge fields, identical to
the one studied previously for the Standard Model. This opens up the
possibility of efficiently computing the order and strength of the electroweak
phase transition, numerically and nonperturbatively, in this extension of the
Standard Model. Understanding the phase diagram is crucial for models of
electroweak baryogenesis and for studying the production of gravitational waves
at thermal phase transitions.
