  Ignoring ten-dimensional heterotic gauge fields, heterotic supergravity
reduced on a $d$-dimensional torus gives rise to a half-maximal supergravity
coupled to $d$ vector multiplets. The reduced theory has a continuous
$O(d,d;\mathbb R)/O(d)_-\times O(d)_+$ symmetry that persists to all
perturbative orders in the string $\alpha'$ expansion. We highlight this
symmetry by explicitly reducing the bosonic sector of four-derivative heterotic
supergravity as well as its fermionic supersymmetry variations. After
appropriate field redefinitions, the resulting action and supersymmetry
variations are manifestly $O(d)_-\times O(d)_+$ invariant. This reduction
allows us to explore the interplay between the gravity and vector multiplets
beyond leading order, where (in our conventions) $O(d)_-$ is the supergravity
R-symmetry while $O(d)_+$ is a flavor symmetry of the $d$ vector multiplets.
