  We present an integration-by-parts reduction of any massless tree-level
string correlator to an equivalence class of logarithmic functions, which can
be used to define a field-theory amplitude via a Cachazo-He-Yuan (CHY) formula.
The string amplitude is then shown to be the double copy of the field-theory
one and a special disk/sphere integral. The construction is generic as it
applies to any correlator that is a rational function of correct SL(2) weight.
By applying the reduction to open bosonic/heterotic strings, we get a
closed-form CHY integrand for the $(DF)^2+\text{YM}+\phi^3$ theory.
