In this talk, I will connect, via tree-level double copy, any massless string amplitudes with QFT amplitudes given by Cachazo-He-Yuan (CHY) formula. This can be derived by a detailed study of integration-by-part (IBP) reduction of string integrands. As an application, we consider general multitrace integrands of heterotic string amplitudes. The new technology generates a recursive expansion of the heterotic string amplitudes in terms of those with fewer gravitons and traces, where the kinematic coefficients are building blocks for BCJ numerators of the (DF)^2+YM+phi^3 theory. Finally, we give a generic CHY integrand for multitrace (DF)^2+YM+phi^3 amplitudes, which reproduce the corresponding heterotic string amplitudes after double copy with a single-valued Z-theory.