  We reconstruct the Hubble function from cosmic chronometers, supernovae, and
baryon acoustic oscillations compiled data sets via the Gaussian process (GP)
method and use it to draw out Horndeski theories that are fully anchored on
expansion history data. In particular, we consider three well-established
formalisms of Horndeski gravity which single out a potential through the
expansion data, namely: quintessence potential, designer Horndeski, and
tailoring Horndeski. We discuss each method in detail and complement it with
the GP reconstructed Hubble function to obtain predictive constraints on the
potentials and the dark energy equation of state.
