A global analytic potential energy surface for the ro-vibrational dynamics of cis- and trans-formic acid is presented, constructed using LASSO-based regression to reproduce CCSD(T)(F12*)/cc-pVTZ-F12 energies. The fit is accurate to 0.25% has an RMS deviation from the ab initio data of 9 cm-1 for the energy range 0-15000 cm-1. Converged J = 0 vibrational eigenstates are reported, computed using vibrational configuration interaction with an internal coordinate path Hamiltonian for the torsional motion connecting the cis and trans rotamers. Methodological choices concerning the appropriate definitions of the curvilinear and diabatic bath coordinates are discussed. The zero point of the cis rotamer is 1412 cm-1 above that of the trans, which lies at 7354 cm-1. The computed fundamentals match the bands recorded from gas-phase IR spectroscopy with an RMSD of only 3 cm-1. A fresh assignment of the overtone spectra of both the cis and trans rotamers is presented for the energy range 0-4720 cm-1, where 14 out of the 51 bands are reassigned on the basis of the VCI calculations.