We consider type IIB string theory with $N$ D3 branes and various configurations of sevenbranes, such that the string coupling $g_s$ is fixed to a constant finite value. These are the simplest realizations of F-theory, and are holographically dual either to a to a rank $N$ gauge for any coupling tau, or to non-Lagrangian CFTs such as Argyres-Douglas and Minahan-Nemeschansky theory. We compute the mass deformed sphere free energy F(m) using localization in the case of the Lagrangian theory, and the Seiberg-Witten curve for the non-Lagrangian theories. We show how F(m) can be used along with the analytic bootstrap to fix the large N expansion of flavor multiplet correlators in these CFTs, which are dual to scattering of gluons on AdS_5 x S^3, and in the flat space limit determine the effective theory of sevenbranes in F-theory. In particular, we compute the log threshold terms for all the theories and the first higher derivative correction F^4 for the Lagrangian theory for finite tau, and find a precise match in the flat space limit in all cases. Finally, we use numerical bootstrap to study the Lagrangian theory at finite N and tau.