Recently it has been important to develop a next generation of parallel circuit simulator different than sequential circuit simulator like SPICE. This paper describes the Sophia Relaxation-based Program (SRP) which is a new circuit simulator for Fast Automatic Differentiation (FAD) on object oriented program. Though this SRP does not work in parallel computers yet, it has been designed for the next generation. The SRP adds the FAD object of the differentiation for a function as its differential elements in Jacobian matrix.