Current artificial intelligence and data science applications typically require complex computations and massive amounts of data handling, presenting unprecedented challenges for embedded platforms. Approximate computing has emerged as the most promising design technique to address this issue, by providing a potential performance increase, while sacrificing accuracy within an acceptable range. Approximate arithmetic units require the creation of design space exploration techniques that can swiftly and automatically form an approximate configuration in fault-tolerant systems. Existing methods, however, use iterative design space sampling, resulting in a large amount of redundant computation. In this work, we propose the efficient FPAX automatic search framework which can learn from prior knowledge regarding the exploration process of known applications and use it to guide design exploration. This avoids excessive redundant computation and quickly provides an impressive approximate configuration. Compared with the Jump Search algorithm known for its efficiency, FPAX can also achieve faster convergence speed and better exploration quality. Even compared to our previous ENAP framework, it exhibits an 18x faster performance while achieving almost identical exploration quality for several commonly used fault-tolerant applications.