We present a practical verification method for safety analysis of the autonomous driving system (ADS). The main idea is to build a surrogate model that quantitatively depicts the behavior of an ADS in the specified traffic scenario. The safety properties proved in the resulting surrogate model apply to the original ADS with a probabilistic guarantee. Given the complexity of a traffic scenario in autonomous driving, our approach further partitions the parameter space of a traffic scenario for the ADS into safe sub-spaces with varying levels of guarantees and unsafe sub-spaces with confirmed counter-examples. Innovatively, the partitioning is based on a branching algorithm that features explainable AI methods. We demonstrate the utility of the proposed approach by evaluating safety properties on the state-of-the-art ADS Interfuser, with a variety of simulated traffic scenarios, and we show that our approach and existing ADS testing work complement each other. We certify five safe scenarios from the verification results and find out three sneaky behavior discrepancies in Interfuser which can hardly be detected by safety testing approaches.