We propose a novel, unified approach to the development of compositional symbolic execution tools, bridging the gap between classical symbolic execution and compositional program reasoning based on separation logic. Using this approach, we build a new analysis tool for JavaScript that follows the semantics of the language without any simplifications, with support for whole-program symbolic testing, verification, and, for the first time, automatic compositional testing based on bi-abduction. The meta-theory underpinning the tool is developed in a modular way, streamlining the proofs and informing the implementation. Our explicit treatment of symbolic execution errors allows us to give meaningful feedback to the developer during whole-program symbolic testing and guides the inference of resource of the bi-abductive execution. We evaluate the performance of our tool on a number of JavaScript data-structure libraries, demonstrating the scalability of whole-program symbolic testing, an improvement over our previous work on JavaScript verification, and automatic creation of useful specifications using bi-abduction.