We propose a new method for runtime checking of a relaxed consistency property called quasi linearizability for concurrent data structures. Quasi linearizability generalizes the standard notion of linearizability by intentionally introducing nondeterminism into the parallel computations and exploiting such nondeterminism to improve the performance. However, ensuring the quantitative aspects of this correctness condition in the low level code is a difficult task. Our method is the first fully automated method for checking quasi linearizability in the unmodified C/C++ code of concurrent data structures. It guarantees that all the reported quasi linearizability violations are real violations. We have implemented our method in a software tool based on LLVM and a concurrency testing tool called Inspect. Our experimental evaluation shows that the new method is effective in detecting quasi linearizability violations in the source code of concurrent data structures.