We present a new approach for stateless model checking (SMC) of multithreaded programs under Sequential Consistency (SC) semantics. To combat state-space explosion, SMC is often equipped with a partial-order reduction technique, which defines an equivalence on executions, and only needs to explore one execution in each equivalence class. Recently, it has been observed that the commonly used equivalence of Mazurkiewicz traces can be coarsened but still cover all program crashes and assertion violations. However, for this coarser equivalence, which preserves only the reads-from relation from writes to reads, there is no SMC algorithm which is (i) \emph{optimal} in the sense that it explores precisely one execution in each reads-from equivalence class, and (ii) \emph{efficient} in the sense that it spends polynomial effort per class. We present the first SMC algorithm for SC that is both optimal and efficient \emph{in practice}, meaning that it spends polynomial time per equivalence class on all programs that we have tried. This is achieved by a \textit{novel test} that checks whether a given reads-from relation can arise in some execution. We have implemented the algorithm by extending Nidhugg, an SMC tool for C/C++ programs, with a new mode called \textsf{rfsc}. Our experimental results show that \textsc{Nidhugg}/\textsf{rfsc}, although slower than the fastest SMC tools in programs where tools happen to examine the same number of executions, always scales similarly or better than them, and outperforms them by an exponential factor in programs where the reads-from equivalence is coarser than the standard one. We also present two non-trivial use cases
where the new equivalence is particularly effective, as well as the significant performance advantage that \textsc{Nidhugg}/\textsf{rfsc} offers compared to state-of-the-art SMC and systematic concurrency testing tools.