Applications are becoming more varied. Architectures are becoming more complex. Yet software implemented by the expert still achieves higher performance than most automatically generated code despite two decades of research in automatic empirical optimization systems. Can we ever get expert-level performance automatically? In this talk, I will discuss how expert-level performance in the dense linear algebra domain can be systematically attained through the use of formal methods and analytical models. Specifically, I will present our analytical models and their underlying hardware principles. I will demonstrate how these analytical models are resilient against changes. I will also share how analytical models from the dense linear algebra domain have been adapted to design high performance implementations for problems in other domains.