What does this equation mean?

Given a memory system built this way, the question for any specific piece of computation is simple to state and consequential to answer: for this kernel, is the bottleneck the arithmetic units or the memory system that feeds them? The quantity that answers it is arithmetic intensity , defined as the number of floating-point operations a kernel performs per byte it moves across the memory boundary that matters. Williams, Waterman and Patterson formalized the relationship between intensity and attainable performance as the roofline model: $P \;\le\; \min\!\left(P_{\max},\; I \cdot B\right), \qquad I = \frac{\text{FLOPs}}{\text{bytes moved}}$. with $P_{\max}$ the peak arithmetic rate of the device, B the achievable bandwidth of the memory tier supplying the operands, and P the attainable performance [ 11 ] . The two terms cross at a ridge point $I^{*}$ = $P_{\max}$/B : below it, runtime is set by how many bytes must move, whatever the peak arithmetic rate promises; above it, the arithmetic units are the limit and the memory system is idle capacity. Because peak compute has grown roughly twice as fast as memory bandwidth for two decades running [ 12 ] , that ridge point has been climbing — a kernel that was comfortably compute-bound on one generation of hardware can become memory-bound on the next without a single line of its code changing.