What does this equation mean?

The roofline model, introduced by Williams, Waterman, and Patterson in 2009, gives the concept its formal shape. It plots two independent ceilings on the same chart: the chip’s peak arithmetic throughput (operations per second) on one axis, and its peak memory bandwidth (bytes per second) combined with a workload-specific ratio on the other. That ratio — arithmetic intensity — is defined as the number of floating-point operations performed per byte of data moved between memory and the arithmetic units [ 4 ] . A workload’s achievable throughput is bounded by whichever ceiling it hits first: $I = \frac{\text{FLOPs performed}}{\text{bytes moved}}, \qquad P_{\text{achievable}} = \min\left(P_{\text{peak compute}},\; I \times BW_{\text{peak memory}}\right)$. When a workload’s intensity I is high enough that I $\times$ B$W_{\text{peak memory}}$ exceeds the chip’s peak compute rate, the workload is compute-bound: more arithmetic throughput would speed it up, more memory bandwidth would not. When I is low, the workload is memory-bound: the chip’s arithmetic units sit idle waiting for bytes, and only additional bandwidth (or a higher-intensity reformulation of the same computation) helps [ 4 ] . This is the exact mechanism behind the bandwidth-meter-pinned, compute-gauge-idle image below: the two gauges are reading two different ceilings, and only one of them is being pushed against.