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Pattainable=min⁡(Pmax⁡,  β⋅I)P_{\mathrm{attainable}} = \min\left(P_{\max},\; \beta \cdot I\right)

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with W operations and Q bytes. Let Pmax⁡P_{\max} be the machine’s peak arithmetic rate and β\beta its achievable memory bandwidth. Then attainable performance is bounded by Pattainable=min⁡(Pmax⁡,  β⋅I)P_{\mathrm{attainable}} = \min\left(P_{\max},\; \beta \cdot I\right). That expression is the whole model, and it has one structural feature that matters more than the rest. The two bounds cross at a ridge point

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Pattainable=min⁡(Pmax⁡,  β⋅I).P_{\mathrm{attainable}} = \min\left(P_{\max},\; \beta \cdot I\right).

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

with W operations and Q bytes. Let Pmax⁡P_{\max} be the machine’s peak arithmetic rate and β\beta its achievable memory bandwidth. Then attainable performance is bounded by Pattainable=min⁡(Pmax⁡,  β⋅I)P_{\mathrm{attainable}} = \min\left(P_{\max},\; \beta \cdot I\right). That expression is the whole model, and it has one structural feature that matters more than the rest. The two bounds cross at a ridge point

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