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where D is the fraction of time spent active. Because $P_{\text{active}}$ is typically one to three orders of magnitude larger than $P_{\text{idle}}$ for a real accelerator, battery life is dominated almost entirely by D and by $P_{\text{idle}}$ — not by how efficient the processor is once it wakes up. This is precisely why an always-on product design effort spends so much of its attention on cheap, low-power triggering stages (a simple always-listening front end that only wakes the expensive processor when something resembling the target event occurs) rather than on the accelerator’s peak TOPS figure, which only matters for the small fraction of time D actually represents.

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