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Equation 1 · Part 4 · Comparing the Main Approaches to AI Datacenter Systems Engineering

Symbol r_f

Δtcp∗=2 wcpNnodes rf\Delta t_{cp}^{*} = \sqrt{\frac{2\,w_{cp}}{N_{\text{nodes}}\,r_f}}
rfr_f

What this part means

the per-node failure rate.

Its job in the formula

rfr_f occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Where the article explains it

where wcpw_{cp} is the time to write a checkpoint, NnodesN_{\text{nodes}} is the job’s node count, and rfr_f is the per-node failure rate.

The passage around this formula

…balances the fixed cost of writing a checkpoint against the expected cost of losing work to a failure: Δtcp∗=2 wcpNnodes rf\Delta t_{cp}^{*} = \sqrt{\frac{2\,w_{cp}}{N_{\text{nodes}}\,r_f}}. where wcpw_{cp} is the time to write a checkpoint, NnodesN_{\text{nodes}} is the job’s node count, and rfr_f is the per-node failure rate. As NnodesN_{\text{nodes}} grows, the failure rate the job experiences as a whole scales with it, which pulls the optimal interval shorter — meaning larger jobs must checkpoint more often even as each individual checkpoint write competes with the same limited storage…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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