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Published equation contexts

C(k)≈kcˉC(k) \approx k\bar{c}

Why this formula appears here

Start with how an agent handles its own failures. Suppose a task is retried up to k times under two different execution policies: sequential retry, where each attempt waits for the previous one to finish before starting, and parallel sampling, where all k attempts run concurrently and the first success is taken. Cost is roughly indifferent to which policy was used — the compute consumed scales with the number of attempts made, C(k) ≈\approx kcˉ\bar{c} , regardless of whether they ran one after another or all at once. Latency is not indifferent at all:

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CC

Symbol C

C is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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kk

Symbol k

k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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cˉ\bar{c}

Symbol barc

barc is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Its accuracy depends on the assumptions and range of use described in the article.

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Published contexts (1)

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C(k)≈kcˉC(k) \approx k\bar{c}

Equation 27 · Model Evaluation

Why Cost and Latency Belong in the Evaluation Score, Not a Footnote

This equation gives an approximation: it relates the quantities while allowing an approximation.

Start with how an agent handles its own failures. Suppose a task is retried up to k times under two different execution policies: sequential retry, where each attempt waits for the previous one to finish before starting, and parallel sampling, where all k attempts run concurrently and the first success is taken. Cost is roughly indifferent to which policy was used — the compute consumed scales with the number of attempts made, C(k) ≈\approx kcˉ\bar{c} , regardless of whether they ran one after another or all at once. Latency is not indifferent at all:

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