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Equation 28 · Part 5 · Why Cost and Latency Belong in the Evaluation Score, Not a Footnote

Symbol epsilon

Lsequential(k)≈k lˉ,Lparallel(k)≈lˉ+ϵ(k),L_{\text{sequential}}(k) \approx k\,\bar{l}, \qquad L_{\text{parallel}}(k) \approx \bar{l} + \epsilon(k),
ϵ\epsilon

What this part means

a small scheduling and aggregation overhead that grows slowly with k.

Its job in the formula

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

Where the article explains it

where ϵ(k)\epsilon(k) is a small scheduling and aggregation overhead that grows slowly with k .

The passage around this formula

…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: Lsequential(k)≈k lˉ,Lparallel(k)≈lˉ+ϵ(k)L_{\text{sequential}}(k) \approx k\,\bar{l}, \qquad L_{\text{parallel}}(k) \approx \bar{l} + \epsilon(k). where ϵ(k)\epsilon(k) is a small scheduling and aggregation overhead that grows slowly with k . Two evaluations that both report “an agent retried up to five times” can therefore report latency figures that differ by nearly a factor of five, purely as an artifact of whether those five attempts ran one after…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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