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Equation 4 · Part 2 · Evaluating Trajectories, Not Answers

Symbol barc

E[cost to first success]=cˉp,\mathbb{E}[\text{cost to first success}] = \frac{\bar{c}}{p},
cˉ\bar{c}

What this part means

barc occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

barc occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

There is also a structural reason cost cannot be separated from reliability. If a run costs cˉ\bar{c} on average and succeeds with probability p , and the operator simply retries until success, the expected spend to first success is E[cost to first success]=cˉp\mathbb{E}[\text{cost to first success}] = \frac{\bar{c}}{p}. which means a cheap unreliable agent and an expensive reliable one can occupy the same operating point. Reporting either number alone conceals which one you have bought. The honest artefact is a curve — quality against spend, produced by sweeping the effort level and the retry policy — rather than a point, and the honest comparison places two systems at matched spend and asks which reaches further.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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