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Published equation contexts

p^=1n∑i=1nYi\hat p=\frac{1}{n}\sum_{i=1}^{n}Y_i

Why this formula appears here

Let YiY_i∈\in\{0,1\} indicate whether evaluation task i is resolved. The familiar score p^=1n∑i=1nYi\hat p=\frac{1}{n}\sum_{i=1}^{n}Y_i. is an estimate of success probability only for a distribution represented by those n instances and the evaluated system. The system is not just a model. It includes context retrieval, tools, prompts, retries, execution limits, and candidate selection. The evaluation distribution is not “software engineering.” It is a constructed sample with inclusion criteria, repository mix, languages, issue styles, and executable tests.

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nn

Symbol n

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

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YiY_i

Symbol Y_i

an estimate of success probability only for a distribution represented by those n instances and the evaluated system.

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i=1i=1

Starting index or lower bound: i=1

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

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nn

Ending index or upper bound: n

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

p^=1n∑i=1nYi\hat p=\frac{1}{n}\sum_{i=1}^{n}Y_i

Equation 3 · Model Evaluation

How to Evaluate Codex Beyond SWE-bench and Vendor Scores

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Let YiY_i∈\in\{0,1\} indicate whether evaluation task i is resolved. The familiar score p^=1n∑i=1nYi\hat p=\frac{1}{n}\sum_{i=1}^{n}Y_i. is an estimate of success probability only for a distribution represented by those n instances and the evaluated system. The system is not just a model. It includes context retrieval, tools, prompts, retries, execution limits, and candidate selection. The evaluation distribution is not “software engineering.” It is a constructed sample with inclusion criteria, repository mix, languages, issue styles, and executable tests.

Meanings in this article

  • ii: resolved.
  • YiY_i: an estimate of success probability only for a distribution represented by those n instances and the evaluated system.
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