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Equation 5 · Part 4 · From Autocomplete to Delegation: The Technical History Behind OpenAI Codex

superscript

pass@⁡k=1−(1−p)k.\operatorname{pass@}k=1-(1-p)^k.
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

The sampling result made the search interpretation explicit. If independent candidates have success probability p , the chance of at least one success among k is pass@⁡k=1−(1−p)k\operatorname{pass@}k=1-(1-p)^k. Real samples are not independent and the paper used estimators appropriate to its setup, but the conceptual point holds: model probability plus an evaluator can search a program space. Without a reliable selector, many candidates become review burden.

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.