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Published equation contexts

CAC=Clicenses+Cusage+Cruntime+Chuman+Crework+CincidentsNaccepted,quality−adjustedCAC=\frac{ C_{\mathrm{licenses}}+C_{\mathrm{usage}}+C_{\mathrm{runtime}} +C_{\mathrm{human}}+C_{\mathrm{rework}}+C_{\mathrm{incidents}} }{N_{\mathrm{accepted,quality-adjusted}}}

Why this formula appears here

A practical organization can report cost per accepted change , CAC=Clicenses+Cusage+Cruntime+Chuman+Crework+CincidentsNaccepted,quality−adjustedCAC=\frac{ C_{\mathrm{licenses}}+C_{\mathrm{usage}}+C_{\mathrm{runtime}} +C_{\mathrm{human}}+C_{\mathrm{rework}}+C_{\mathrm{incidents}} }{N_{\mathrm{accepted,quality-adjusted}}}. The metric should be sliced by task class. Documentation and test scaffolding, unfamiliar-repository bugs, migrations, UI work, security patches, and architecture decisions have different verification costs. A global mean can hide that agents create value in one class and consume it in another.

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ClicensesC_{\mathrm{licenses}}

Symbol C_licenses

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

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CusageC_{\mathrm{usage}}

Symbol C_usage

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

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CruntimeC_{\mathrm{runtime}}

Symbol C_runtime

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

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ChumanC_{\mathrm{human}}

Symbol C_human

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

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CreworkC_{\mathrm{rework}}

Symbol C_rework

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

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CincidentsC_{\mathrm{incidents}}

Symbol C_incidents

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

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Naccepted,quality−adjustedN_{\mathrm{accepted,quality-adjusted}}

Symbol N_accepted,quality-adjusted

NaN_accepted,quality-adjusted 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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Clicenses+Cusage+Cruntime+Chuman+Crework+CincidentsC_{\mathrm{licenses}}+C_{\mathrm{usage}}+C_{\mathrm{runtime}} +C_{\mathrm{human}}+C_{\mathrm{rework}}+C_{\mathrm{incidents}}

Numerator: C_licenses+C_usage+C_runtime +C_human+C_rework+C_incidents

The complete quantity above the fraction bar.

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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.

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Published contexts (1)

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

CAC=Clicenses+Cusage+Cruntime+Chuman+Crework+CincidentsNaccepted,quality−adjusted.CAC=\frac{ C_{\mathrm{licenses}}+C_{\mathrm{usage}}+C_{\mathrm{runtime}} +C_{\mathrm{human}}+C_{\mathrm{rework}}+C_{\mathrm{incidents}} }{N_{\mathrm{accepted,quality-adjusted}}}.

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The Economics of Codex: Tokens, Sandboxes, Review Time, and Software Throughput

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

A practical organization can report cost per accepted change , CAC=Clicenses+Cusage+Cruntime+Chuman+Crework+CincidentsNaccepted,quality−adjustedCAC=\frac{ C_{\mathrm{licenses}}+C_{\mathrm{usage}}+C_{\mathrm{runtime}} +C_{\mathrm{human}}+C_{\mathrm{rework}}+C_{\mathrm{incidents}} }{N_{\mathrm{accepted,quality-adjusted}}}. The metric should be sliced by task class. Documentation and test scaffolding, unfamiliar-repository bugs, migrations, UI work, security patches, and architecture decisions have different verification costs. A global mean can hide that agents create value in one class and consume it in another.

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