Equation 10 · Part 15 · The Economics of Codex: Tokens, Sandboxes, Review Time, and Software Throughput

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

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}}}.

C_{\mathrm{licenses}}+C_{\mathrm{usage}}+C_{\mathrm{runtime}} +C_{\mathrm{human}}+C_{\mathrm{rework}}+C_{\mathrm{incidents}}

What this part means

The complete quantity above the fraction bar.

Its job in the formula

$C_l$ icenses+ $C_u$ sage+ $C_r$ untime + $C_h$ uman+ $C_r$ ework+ $C_i$ ncidents occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Full expressionNumerator: C_licenses+C_usage+C_runtime +C_human+C_rework+C_incidentsArticle meaning

The passage around this formula

A practical organization can report cost per accepted change , $CAC=\frac{ C_{\mathrm{licenses}}+C_{\mathrm{usage}}+C_{\mathrm{runtime}} +C_{\mathrm{human}}+C_{\mathrm{rework}}+C_{\mathrm{incidents}} }{N_{\mathrm{accepted,quality-adjusted}}}$ . 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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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

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