Equation 33 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →superscript
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.
See an illustrated explanation →Probability operator
The probability operator gives the chance of the event named inside its brackets or parentheses.
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What the article says around this equation
Code-generation research often reports k : the probability that at least one of k sampled solutions passes. If independent attempts each succeed with probability q , then . This is valuable for search: more attempts increase the chance of finding one acceptable candidate. Production consistency asks a different question. If k required deployments must all succeed, the same independence simplification gives
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