Equation 20 · Part 5 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

Symbol r_i

p_i^*=p_i+(1-p_i)d_i c_i r_i.

r_i

What this part means

the probability repair succeeds without creating another material defect.

Its job in the formula

$r_i$ is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol r_iArticle meaning

Where the article explains it

If failure occurs, let $d_i$ be the probability it is detected, $c_i$ the probability the cause is diagnosed correctly, and $r_i$ the probability repair succeeds without creating another material defect.

The passage around this formula

An agent can recover only if the system generates a discriminating observation. Let stage i have direct success probability $p_i$ . If failure occurs, let $d_i$ be the probability it is detected, $c_i$ the probability the cause is diagnosed correctly, and $r_i$ the probability repair succeeds without creating another material defect. A simplified effective stage reliability is $p_i^*=p_i+(1-p_i)d_i c_i r_i$ . The formula is intentionally conservative and incomplete. Multiple retries, repair costs, correlated defects, and false alarms require richer models. Its value is conceptual: “the agent can iterate” improves reliability only through detection, diagnosis, and repair.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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