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Equation 20 · Part 2 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

Symbol p_i

pi∗=pi+(1−pi)diciri.p_i^*=p_i+(1-p_i)d_i c_i r_i.
pip_i

What this part means

the direct success probability.

Its job in the formula

pip_i is part of the quantity the equation computes from the expression on the right.

Where the article explains it

Let stage i have direct success probability pip_i .

The passage around this formula

An agent can recover only if the system generates a discriminating observation. Let stage i have direct success probability pip_i . If failure occurs, let did_i be the probability it is detected, cic_i the probability the cause is diagnosed correctly, and rir_i the probability repair succeeds without creating another material defect. A simplified effective stage reliability is pi∗=pi+(1−pi)dicirip_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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