Equation 20 · Part 8 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

subscript

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

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle meaning

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.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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