Equation 20 · Part 6 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

Full expression=Article 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.

Read this part in the article →

Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.