Equation 8 · Part 5 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

Symbol P

R=\mathbb{E}_{g\sim D}\mathbb{E}_{\tau\sim P(\tau\mid g)} \left[V(s_T,g)\right].

P

What this part means

P appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.

Its job in the formula

P appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.

Full expressionSymbol PArticle meaning

The passage around this formula

where $s_t$ is environmental state, $o_t$ the agent’s observation, and $a_t$ its action. Task success is not a property of the final message. It is an externally evaluated predicate V( $s_T$ ,g) over final state and goal g . System reliability under task distribution D is $R=\mathbb{E}_{g\sim D}\mathbb{E}_{\tau\sim P(\tau\mid g)} \left[V(s_T,g)\right]$ . Every term matters. Change the task distribution, model, harness, tools, retry budget, permissions, environment, or evaluator and the reliability estimate changes.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

[2] Introducing GPT-5.3-Codex ↗

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