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Equation 35 · Part 4 · Why Coding Agents Fail: Long-Horizon Reliability in OpenAI Codex

superscript

Pr⁡(all k succeed)=qk.\Pr(\text{all }k\text{ succeed})=q^k.
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

This is valuable for search: more attempts increase the chance of finding one acceptable candidate. Production consistency asks a different question. If k required deployments must all succeed, the same independence simplification gives Pr⁡(all k succeed)=qk\Pr(\text{all }k\text{ succeed})=q^k. The first rises with k ; the second falls. τ\tau -bench introduced a repeated-trial metric in this spirit and reported substantial deterioration across repeated tool-agent-user runs in its evaluated setting [ 9 ] . Coding-agent reports should state whether multiple trajectories were sampled and selected, or whether one configured system succeeds repeatedly.

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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