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Equation 3 · Part 5 · Ten Failure Modes That Define Production Claude Code Use

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T50(t)≈T50(t0)⋅2 (t−t0)/d,d≈7 months,T_{50}(t) \approx T_{50}(t_0) \cdot 2^{\,(t - t_0)/d}, \qquad d \approx 7\ \text{months},
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What this part means

Approximately equal to; the equality is not exact.

Its job in the formula

Approximately equal to; the equality is not exact.

The passage around this formula

It is intuitive to expect an agentic session to improve as it accumulates context about a task. The measured pattern runs the other way. METR’s time-horizon research tracks the length of task — measured in how long a skilled human would take — that a frontier model can complete autonomously with a given reliability, and finds current frontier models near 100% success on tasks taking a human under four minutes, collapsing to under 10% success on tasks taking more than about four hours, with Claude 3.7 Sonnet reported specifically among the models exhibiting this drop-off [ 13 ] . The organization’s headline trend — the task length completable at 50% reliability doubling roughly every seven…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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