fraction

The passage around this formula

If a step fails and is retried with probability $q_i$ , independent of other steps, the expected cost of the trajectory becomes $\mathbb{E}[C_n] \approx \sum_{i=1}^{n} \frac{c_i}{1-q_i}$. Holding $q_i$ = q constant across the trajectory — a simplification, since real failure rates are neither constant nor independent — the expected extra cost from retries is $\frac{q}{1-q}$$\sum_i$ $c_i$ , and because $c_i$ increases with i , that extra cost is weighted toward the trajectory’s most expensive, latest steps rather than distributed evenly across it. A one-percent per-step retry rate is a rounding error at step five. Applied at step two hundred of an uncached or lightly cached loop, it is a rounding error on a much larger number.

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