Numerator: σ + mbars

The passage around this formula

…55,000-token example described above, that reframes the earlier formula: instead of the full T(n) $\approx$ $\tau_0$ + n$\bar{s}$ , a session that only ever actually needs m of the n available tools pays approximately $\tau_0$ + $\sigma$ + m$\bar{s}$ , where $\sigma$ is the search tool’s own fixed overhead. The fraction of the original tax avoided is $\rho(n, m) \;=\; 1 - \frac{\sigma + m\bar{s}}{\tau_0 + n\bar{s}}$. which grows toward its ceiling as m shrinks relative to n . Anthropic reports a measured outcome consistent with that shape at their own scale: “Tool Search…

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