Published equation contexts

$R^{*} \approx 2.11$

Why this formula appears here

is exceeded. At Anthropic’s five-minute rate, w = 1.25 and $R^{*}$ $\approx$ 1.28 : the prefix pays for itself starting with the first read after the write, matching the break-even Anthropic’s pricing page states for that duration [ 6 ] . At the one-hour rate, w = 2 and $R^{*}$ $\approx$ 2.11 , matching the stated two-read break-even for that window [ 6 ] . The formula’s use is computing the same threshold for a w and r that are not round numbers, and deciding, before writing code, whether a prefix’s expected reuse clears the bar for the TTL about to be selected.

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R^{*}

Symbol R^*

$R^*$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Its accuracy depends on the assumptions and range of use described in the article.

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[6] Pricing ↗

Published contexts (1)

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R^{*} \approx 2.11

Equation 9 · Inference Economics

AI Inference Economics in Practice: An Advanced Technical Guide

This equation gives an approximation: it relates the quantities while allowing an approximation.

is exceeded. At Anthropic’s five-minute rate, w = 1.25 and $R^{*}$ $\approx$ 1.28 : the prefix pays for itself starting with the first read after the write, matching the break-even Anthropic’s pricing page states for that duration [ 6 ] . At the one-hour rate, w = 2 and $R^{*}$ $\approx$ 2.11 , matching the stated two-read break-even for that window [ 6 ] . The formula’s use is computing the same threshold for a w and r that are not round numbers, and deciding, before writing code, whether a prefix’s expected reuse clears the bar for the TTL about to be selected.

Equation guide → · Article →

R∗≈2.11R^{*} \approx 2.11R∗≈2.11