Equation 6 · AI Inference Economics in Practice: An Advanced Technical Guide
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol w
w is part of the quantity the equation computes from the expression on the right.
=
The expressions on both sides represent the same quantity under the stated assumptions.
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What the article says around this equation
is exceeded. At Anthropic’s five-minute rate, w = 1.25 and 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 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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