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Equation 5 · Part 2 · AI Inference Economics in Practice: An Advanced Technical Guide

Symbol w

R∗=w−r1−rR^{*} = \frac{w - r}{1 - r}
ww

What this part means

w occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

w occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

That convergence on roughly one tenth of base input for a cache read — independently verified today across all three platforms [ 2 , 6 , 10 ] — supports a design rule. Let w be the write-price multiplier for the chosen retention window and r ≈\approx 0.1 the read-price multiplier. For a prefix served identically R times within that window — the first serving is the write, the remaining R-1 are reads — caching beats never caching once R∗=w−r1−rR^{*} = \frac{w - r}{1 - r}. is exceeded.…

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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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