Equation 6 · Part 1 · The Real Cost of Running Claude in Production, Beyond the Per-Token Price

Symbol τ

\tau

\tau

What this part means

the fixed tool and system-prompt tokens added regardless of content.

Its job in the formula

τ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol τArticle meaning

Where the article explains it

For a single request, let n be new input tokens, w cache-write tokens, r cache-read tokens, y visible output tokens, z billed-but-invisible thinking tokens, and $\tau$ the fixed tool and system-prompt tokens added regardless of content.

The passage around this formula

…gap between a rate card and an invoice becomes explicit. For a single request, let n be new input tokens, w cache-write tokens, r cache-read tokens, y visible output tokens, z billed-but-invisible thinking tokens, and $\tau$ the fixed tool and system-prompt tokens added regardless of content. Let $p_{\mathrm{in}}$ , $p_{\mathrm{cw}}$ , $p_{\mathrm{cr}}$ , and $p_{\mathrm{out}}$ be the published rates, and let a $\in$ (0, 1] be the fraction of attempts an application accepts without needing to reissue the request, because it…

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Learn the underlying idea

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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