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Equation 12 · Part 5 · The Real Cost of Running Claude in Production, Beyond the Per-Token Price

Symbol p_cw

C=pin(n+τ)+pcww+pcrr+pout(y+z)aC = \frac{p_{\mathrm{in}}(n + \tau) + p_{\mathrm{cw}} w + p_{\mathrm{cr}} r + p_{\mathrm{out}}(y + z)}{a}
pcwp_{\mathrm{cw}}

What this part means

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

Its job in the formula

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

The passage around this formula

…tokens, w cache-write tokens, r cache-read tokens, y visible output tokens, z billed-but-invisible thinking tokens, and τ\tau the fixed tool and system-prompt tokens added regardless of content. Let pinp_{\mathrm{in}} , pcwp_{\mathrm{cw}} , pcrp_{\mathrm{cr}} , and poutp_{\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 was neither truncated at the maximum-tokens cap nor lost to a timeout, an overload error, or a…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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