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Equation 2 · Part 6 · The Economics, Energy, and Physical Limits of Claude Code and Agentic Development Tools

addition

ttoken  ≳  2 Nactive β+KV(c)BW,t_{\mathrm{token}} \;\gtrsim\; \frac{2\,N_{\mathrm{active}}\,\beta + \mathrm{KV}(c)}{\mathrm{BW}},
addition

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

The passage around this formula

Underneath all of the pricing mechanics sits a constraint pricing cannot remove: generating one token from a large language model is, for most of a request, bound by how fast bytes can move through accelerator memory rather than by how much arithmetic the accelerator can perform. Producing each token requires reading the model’s active weights and the accumulated key-value cache for that request from memory once; the arithmetic performed per byte read is low, so decoding is memory-bandwidth-bound while only the initial processing of a long prompt is compute-bound, a distinction Pope and colleagues formalized in their analysis of transformer inference efficiency [ 15 ] . Approximately,…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

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