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Equation 4 · How AI Inference Economics Actually Work

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Tmax⁡T_{\max}

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the chip’s maximum achievable token throughput under ideal batching. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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Tmax⁡T_{\max}

Symbol T_max

the chip’s maximum achievable token throughput under ideal batching.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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What the article says around this equation

Here CfixedC_{\text{fixed}} is the amortized hardware and facility cost per unit time, CenergyC_{\text{energy}} the energy cost per unit time, Tmax⁡T_{\max} the chip’s maximum achievable token throughput under ideal batching, U ∈\in (0,1] the realized utilization fraction, and m a margin term. This is not a model any provider discloses or that this article claims to have measured; it is a bookkeeping identity stated to make one point precisely: U appears in the denominator, so it multiplies with, rather than merely adds to, every other lever in this article. Halving fixed cost through better batching and halving it again through utilization gains compound rather than add. (Analysis: an accounting identity…
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Here CfixedC_{\text{fixed}} is the amortized hardware and facility cost per unit time, CenergyC_{\text{energy}} the energy cost per unit time, Tmax⁡T_{\max} the chip’s maximum achievable token throughput under ideal batching, U ∈\in (0,1] the realized utilization fraction, and m a margin term. This is not a model any provider discloses or that this article claims to have measured; it is a bookkeeping identity stated to make one point precisely: U appears in the denominator, so it multiplies with, rather than merely adds to, every other lever in this article. Halving fixed cost through better batching and halving it again through utilization gains compound rather than add. (Analysis: an accounting identity offered to expose the assumption, not a fitted or disclosed cost model.)

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