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Equation 1 · Part 2 · How AI Inference Economics Actually Work

Symbol C_energy

price per token≳Cfixed+CenergyU⋅Tmax⁡+m\text{price per token} \gtrsim \frac{C_{\text{fixed}} + C_{\text{energy}}}{U \cdot T_{\max}} + m
CenergyC_{\text{energy}}

What this part means

the energy cost per unit time.

Its job in the formula

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

Where the article explains it

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.

The passage around this formula

…a direct measurement of any specific commercial provider’s live-traffic utilization, which providers do not publish.) price per token≳Cfixed+CenergyU⋅Tmax⁡+m\text{price per token} \gtrsim \frac{C_{\text{fixed}} + C_{\text{energy}}}{U \cdot T_{\max}} + m. 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…

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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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Sources cited in the surrounding passage

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