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Equation 14 · Part 11 · The Real Economics of Shipping a Model to a Device

addition

TCdevice=Cdev+U+Q⋅cd,TCcloud=Q⋅ccloud,TC_{\mathrm{device}} = C_{\mathrm{dev}} + U + Q \cdot c_{d}, \qquad TC_{\mathrm{cloud}} = Q \cdot c_{\mathrm{cloud}},
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

Define CdevC_{\mathrm{dev}} as the fixed, per-release engineering and QA cost of producing and validating the device-tier variant matrix described above — the harness time, the pass/fail sign-off per tier, per quantization scheme, per chip target. Define U as the cost of distributing model updates to the installed fleet, expanded in the next section. Define cdc_{d} as the marginal cost of one additional on-device inference and ccloudc_{\mathrm{cloud}} as the marginal cost of one additional cloud-served inference of the same model. Total cost over Q queries under each placement is TCdevice=Cdev+U+Q⋅cd,TCcloud=Q⋅ccloudTC_{\mathrm{device}} = C_{\mathrm{dev}} + U + Q \cdot c_{d}, \qquad TC_{\mathrm{cloud}} = Q \cdot c_{\mathrm{cloud}}. and the break-even query volume — the point at which on-device placement stops costing more than cloud…

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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 article section

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