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Equation 15 · Part 13 · The Real Economics of Shipping a Model to a Device

Denominator: c_cloud - c_d

Qdevice∗=Cdev+Uccloud−cd.Q^{*}_{\mathrm{device}} = \frac{C_{\mathrm{dev}} + U}{c_{\mathrm{cloud}} - c_{d}}.
ccloud−cdc_{\mathrm{cloud}} - c_{d}

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

ccc_cloud - cdc_d occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

…cost per query is estimated to increase by 10 times compared to traditional search methods” [ 9 ] — a claim, again, from a party that benefits from cloud inference looking expensive, but directionally consistent with why ccloudc_{\mathrm{cloud}} - cdc_{d} is large enough for the equation above to ever favor the device at all.

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.