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Equation 3 · Part 4 · How AI Inference Serving Actually Works

Numerator: FLOPs performed

I=FLOPs performedbytes read and writtenI = \frac{\text{FLOPs performed}}{\text{bytes read and written}}
FLOPs performed\text{FLOPs performed}

What this part means

The complete quantity above the fraction bar. FLOPs count floating-point arithmetic operations.

Its job in the formula

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

The passage around this formula

The standard way to make this precise is a piece of hardware-performance reasoning called the roofline model, and stating it once explains why every mitigation below targets one phase and not the other. Every accelerator has two ceilings: a peak arithmetic rate, in floating-point operations per second, and a peak memory-bandwidth rate, in bytes per second. Which one binds a given piece of work depends on that work’s arithmetic intensity — the ratio of arithmetic performed to bytes moved: I=FLOPs performedbytes read and writtenI = \frac{\text{FLOPs performed}}{\text{bytes read and written}}. A computation is compute-bound when I exceeds the hardware’s own ratio of FLOPs to bandwidth, and memory-bound when it falls below it. Prefill, processing every position of a prompt…

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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.

Open the illustrated fractions: division written vertically guide →

Sources cited in the surrounding passage

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