← All parts of this equation

Equation 1 · Part 11 · The Unit Economics of a Token

=

c=pinn+pcww+pcrr+pout(y+z)c = p_{\mathrm{in}} n + p_{\mathrm{cw}} w + p_{\mathrm{cr}} r + p_{\mathrm{out}} \left( y + z \right)
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Instrument each request to record five quantities: new input tokens, cache-write tokens, cache-read tokens, visible output tokens, and reasoning tokens. The cost of a single request is then c=pinn+pcww+pcrr+pout(y+z)c = p_{\mathrm{in}} n + p_{\mathrm{cw}} w + p_{\mathrm{cr}} r + p_{\mathrm{out}} \left( y + z \right). where n , w , r , y and z are the five counts in that order and each p is the corresponding published rate. The important feature is the last term: visible output and reasoning share one price, and the reasoning count is the only one of the five you cannot recover by inspecting what came back.

Read this part in the article →

Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

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