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Equation 6 · Part 4 · Actually Building with the Grok API

Symbol p_o^L

Cost(ni,no)={ni piL+no poL,ni<Tni piH+no poH,ni≥T\text{Cost}(n_i, n_o) = \begin{cases} n_i\, p_i^{L} + n_o\, p_o^{L}, & n_i < T \\ n_i\, p_i^{H} + n_o\, p_o^{H}, & n_i \geq T \end{cases}
poLp_o^{L}

What this part means

poLp_o^L is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

poLp_o^L is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…higher rate applies to the entire request, not just the tokens past the line [ 1 ] . Written as a cost function of input tokens nin_i and output tokens non_o against a threshold T = 200{,}000 , with low-tier prices piLp_i^{L}, poLp_o^{L} and high-tier prices piHp_i^{H}, poHp_o^{H} : Cost(ni,no)={ni piL+no poL,ni<Tni piH+no poH,ni≥T\text{Cost}(n_i, n_o) = \begin{cases} n_i\, p_i^{L} + n_o\, p_o^{L}, & n_i < T \\ n_i\, p_i^{H} + n_o\, p_o^{H}, & n_i \geq T \end{cases}. For grok-4.6 that means a 199,999-token prompt is billed at two dollars per million input tokens, and a 200,001-token prompt — one token longer — is billed at four dollars per million input tokens and twelve dollars per million…

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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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