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m∗(x)=arg⁡max⁡m[pm(x)V(x)−Cm(x)−Hm(x)−Rm(x)]m^*(x)=\arg\max_m \left[p_m(x)V(x)-C_m(x)-H_m(x)-R_m(x)\right]

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For task features x , choose model and reasoning configuration m to maximize m∗(x)=arg⁡max⁡m[pm(x)V(x)−Cm(x)−Hm(x)−Rm(x)]m^*(x)=\arg\max_m \left[p_m(x)V(x)-C_m(x)-H_m(x)-R_m(x)\right]. where HmH_m is human supervision and RmR_m expected residual risk. The cheapest model can cost more if it creates repeated attempts or review. The strongest model can be wasteful on deterministic extraction.

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m∗(x)=arg⁡max⁡m[pm(x)V(x)−Cm(x)−Hm(x)−Rm(x)],m^*(x)=\arg\max_m \left[p_m(x)V(x)-C_m(x)-H_m(x)-R_m(x)\right],

Equation 13 · AI Industry

The Economics of Codex: Tokens, Sandboxes, Review Time, and Software Throughput

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

For task features x , choose model and reasoning configuration m to maximize m∗(x)=arg⁡max⁡m[pm(x)V(x)−Cm(x)−Hm(x)−Rm(x)]m^*(x)=\arg\max_m \left[p_m(x)V(x)-C_m(x)-H_m(x)-R_m(x)\right]. where HmH_m is human supervision and RmR_m expected residual risk. The cheapest model can cost more if it creates repeated attempts or review. The strongest model can be wasteful on deterministic extraction.

Meanings in this article

  • HmH_m: human supervision and RmR_m expected residual risk.
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