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Published equation contexts

Interaction cost≈ng c\text{Interaction cost} \approx \frac{n}{g}\,c

Why this formula appears here

The genuine trade this design makes can be stated without hand-waving. Suppose a task requires n discrete tool calls before it is complete, and let g be the number of those calls that execute between one human checkpoint and the next — the granularity of approval. A tool that asks before every action sets g=1 ; a tool that asks once for an entire plan, or once for an entire background task, sets g close to n . At a fixed cost c for each checkpoint a person has to evaluate, total interaction cost scales with the number of checkpoints: Interaction cost≈ng c\text{Interaction cost} \approx \frac{n}{g}\,c. Now suppose each individual tool call has some small, independent probability p of being consequential and wrong in a way a reviewer would…

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gg

Symbol g

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

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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Its accuracy depends on the assumptions and range of use described in the article.

Published contexts (1)

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Interaction cost≈ng c\text{Interaction cost} \approx \frac{n}{g}\,c

Equation 7 · AI Agents & Systems

Comparing the Main Approaches to Claude Code and Agentic Development Tools

This equation gives an approximation: it relates the quantities while allowing an approximation.

The genuine trade this design makes can be stated without hand-waving. Suppose a task requires n discrete tool calls before it is complete, and let g be the number of those calls that execute between one human checkpoint and the next — the granularity of approval. A tool that asks before every action sets g=1 ; a tool that asks once for an entire plan, or once for an entire background task, sets g close to n . At a fixed cost c for each checkpoint a person has to evaluate, total interaction cost scales with the number of checkpoints: Interaction cost≈ng c\text{Interaction cost} \approx \frac{n}{g}\,c. Now suppose each individual tool call has some small, independent probability p of being consequential and wrong in a way a reviewer would…

Meanings in this article

  • nn: the sets g close to.
  • cc: the fixed cost.
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