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Equation 21 · Part 2 · Measuring AI Agent Reliability: What the Evidence Actually Supports

=

k=1k=1
=

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

The tau-bench numbers make the distinction concrete rather than abstract. Testing function-calling agents built on frontier models against realistic retail and airline customer-service scenarios — each requiring the agent to follow domain policy, call the right APIs, and leave the backend database in a state matching an annotated goal — the authors found that even strong agents succeeded on well under half of tasks at pass@1, and that reliability across repeats fell sharply as k increased: an agent’s pass ^k score in the retail domain dropped below 25% by k=8 , and airline-domain performance, already lower at k=1 , degraded further from there [ 3 ] . Put in words rather than symbols: an…

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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.

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Sources cited in the surrounding passage

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