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Equation 20 · Part 9 · How to Evaluate Codex Beyond SWE-bench and Vendor Scores

=

U=∑i[pivi−Ci−Hi−(1−pi) qiLi],U=\sum_i\left[p_i v_i-C_i-H_i-(1-p_i)\,q_i L_i\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

Let viv_i be the value of correctly completing task i , CiC_i direct inference and infrastructure cost, HiH_i human specification and review cost, and LiL_i loss from an accepted failure. Expected net value is U=∑i[pivi−Ci−Hi−(1−pi) qiLi]U=\sum_i\left[p_i v_i-C_i-H_i-(1-p_i)\,q_i L_i\right]. where qiq_i is the probability a failure escapes detection and is accepted. A high resolve rate can have negative utility if it requires extreme review or creates rare, expensive escapes. A lower autonomous rate can be valuable if the system reliably identifies useful partial progress and makes review cheap.

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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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