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Equation 20 · Part 7 · How to Evaluate Codex Beyond SWE-bench and Vendor Scores

Symbol q_i

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],
qiq_i

What this part means

the probability a failure escapes detection and is accepted.

Its job in the formula

qiq_i is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

where qiq_i is the probability a failure escapes detection and is accepted.

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

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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See this notation across published equations →

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