Equation 20 · Part 12 · How to Evaluate Codex Beyond SWE-bench and Vendor Scores

Starting index or lower bound: i

U=\sum_i\left[p_i v_i-C_i-H_i-(1-p_i)\,q_i L_i\right],

i

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionStarting index or lower bound: iArticle meaning

The passage around this formula

Let $v_i$ be the value of correctly completing task i , $C_i$ direct inference and infrastructure cost, $H_i$ human specification and review cost, and $L_i$ loss from an accepted failure. Expected net value is $U=\sum_i\left[p_i v_i-C_i-H_i-(1-p_i)\,q_i L_i\right]$ . where $q_i$ 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

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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