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Equation 8 · How to Evaluate Codex Beyond SWE-bench and Vendor Scores

What does this equation mean?

Bj=(Ntokens,Nturns,Ntools,twall,Ccompute,kattempts).B_j=(N_{\mathrm{tokens}},N_{\mathrm{turns}},N_{\mathrm{tools}},t_{\mathrm{wall}},C_{\mathrm{compute}},k_{\mathrm{attempts}}).

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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BjB_j

Symbol B_j

BjB_j is part of the quantity the equation computes from the expression on the right.

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NtokensN_{\mathrm{tokens}}

Symbol N_tokens

NtN_tokens is an input to the expression that computes the quantity on the left.

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NturnsN_{\mathrm{turns}}

Symbol N_turns

NtN_turns is an input to the expression that computes the quantity on the left.

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NtoolsN_{\mathrm{tools}}

Symbol N_tools

NtN_tools is an input to the expression that computes the quantity on the left.

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twallt_{\mathrm{wall}}

Symbol t_wall

twt_wall is an input to the expression that computes the quantity on the left.

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CcomputeC_{\mathrm{compute}}

Symbol C_compute

CcC_compute is an input to the expression that computes the quantity on the left.

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kattemptsk_{\mathrm{attempts}}

Symbol k_attempts

kak_attempts is an input to the expression that computes the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

For system j , report a resource vector Bj=(Ntokens,Nturns,Ntools,twall,Ccompute,kattempts)B_j=(N_{\mathrm{tokens}},N_{\mathrm{turns}},N_{\mathrm{tools}},t_{\mathrm{wall}},C_{\mathrm{compute}},k_{\mathrm{attempts}}). A resolution curve p(B) is more informative than one point. It reveals marginal returns: whether twice the budget buys substantial success, tiny gains, or merely longer trajectories. It also lets organizations choose configurations on a cost-quality frontier.

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