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Equation 6 · Part 1 · How Training Data and Synthetic Data Actually Work

Symbol p_fail

pfailp_{\text{fail}}
pfailp_{\text{fail}}

What this part means

the fraction that fail correctness or contamination filtering and must be regenerated.

Its job in the formula

pfp_fail is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

where N is the number of exercises targeted, cgeneratec_{\text{generate}} is the compute cost of producing one candidate item, pfailp_{\text{fail}} is the fraction that fail correctness or contamination filtering and must be regenerated, and cregeneratec_{\text{regenerate}} is the cost of another attempt.

The passage around this formula

where N is the number of exercises targeted, cgeneratec_{\text{generate}} is the compute cost of producing one candidate item, pfailp_{\text{fail}} is the fraction that fail correctness or contamination filtering and must be regenerated, and cregeneratec_{\text{regenerate}} is the cost of another attempt. This is not drawn from a specific paper’s disclosed cost model — none of the sources here publish exact figures — it is included only…

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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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Sources cited in the article section

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