Table G.2
Structured versus base step-by-step plan comparison, by difficulty (with self-correction).
| Medium | Hard | |||
|---|---|---|---|---|
| Model | Free-form | Structured outputs | Free-form | Structured outputs |
| Rows | ||||
| Gemini 3 Flash | 0.40 ± 0.000 | 0.30 ± 0.100 ↓ | 0.40 ± 0.000 | 0.38 ± 0.045 ~ |
| Gemini 2.5 Pro | 0.50 ± 0.000 | 0.50 ± 0.000 | 0.37 ± 0.048 | 0.34 ± 0.055 ~ |
| Claude Opus 4.6 | 0.44 ± 0.070 | 0.30 ± 0.000 ↓ | 0.59 ± 0.032 | 0.58 ± 0.130 ~ |
| Columns | ||||
| Gemini 3 Flash | 0.81 ± 0.032 | 0.88 ± 0.045 ↑ | 0.30 ± 0.000 | 0.30 ± 0.000 |
| Gemini 2.5 Pro | 0.80 ± 0.047 | 0.84 ± 0.055 ~ | 0.31 ± 0.057 | 0.28 ± 0.045 ~ |
| Claude Opus 4.6 | 0.72 ± 0.042 | 0.70 ± 0.000 ~ | 0.31 ± 0.032 | 0.28 ± 0.045 ~ |
Notes. Each pair shows rows and columns as mean ± std over run-level means; the best value per column is bolded. Markers on structured cells reflect a unpaired permutation test, ↑/↓ when the adjusted p-value rejects equality, ~ otherwise.
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