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數值誤差密度：residual、forward error與conditioning基礎 · 脈衝 R05
本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261015-advance-20261119-r05-numerical-approximation-error-foundations · 2026-10-15 · 100 題
欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。
欄序與來源綁定資料
1. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":-4,"intercept":1,"slope":-3}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(-3, 1, -4, 1/3, 13, 13/3, 13, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(-3, 1, -4, 1/3, 13, 13/3, 13, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
2. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":-3,"intercept":2,"slope":-2}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(-2, 2, -3, 1, 8, 4, 8, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(-2, 2, -3, 1, 8, 4, 8, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
3. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":-2,"intercept":3,"slope":-1}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(-1, 3, -2, 3, 5, 5, 5, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(-1, 3, -2, 3, 5, 5, 5, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
4. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":-1,"intercept":4,"slope":2}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(2, 4, -1, -2, 2, 1, 2, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(2, 4, -1, -2, 2, 1, 2, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
5. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":0,"intercept":5,"slope":1}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(1, 5, 0, -5, 5, 5, 5, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(1, 5, 0, -5, 5, 5, 5, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
6. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":1,"intercept":6,"slope":2}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(2, 6, 1, -3, 8, 4, 8, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(2, 6, 1, -3, 8, 4, 8, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
7. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":2,"intercept":7,"slope":3}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(3, 7, 2, -7/3, 13, 13/3, 13, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(3, 7, 2, -7/3, 13, 13/3, 13, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
8. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":3,"intercept":8,"slope":-3}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(-3, 8, 3, 8/3, 1, 1/3, 1, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(-3, 8, 3, 8/3, 1, 1/3, 1, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
9. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":4,"intercept":9,"slope":-2}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(-2, 9, 4, 9/2, 1, 1/2, 1, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(-2, 9, 4, 9/2, 1, 1/2, 1, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
10. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":5,"intercept":10,"slope":-1}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(-1, 10, 5, 10, 5, 5, 5, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(-1, 10, 5, 10, 5, 5, 5, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
11. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":6,"intercept":11,"slope":2}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(2, 11, 6, -11/2, 23, 23/2, 23, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(2, 11, 6, -11/2, 23, 23/2, 23, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
12. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":7,"intercept":12,"slope":1}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(1, 12, 7, -12, 19, 19, 19, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(1, 12, 7, -12, 19, 19, 19, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
13. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":8,"intercept":13,"slope":2}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(2, 13, 8, -13/2, 29, 29/2, 29, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(2, 13, 8, -13/2, 29, 29/2, 29, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
14. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":9,"intercept":14,"slope":3}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(3, 14, 9, -14/3, 41, 41/3, 41, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(3, 14, 9, -14/3, 41, 41/3, 41, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
15. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":10,"intercept":15,"slope":-3}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(-3, 15, 10, 5, 15, 5, 15, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(-3, 15, 10, 5, 15, 5, 15, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
16. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":11,"intercept":16,"slope":-2}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(-2, 16, 11, 8, 6, 3, 6, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(-2, 16, 11, 8, 6, 3, 6, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
17. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":12,"intercept":17,"slope":-1}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(-1, 17, 12, 17, 5, 5, 5, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(-1, 17, 12, 17, 5, 5, 5, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
18. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":13,"intercept":18,"slope":2}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(2, 18, 13, -9, 44, 22, 44, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(2, 18, 13, -9, 44, 22, 44, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
19. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":14,"intercept":19,"slope":1}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(1, 19, 14, -19, 33, 33, 33, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(1, 19, 14, -19, 33, 33, 33, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
20. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":15,"intercept":20,"slope":2}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(2, 20, 15, -10, 50, 25, 50, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(2, 20, 15, -10, 50, 25, 50, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
21. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":16,"intercept":21,"slope":3}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(3, 21, 16, -7, 69, 23, 69, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(3, 21, 16, -7, 69, 23, 69, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
22. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":17,"intercept":22,"slope":-3}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(-3, 22, 17, 22/3, 29, 29/3, 29, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(-3, 22, 17, 22/3, 29, 29/3, 29, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
23. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":18,"intercept":23,"slope":-2}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(-2, 23, 18, 23/2, 13, 13/2, 13, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(-2, 23, 18, 23/2, 13, 13/2, 13, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
24. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":19,"intercept":24,"slope":-1}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(-1, 24, 19, 24, 5, 5, 5, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(-1, 24, 19, 24, 5, 5, 5, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
25. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-residual-forward；明示資料={"approximation":20,"intercept":25,"slope":2}；請依 [slope, intercept, approximation, exact_root, absolute_residual, forward_error, slope_scaled_forward_error, scale_identity, quantity_distinction] 回答。
查看答案與解釋
(2, 25, 20, -25/2, 65, 65/2, 65, 是, residual_and_forward_error_are_distinct_quantities)
Wave6第十三層核對=(2, 25, 20, -25/2, 65, 65/2, 65, 是, residual_and_forward_error_are_distinct_quantities)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-residual-forward · candidate
26. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[1,3],"slope":-3}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(-3, 1/3, 1, affine_output_absolute_error_bound)
Wave6第十三層核對=(-3, 1/3, 1, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
27. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[2,3],"slope":-2}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(-2, 2/3, 4/3, affine_output_absolute_error_bound)
Wave6第十三層核對=(-2, 2/3, 4/3, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
28. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[3,3],"slope":-1}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(-1, 1, 1, affine_output_absolute_error_bound)
Wave6第十三層核對=(-1, 1, 1, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
29. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[4,3],"slope":2}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(2, 4/3, 8/3, affine_output_absolute_error_bound)
Wave6第十三層核對=(2, 4/3, 8/3, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
30. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[5,3],"slope":1}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(1, 5/3, 5/3, affine_output_absolute_error_bound)
Wave6第十三層核對=(1, 5/3, 5/3, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
31. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[6,3],"slope":2}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(2, 2, 4, affine_output_absolute_error_bound)
Wave6第十三層核對=(2, 2, 4, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
32. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[7,3],"slope":3}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(3, 7/3, 7, affine_output_absolute_error_bound)
Wave6第十三層核對=(3, 7/3, 7, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
33. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[8,3],"slope":-3}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(-3, 8/3, 8, affine_output_absolute_error_bound)
Wave6第十三層核對=(-3, 8/3, 8, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
34. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[9,3],"slope":-2}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(-2, 3, 6, affine_output_absolute_error_bound)
Wave6第十三層核對=(-2, 3, 6, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
35. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[10,3],"slope":-1}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(-1, 10/3, 10/3, affine_output_absolute_error_bound)
Wave6第十三層核對=(-1, 10/3, 10/3, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
36. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[11,3],"slope":2}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(2, 11/3, 22/3, affine_output_absolute_error_bound)
Wave6第十三層核對=(2, 11/3, 22/3, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
37. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[12,3],"slope":1}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(1, 4, 4, affine_output_absolute_error_bound)
Wave6第十三層核對=(1, 4, 4, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
38. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[13,3],"slope":2}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(2, 13/3, 26/3, affine_output_absolute_error_bound)
Wave6第十三層核對=(2, 13/3, 26/3, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
39. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[14,3],"slope":3}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(3, 14/3, 14, affine_output_absolute_error_bound)
Wave6第十三層核對=(3, 14/3, 14, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
40. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[15,3],"slope":-3}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(-3, 5, 15, affine_output_absolute_error_bound)
Wave6第十三層核對=(-3, 5, 15, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
41. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[16,3],"slope":-2}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(-2, 16/3, 32/3, affine_output_absolute_error_bound)
Wave6第十三層核對=(-2, 16/3, 32/3, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
42. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[17,3],"slope":-1}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(-1, 17/3, 17/3, affine_output_absolute_error_bound)
Wave6第十三層核對=(-1, 17/3, 17/3, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
43. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[18,3],"slope":2}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(2, 6, 12, affine_output_absolute_error_bound)
Wave6第十三層核對=(2, 6, 12, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
44. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[19,3],"slope":1}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(1, 19/3, 19/3, affine_output_absolute_error_bound)
Wave6第十三層核對=(1, 19/3, 19/3, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
45. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[20,3],"slope":2}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(2, 20/3, 40/3, affine_output_absolute_error_bound)
Wave6第十三層核對=(2, 20/3, 40/3, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
46. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[21,3],"slope":3}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(3, 7, 21, affine_output_absolute_error_bound)
Wave6第十三層核對=(3, 7, 21, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
47. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[22,3],"slope":-3}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(-3, 22/3, 22, affine_output_absolute_error_bound)
Wave6第十三層核對=(-3, 22/3, 22, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
48. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[23,3],"slope":-2}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(-2, 23/3, 46/3, affine_output_absolute_error_bound)
Wave6第十三層核對=(-2, 23/3, 46/3, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
49. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[24,3],"slope":-1}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(-1, 8, 8, affine_output_absolute_error_bound)
Wave6第十三層核對=(-1, 8, 8, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
50. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-affine-propagation；明示資料={"input_error_bound":[25,3],"slope":2}；請依 [slope, input_absolute_error_bound, output_absolute_error_bound, scope] 回答。
查看答案與解釋
(2, 25/3, 50/3, affine_output_absolute_error_bound)
Wave6第十三層核對=(2, 25/3, 50/3, affine_output_absolute_error_bound)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-affine-propagation · candidate
51. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":1,"slope_a":1,"slope_b":2}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(1, 1, 1, 2, 1/2, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(1, 1, 1, 2, 1/2, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
52. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":2,"slope_a":1,"slope_b":3}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(2, 1, 2, 3, 2/3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(2, 1, 2, 3, 2/3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
53. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":3,"slope_a":1,"slope_b":4}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(3, 1, 3, 4, 3/4, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(3, 1, 3, 4, 3/4, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
54. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":4,"slope_a":1,"slope_b":5}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(4, 1, 4, 5, 4/5, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(4, 1, 4, 5, 4/5, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
55. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":5,"slope_a":1,"slope_b":6}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(5, 1, 5, 6, 5/6, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(5, 1, 5, 6, 5/6, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
56. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":6,"slope_a":1,"slope_b":2}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(6, 1, 6, 2, 3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(6, 1, 6, 2, 3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
57. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":7,"slope_a":1,"slope_b":3}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(7, 1, 7, 3, 7/3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(7, 1, 7, 3, 7/3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
58. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":8,"slope_a":1,"slope_b":4}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(8, 1, 8, 4, 2, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(8, 1, 8, 4, 2, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
59. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":9,"slope_a":1,"slope_b":5}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(9, 1, 9, 5, 9/5, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(9, 1, 9, 5, 9/5, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
60. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":10,"slope_a":1,"slope_b":6}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(10, 1, 10, 6, 5/3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(10, 1, 10, 6, 5/3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
61. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":11,"slope_a":1,"slope_b":2}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(11, 1, 11, 2, 11/2, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(11, 1, 11, 2, 11/2, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
62. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":12,"slope_a":1,"slope_b":3}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(12, 1, 12, 3, 4, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(12, 1, 12, 3, 4, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
63. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":13,"slope_a":1,"slope_b":4}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(13, 1, 13, 4, 13/4, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(13, 1, 13, 4, 13/4, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
64. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":14,"slope_a":1,"slope_b":5}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(14, 1, 14, 5, 14/5, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(14, 1, 14, 5, 14/5, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
65. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":15,"slope_a":1,"slope_b":6}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(15, 1, 15, 6, 5/2, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(15, 1, 15, 6, 5/2, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
66. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":16,"slope_a":1,"slope_b":2}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(16, 1, 16, 2, 8, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(16, 1, 16, 2, 8, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
67. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":17,"slope_a":1,"slope_b":3}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(17, 1, 17, 3, 17/3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(17, 1, 17, 3, 17/3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
68. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":18,"slope_a":1,"slope_b":4}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(18, 1, 18, 4, 9/2, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(18, 1, 18, 4, 9/2, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
69. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":19,"slope_a":1,"slope_b":5}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(19, 1, 19, 5, 19/5, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(19, 1, 19, 5, 19/5, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
70. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":20,"slope_a":1,"slope_b":6}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(20, 1, 20, 6, 10/3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(20, 1, 20, 6, 10/3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
71. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":21,"slope_a":1,"slope_b":2}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(21, 1, 21, 2, 21/2, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(21, 1, 21, 2, 21/2, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
72. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":22,"slope_a":1,"slope_b":3}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(22, 1, 22, 3, 22/3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(22, 1, 22, 3, 22/3, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
73. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":23,"slope_a":1,"slope_b":4}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(23, 1, 23, 4, 23/4, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(23, 1, 23, 4, 23/4, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
74. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":24,"slope_a":1,"slope_b":5}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(24, 1, 24, 5, 24/5, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(24, 1, 24, 5, 24/5, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
75. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-conditioning-witness；明示資料={"residual":25,"slope_a":1,"slope_b":6}；請依 [absolute_residual, first_slope, first_forward_error, second_slope, second_forward_error, forward_errors_differ, conditioning_scope] 回答。
查看答案與解釋
(25, 1, 25, 6, 25/6, 是, same_residual_can_have_different_forward_error_under_different_conditioning)
Wave6第十三層核對=(25, 1, 25, 6, 25/6, 是, same_residual_can_have_different_forward_error_under_different_conditioning)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-conditioning-witness · candidate
76. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"zero_reference","model":{"approximation":1}}；請依 [mode, approximation, reference_description, relative_error_status, relative_error_defined_claim] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(zero_reference, 1, reference=0, relative_error=undefined, 否)
Wave6第十三層核對=(zero_reference, 1, reference=0, relative_error=undefined, 否)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
77. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"inclusive_tolerance","model":{"error":[2,2],"tolerance":[2,2]}}；請依 [mode, absolute_error, tolerance, inclusive_test_result, equality_convention] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(inclusive_tolerance, 1, 1, 是, error<=tolerance_is_true_at_equality)
Wave6第十三層核對=(inclusive_tolerance, 1, 1, 是, error<=tolerance_is_true_at_equality)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
78. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"strict_tolerance","model":{"error":[3,2],"tolerance":[3,2]}}；請依 [mode, absolute_error, tolerance, strict_test_result, equality_convention] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(strict_tolerance, 3/2, 3/2, 否, error<tolerance_is_false_at_equality)
Wave6第十三層核對=(strict_tolerance, 3/2, 3/2, 否, error<tolerance_is_false_at_equality)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
79. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"signed_vs_absolute","model":{"approximation":4,"reference":-4}}；請依 [mode, approximation, reference, signed_error, absolute_error, quantity_identification_claim, boundary] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(signed_vs_absolute, 4, -4, 8, 8, 否, signed_error_and_absolute_error_preserve_different_information)
Wave6第十三層核對=(signed_vs_absolute, 4, -4, 8, 8, 否, signed_error_and_absolute_error_preserve_different_information)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
80. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"zero_reference","model":{"approximation":5}}；請依 [mode, approximation, reference_description, relative_error_status, relative_error_defined_claim] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(zero_reference, 5, reference=0, relative_error=undefined, 否)
Wave6第十三層核對=(zero_reference, 5, reference=0, relative_error=undefined, 否)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
81. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"inclusive_tolerance","model":{"error":[6,2],"tolerance":[6,2]}}；請依 [mode, absolute_error, tolerance, inclusive_test_result, equality_convention] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(inclusive_tolerance, 3, 3, 是, error<=tolerance_is_true_at_equality)
Wave6第十三層核對=(inclusive_tolerance, 3, 3, 是, error<=tolerance_is_true_at_equality)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
82. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"strict_tolerance","model":{"error":[7,2],"tolerance":[7,2]}}；請依 [mode, absolute_error, tolerance, strict_test_result, equality_convention] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(strict_tolerance, 7/2, 7/2, 否, error<tolerance_is_false_at_equality)
Wave6第十三層核對=(strict_tolerance, 7/2, 7/2, 否, error<tolerance_is_false_at_equality)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
83. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"signed_vs_absolute","model":{"approximation":8,"reference":-8}}；請依 [mode, approximation, reference, signed_error, absolute_error, quantity_identification_claim, boundary] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(signed_vs_absolute, 8, -8, 16, 16, 否, signed_error_and_absolute_error_preserve_different_information)
Wave6第十三層核對=(signed_vs_absolute, 8, -8, 16, 16, 否, signed_error_and_absolute_error_preserve_different_information)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
84. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"zero_reference","model":{"approximation":9}}；請依 [mode, approximation, reference_description, relative_error_status, relative_error_defined_claim] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(zero_reference, 9, reference=0, relative_error=undefined, 否)
Wave6第十三層核對=(zero_reference, 9, reference=0, relative_error=undefined, 否)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
85. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"inclusive_tolerance","model":{"error":[10,2],"tolerance":[10,2]}}；請依 [mode, absolute_error, tolerance, inclusive_test_result, equality_convention] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(inclusive_tolerance, 5, 5, 是, error<=tolerance_is_true_at_equality)
Wave6第十三層核對=(inclusive_tolerance, 5, 5, 是, error<=tolerance_is_true_at_equality)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
86. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"strict_tolerance","model":{"error":[11,2],"tolerance":[11,2]}}；請依 [mode, absolute_error, tolerance, strict_test_result, equality_convention] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(strict_tolerance, 11/2, 11/2, 否, error<tolerance_is_false_at_equality)
Wave6第十三層核對=(strict_tolerance, 11/2, 11/2, 否, error<tolerance_is_false_at_equality)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
87. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"signed_vs_absolute","model":{"approximation":12,"reference":-12}}；請依 [mode, approximation, reference, signed_error, absolute_error, quantity_identification_claim, boundary] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(signed_vs_absolute, 12, -12, 24, 24, 否, signed_error_and_absolute_error_preserve_different_information)
Wave6第十三層核對=(signed_vs_absolute, 12, -12, 24, 24, 否, signed_error_and_absolute_error_preserve_different_information)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
88. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"zero_reference","model":{"approximation":13}}；請依 [mode, approximation, reference_description, relative_error_status, relative_error_defined_claim] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(zero_reference, 13, reference=0, relative_error=undefined, 否)
Wave6第十三層核對=(zero_reference, 13, reference=0, relative_error=undefined, 否)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
89. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"inclusive_tolerance","model":{"error":[14,2],"tolerance":[14,2]}}；請依 [mode, absolute_error, tolerance, inclusive_test_result, equality_convention] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(inclusive_tolerance, 7, 7, 是, error<=tolerance_is_true_at_equality)
Wave6第十三層核對=(inclusive_tolerance, 7, 7, 是, error<=tolerance_is_true_at_equality)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
90. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"strict_tolerance","model":{"error":[15,2],"tolerance":[15,2]}}；請依 [mode, absolute_error, tolerance, strict_test_result, equality_convention] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(strict_tolerance, 15/2, 15/2, 否, error<tolerance_is_false_at_equality)
Wave6第十三層核對=(strict_tolerance, 15/2, 15/2, 否, error<tolerance_is_false_at_equality)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
91. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"signed_vs_absolute","model":{"approximation":16,"reference":-16}}；請依 [mode, approximation, reference, signed_error, absolute_error, quantity_identification_claim, boundary] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(signed_vs_absolute, 16, -16, 32, 32, 否, signed_error_and_absolute_error_preserve_different_information)
Wave6第十三層核對=(signed_vs_absolute, 16, -16, 32, 32, 否, signed_error_and_absolute_error_preserve_different_information)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
92. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"zero_reference","model":{"approximation":17}}；請依 [mode, approximation, reference_description, relative_error_status, relative_error_defined_claim] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(zero_reference, 17, reference=0, relative_error=undefined, 否)
Wave6第十三層核對=(zero_reference, 17, reference=0, relative_error=undefined, 否)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
93. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"inclusive_tolerance","model":{"error":[18,2],"tolerance":[18,2]}}；請依 [mode, absolute_error, tolerance, inclusive_test_result, equality_convention] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(inclusive_tolerance, 9, 9, 是, error<=tolerance_is_true_at_equality)
Wave6第十三層核對=(inclusive_tolerance, 9, 9, 是, error<=tolerance_is_true_at_equality)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
94. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"strict_tolerance","model":{"error":[19,2],"tolerance":[19,2]}}；請依 [mode, absolute_error, tolerance, strict_test_result, equality_convention] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(strict_tolerance, 19/2, 19/2, 否, error<tolerance_is_false_at_equality)
Wave6第十三層核對=(strict_tolerance, 19/2, 19/2, 否, error<tolerance_is_false_at_equality)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
95. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"signed_vs_absolute","model":{"approximation":20,"reference":-20}}；請依 [mode, approximation, reference, signed_error, absolute_error, quantity_identification_claim, boundary] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(signed_vs_absolute, 20, -20, 40, 40, 否, signed_error_and_absolute_error_preserve_different_information)
Wave6第十三層核對=(signed_vs_absolute, 20, -20, 40, 40, 否, signed_error_and_absolute_error_preserve_different_information)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
96. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"zero_reference","model":{"approximation":21}}；請依 [mode, approximation, reference_description, relative_error_status, relative_error_defined_claim] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(zero_reference, 21, reference=0, relative_error=undefined, 否)
Wave6第十三層核對=(zero_reference, 21, reference=0, relative_error=undefined, 否)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
97. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"inclusive_tolerance","model":{"error":[22,2],"tolerance":[22,2]}}；請依 [mode, absolute_error, tolerance, inclusive_test_result, equality_convention] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(inclusive_tolerance, 11, 11, 是, error<=tolerance_is_true_at_equality)
Wave6第十三層核對=(inclusive_tolerance, 11, 11, 是, error<=tolerance_is_true_at_equality)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
98. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"strict_tolerance","model":{"error":[23,2],"tolerance":[23,2]}}；請依 [mode, absolute_error, tolerance, strict_test_result, equality_convention] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(strict_tolerance, 23/2, 23/2, 否, error<tolerance_is_false_at_equality)
Wave6第十三層核對=(strict_tolerance, 23/2, 23/2, 否, error<tolerance_is_false_at_equality)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
99. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"signed_vs_absolute","model":{"approximation":24,"reference":-24}}；請依 [mode, approximation, reference, signed_error, absolute_error, quantity_identification_claim, boundary] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(signed_vs_absolute, 24, -24, 48, 48, 否, signed_error_and_absolute_error_preserve_different_information)
Wave6第十三層核對=(signed_vs_absolute, 24, -24, 48, 48, 否, signed_error_and_absolute_error_preserve_different_information)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
100. 數值近似誤差
exact residual、forward error、conditioning與tolerance convention。操作=numerr-boundary；明示資料={"mode":"zero_reference","model":{"approximation":25}}；請依 [mode, approximation, reference_description, relative_error_status, relative_error_defined_claim] 回答。
四種mode為5/5/5/7欄；strict與inclusive兩mode雖同欄數，等號處結果相反。reference=0時relative error未定義。
查看答案與解釋
(zero_reference, 25, reference=0, relative_error=undefined, 否)
Wave6第十三層核對=(zero_reference, 25, reference=0, relative_error=undefined, 否)；依完整明示資料精確重算；affine residual=abs(slope)*forward error，兩者不可混同；zero reference relative error未定義；strict與inclusive tolerance在等號處不同。
本題逐步詳解（AI 二次覆核）
數值近似與誤差 · qf-mod50-numerr-boundary · candidate
原始題目 JSONL · 驗收報告