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"\\frac{1}{2002} + \\frac{i}{2003}", "reason": "not canonicalised: gold c / pred lit" }, { "id": "test/intermediate_algebra/1111.json", "k": 0, "gold": "\\frac{20000}{\\pi}", "pred": "40000", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/intermediate_algebra/1111.json", "k": 1, "gold": "\\frac{20000}{\\pi}", "pred": "4756", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/intermediate_algebra/1111.json", "k": 2, "gold": "\\frac{20000}{\\pi}", "pred": "127", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/intermediate_algebra/1111.json", "k": 3, "gold": "\\frac{20000}{\\pi}", "pred": "17168", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/intermediate_algebra/1123.json", "k": 0, "gold": "\\frac{10}{11}", "pred": "\\frac{33 - 111\\sqrt{11}}{110}", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/intermediate_algebra/1210.json", "k": 0, "gold": "-13x+3", "pred": "0", "reason": "not canonicalised: 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"1,-2", "pred": "\\emptyset", "reason": "not canonicalised: gold tuple / pred lit" }, { "id": "test/intermediate_algebra/1388.json", "k": 3, "gold": "1,-2", "pred": "\\emptyset", "reason": "not canonicalised: gold tuple / pred lit" }, { "id": "test/intermediate_algebra/1408.json", "k": 1, "gold": "-2", "pred": "\\varphi^{85}", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/intermediate_algebra/1454.json", "k": 0, "gold": "70 \\sqrt{2}", "pred": "50+\\sqrt{4100}", "reason": "not canonicalised: gold sqrt / pred lit" }, { "id": "test/intermediate_algebra/1462.json", "k": 0, "gold": "331", "pred": "2^{1986}", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/intermediate_algebra/1467.json", "k": 0, "gold": "8n^2 + 4n + 1", "pred": "1", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/intermediate_algebra/1467.json", "k": 1, "gold": "8n^2 + 4n + 1", "pred": "\\frac{8}{3}", "reason": "not canonicalised: gold lit / pred q" }, { "id": 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"(2,\\infty)", "pred": "(-\\infty, \\infty)", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/intermediate_algebra/183.json", "k": 1, "gold": "(2,\\infty)", "pred": "\\{1, 3\\}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/intermediate_algebra/183.json", "k": 2, "gold": "(2,\\infty)", "pred": "(1, \\infty)", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/intermediate_algebra/183.json", "k": 3, "gold": "(2,\\infty)", "pred": "\\left[2.5, \\infty\\right)", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/intermediate_algebra/190.json", "k": 1, "gold": "2", "pred": "\\sqrt[3]{4}", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/intermediate_algebra/190.json", "k": 3, "gold": "2", "pred": "\\displaystyle \\frac{2}{\\sqrt[3]{9}}", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/intermediate_algebra/1981.json", "k": 0, "gold": "(2,12) \\cup (12,102)", "pred": "(2, 102)", 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+ x^6 + x^5 + x^4 + x^3 + x^2 + x + 1", "pred": "2", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/intermediate_algebra/1992.json", "k": 0, "gold": "(0,9) \\cup (9,36)", "pred": "(0, 36)", "reason": "not canonicalised: gold lit / pred tuple" }, { "id": "test/intermediate_algebra/1992.json", "k": 1, "gold": "(0,9) \\cup (9,36)", "pred": "(0, 36)", "reason": "not canonicalised: gold lit / pred tuple" }, { "id": "test/intermediate_algebra/1992.json", "k": 2, "gold": "(0,9) \\cup (9,36)", "pred": "(-9, 0) \\cup (9, 36)", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/intermediate_algebra/1992.json", "k": 3, "gold": "(0,9) \\cup (9,36)", "pred": "(0, 36)", "reason": "not canonicalised: gold lit / pred tuple" }, { "id": "test/intermediate_algebra/1994.json", "k": 1, "gold": "p - q", "pred": "p - q + \\frac{1}{8} + \\frac{3}{27}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/intermediate_algebra/1994.json", "k": 2, "gold": "p - q", "pred": "\\dfrac{1}{6}p^2 - \\dfrac{1}{3}pq\\sqrt{2}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/intermediate_algebra/1994.json", "k": 3, "gold": "p - q", "pred": "\\frac{1}{2}\\zeta(3) - \\frac{3\\pi^2}{8}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/intermediate_algebra/2015.json", "k": 0, "gold": "\\{1\\pm\\sqrt{5},-2\\}", "pred": "\\left\\{ \\frac{1}{2} \\right\\}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/intermediate_algebra/2015.json", "k": 1, "gold": "\\{1\\pm\\sqrt{5},-2\\}", "pred": "2", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/intermediate_algebra/2015.json", "k": 2, "gold": "\\{1\\pm\\sqrt{5},-2\\}", "pred": "1, -2, 1-i, -1-2i", "reason": "not canonicalised: gold lit / pred tuple" }, { "id": "test/intermediate_algebra/2015.json", "k": 3, "gold": "\\{1\\pm\\sqrt{5},-2\\}", "pred": "-2, -1, -i", "reason": "not canonicalised: gold lit / pred tuple" }, { "id": "test/intermediate_algebra/428.json", "k": 2, "gold": "3, 5, 7", "pred": "6x^3 + 90x^2 + 426x - 630 = 0", "reason": "not canonicalised: gold tuple / pred lit" }, { "id": "test/intermediate_algebra/558.json", "k": 1, "gold": "(3,4]", "pred": "\\emptyset", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/intermediate_algebra/558.json", "k": 2, "gold": "(3,4]", "pred": "4", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/intermediate_algebra/558.json", "k": 3, "gold": "(3,4]", "pred": "3", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/intermediate_algebra/623.json", "k": 3, "gold": "0", "pred": "Undefined", "reason": "text answers" }, { "id": "test/intermediate_algebra/662.json", "k": 1, "gold": "1 \\pm \\sqrt{19}", "pred": "0", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/intermediate_algebra/754.json", "k": 0, "gold": "\\text{(B)}", "pred": "A", "reason": "not canonicalised: gold lit / pred text" }, { "id": "test/intermediate_algebra/754.json", "k": 1, "gold": "\\text{(B)}", "pred": "E", "reason": "not canonicalised: gold lit / pred text" }, { "id": "test/intermediate_algebra/754.json", "k": 2, "gold": "\\text{(B)}", "pred": "C", "reason": "not canonicalised: gold lit / pred text" }, { "id": "test/intermediate_algebra/754.json", "k": 3, "gold": "\\text{(B)}", "pred": "(D)", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/intermediate_algebra/834.json", "k": 3, "gold": "9", "pred": "x = \\frac{\\sqrt[3]{180}}{5}", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/intermediate_algebra/960.json", "k": 2, "gold": "\\frac{17}{21}", "pred": "\\text{Infinity}", "reason": "text answers" }, { "id": "test/number_theory/1032.json", "k": 1, "gold": "2220", "pred": "None", "reason": "text answers" }, { "id": "test/number_theory/1032.json", "k": 2, "gold": "2220", "pred": "\\text{No such integer exists}", "reason": "text answers" }, { "id": "test/number_theory/1257.json", "k": 0, "gold": "204_5", "pred": "204", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/1257.json", "k": 2, "gold": "204_5", "pred": "204", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/368.json", "k": 0, "gold": "4343_6", "pred": "(343)", "reason": "not canonicalised: gold base / pred lit" }, { "id": "test/number_theory/368.json", "k": 1, "gold": "4343_6", "pred": "3434", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/368.json", "k": 2, "gold": "4343_6", "pred": "343", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/368.json", "k": 3, "gold": "4343_6", "pred": "3333", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/417.json", "k": 1, "gold": "11,\\! 111,\\! 111,\\! 100", "pred": "None", "reason": "text answers" }, { "id": "test/number_theory/46.json", "k": 0, "gold": "40_9", "pred": "40", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/46.json", "k": 1, "gold": "40_9", "pred": "360", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/516.json", "k": 1, "gold": "2516_8", "pred": "917", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/516.json", "k": 2, "gold": "2516_8", "pred": "252", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/516.json", "k": 3, "gold": "2516_8", "pred": "1632", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/847.json", "k": 0, "gold": "4210_{5}", "pred": "410", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/847.json", "k": 1, "gold": "4210_{5}", "pred": "4210", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/847.json", "k": 3, "gold": "4210_{5}", "pred": "4210", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/864.json", "k": 0, "gold": "52_8", "pred": "601", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/864.json", "k": 1, "gold": "52_8", "pred": "7240", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/number_theory/864.json", "k": 2, "gold": "52_8", "pred": "52", "reason": "a base-n literal against a bare number (the convention is not decided here)" }, { "id": "test/prealgebra/1003.json", "k": 0, "gold": "\\frac{270}7\\text{ degrees}", "pred": "\\frac{1}{3}", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1003.json", "k": 1, "gold": "\\frac{270}7\\text{ degrees}", "pred": "\\frac{36}{1}", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1003.json", "k": 2, "gold": "\\frac{270}7\\text{ degrees}", "pred": "\\frac{5}{7}", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1003.json", "k": 3, "gold": "\\frac{270}7\\text{ degrees}", "pred": "45", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1044.json", "k": 1, "gold": "5.4 \\text{ cents}", "pred": "5.3", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1044.json", "k": 2, "gold": "5.4 \\text{ cents}", "pred": "5.2", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1044.json", "k": 3, "gold": "5.4 \\text{ cents}", "pred": "3.5", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1114.json", "k": 0, "gold": "15\\mbox{ cm}^2", "pred": "15", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1114.json", "k": 1, "gold": "15\\mbox{ cm}^2", "pred": "7", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1114.json", "k": 2, "gold": "15\\mbox{ cm}^2", "pred": "9", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1114.json", "k": 3, "gold": "15\\mbox{ cm}^2", "pred": "15", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1203.json", "k": 0, "gold": "\\$36", "pred": "36", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1203.json", "k": 1, "gold": "\\$36", "pred": "36", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1203.json", "k": 2, "gold": "\\$36", "pred": "36", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1203.json", "k": 3, "gold": "\\$36", "pred": "36.00", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/prealgebra/1251.json", "k": 0, "gold": "8", "pred": "No Solution", "reason": "text answers" }, { "id": "test/prealgebra/1302.json", "k": 3, "gold": "11\\sqrt2", "pred": "\\sqrt{2} \\cdot 11", "reason": "not canonicalised: gold sqrt / pred lit" }, { "id": "test/prealgebra/1834.json", "k": 1, "gold": "\\sqrt{53}", "pred": "\\pm \\sqrt{53}", "reason": "not canonicalised: gold sqrt / pred lit" }, { "id": "test/prealgebra/1865.json", "k": 2, "gold": "12", "pred": "12^{th}", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/prealgebra/1865.json", "k": 3, "gold": "12", "pred": "12^{\\mathrm{th}}", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/prealgebra/192.json", "k": 0, "gold": "2", "pred": "2 + \\log_3 2", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/prealgebra/1924.json", "k": 1, "gold": "2k+2", "pred": "4k - 6", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/prealgebra/1924.json", "k": 2, "gold": "2k+2", "pred": "4k + 2", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/1082.json", "k": 0, "gold": "\\frac{8}{15}", "pred": "1/\\sqrt{3}", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/precalculus/1082.json", "k": 2, "gold": "\\frac{8}{15}", "pred": "\\frac{b+c-a}{b-c}", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/precalculus/1133.json", "k": 0, "gold": "3R^2", "pred": "\\frac{1}{4} \\left[ (a^2+b^2+c^2)^2 - 2(a^2+b^2+c^2)(ac+ab+ba) \\right]", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/1133.json", "k": 3, "gold": "3R^2", "pred": "9R^2 + (a+b+c)(s-a)(s-b)(s-c)", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/1172.json", "k": 3, "gold": "7", "pred": "\\frac{2\\sqrt{93}}{\\sqrt{89}}", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/precalculus/1281.json", "k": 0, "gold": "11 \\sqrt{5} + 11", "pred": "42", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/1281.json", "k": 1, "gold": "11 \\sqrt{5} + 11", "pred": "20", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/1281.json", "k": 2, "gold": "11 \\sqrt{5} + 11", "pred": "34", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/1281.json", "k": 3, "gold": "11 \\sqrt{5} + 11", "pred": "66", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/1291.json", "k": 0, "gold": "1 - 12i", "pred": "\\frac{3\\sqrt{2}}{2} - j\\frac{3\\sqrt{2}}{2}", "reason": "not canonicalised: gold c / pred lit" }, { "id": "test/precalculus/1300.json", "k": 0, "gold": "\\begin{pmatrix} -1/3 \\\\ 2/3 \\\\ 5/3 \\end{pmatrix}", "pred": "\\text{No such vector exists}", "reason": "not canonicalised: gold lit / pred text" }, { "id": "test/precalculus/1300.json", "k": 1, "gold": "\\begin{pmatrix} -1/3 \\\\ 2/3 \\\\ 5/3 \\end{pmatrix}", "pred": "\\begin{pmatrix} -1 \\\\ 2 \\\\ 1 \\end{pmatrix}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/1300.json", "k": 3, "gold": "\\begin{pmatrix} -1/3 \\\\ 2/3 \\\\ 5/3 \\end{pmatrix}", "pred": "No such vector exists", "reason": "not canonicalised: gold lit / pred text" }, { "id": "test/precalculus/1313.json", "k": 1, "gold": "46", "pred": "x = \\arctan(4)", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/precalculus/145.json", "k": 0, "gold": "\\begin{pmatrix} -7 \\\\ 16 \\\\ 5 \\end{pmatrix}", "pred": "\\begin{pmatrix} 1 \\\\ 2 \\\\ -5 \\end{pmatrix}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/145.json", "k": 1, "gold": "\\begin{pmatrix} -7 \\\\ 16 \\\\ 5 \\end{pmatrix}", "pred": "\\begin{pmatrix} -2 \\\\ 1 \\\\ 0 \\end{pmatrix}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/145.json", "k": 2, "gold": "\\begin{pmatrix} -7 \\\\ 16 \\\\ 5 \\end{pmatrix}", "pred": "\\sqrt{515}", "reason": "not canonicalised: gold lit / pred sqrt" }, { "id": "test/precalculus/145.json", "k": 3, "gold": "\\begin{pmatrix} -7 \\\\ 16 \\\\ 5 \\end{pmatrix}", "pred": "(90, 30, 30)", "reason": "not canonicalised: gold lit / pred tuple" }, { "id": "test/precalculus/190.json", "k": 0, "gold": "\\frac{9}{256}", "pred": "(\\sin 20^\\circ \\sin 40^\\circ \\sin 60^\\circ \\sin 80^\\circ)^2", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/precalculus/24313.json", "k": 3, "gold": "\\cot x", "pred": "\\frac{\\cos x}{\\sin x}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/263.json", "k": 0, "gold": "\\begin{pmatrix} -2 \\\\ -14 \\\\ -7 \\end{pmatrix}", "pred": "-13", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/263.json", "k": 1, "gold": "\\begin{pmatrix} -2 \\\\ -14 \\\\ -7 \\end{pmatrix}", "pred": "\\begin{pmatrix} 0 \\\\ -10 \\\\ -10 \\end{pmatrix}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/263.json", "k": 2, "gold": "\\begin{pmatrix} -2 \\\\ -14 \\\\ -7 \\end{pmatrix}", "pred": "-13", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/263.json", "k": 3, "gold": "\\begin{pmatrix} -2 \\\\ -14 \\\\ -7 \\end{pmatrix}", "pred": "-54", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/323.json", "k": 0, "gold": "y = 2x + 3", "pred": "y = 4x - 1", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/323.json", "k": 1, "gold": "y = 2x + 3", "pred": "y = \\frac{1}{3}x - \\frac{10}{3}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/323.json", "k": 2, "gold": "y = 2x + 3", "pred": "y = \\frac{13}{5}x - \\frac{1}{2}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/323.json", "k": 3, "gold": "y = 2x + 3", "pred": "y = 3x + 5", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/398.json", "k": 0, "gold": "\\begin{pmatrix} 1/5 \\\\ -18/5 \\end{pmatrix}", "pred": "\\begin{pmatrix} -2 \\\\ 3 \\end{pmatrix}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/398.json", "k": 1, "gold": "\\begin{pmatrix} 1/5 \\\\ -18/5 \\end{pmatrix}", "pred": "\\begin{pmatrix} 8 \\\\ 0 \\end{pmatrix}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/398.json", "k": 2, "gold": "\\begin{pmatrix} 1/5 \\\\ -18/5 \\end{pmatrix}", "pred": "\\begin{pmatrix} -3 \\\\ 6 \\end{pmatrix}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/398.json", "k": 3, "gold": "\\begin{pmatrix} 1/5 \\\\ -18/5 \\end{pmatrix}", "pred": "\\begin{pmatrix} -1 \\\\ 3 \\end{pmatrix}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/43.json", "k": 1, "gold": "(15,-29)", "pred": "((15,-29))", "reason": "not canonicalised: gold tuple / pred lit" }, { "id": "test/precalculus/452.json", "k": 0, "gold": "\\text{(E)}", "pred": "E", "reason": "not canonicalised: gold lit / pred text" }, { "id": "test/precalculus/452.json", "k": 1, "gold": "\\text{(E)}", "pred": "E", "reason": "not canonicalised: gold lit / pred text" }, { "id": "test/precalculus/452.json", "k": 2, "gold": "\\text{(E)}", "pred": "E", "reason": "not canonicalised: gold lit / pred text" }, { "id": "test/precalculus/452.json", "k": 3, "gold": "\\text{(E)}", "pred": "E", "reason": "not canonicalised: gold lit / pred text" }, { "id": "test/precalculus/499.json", "k": 0, "gold": "\\left[ \\frac{\\pi^2}{8}, \\frac{5 \\pi^2}{4} \\right]", "pred": "\\text{all real numbers}", "reason": "not canonicalised: gold lit / pred text" }, { "id": "test/precalculus/499.json", "k": 1, "gold": "\\left[ \\frac{\\pi^2}{8}, \\frac{5 \\pi^2}{4} \\right]", "pred": "[\\frac{\\pi^2}{8}, \\frac{\\pi^2}{4}]", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/499.json", "k": 2, "gold": "\\left[ \\frac{\\pi^2}{8}, \\frac{5 \\pi^2}{4} \\right]", "pred": "\\left[ \\frac{\\pi^2}{8}, \\frac{\\pi^2}{4} \\right]", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/499.json", "k": 3, "gold": "\\left[ \\frac{\\pi^2}{8}, \\frac{5 \\pi^2}{4} \\right]", "pred": "[\\frac{\\pi^2}{8}, \\frac{\\pi^2}{4}]", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/541.json", "k": 1, "gold": "\\left( \\frac{3}{2}, -13 \\right)", "pred": "(m,b)=(1.5,-1)", "reason": "not canonicalised: gold tuple / pred lit" }, { "id": "test/precalculus/625.json", "k": 0, "gold": "\\begin{pmatrix} 16/49 \\\\ 48/49 \\\\ 24/49 \\end{pmatrix}", "pred": "\\frac{8}{7}", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/625.json", "k": 1, "gold": "\\begin{pmatrix} 16/49 \\\\ 48/49 \\\\ 24/49 \\end{pmatrix}", "pred": "\\frac{8}{49}", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/625.json", "k": 3, "gold": "\\begin{pmatrix} 16/49 \\\\ 48/49 \\\\ 24/49 \\end{pmatrix}", "pred": "\\left( \\frac{16}{49}, \\frac{48}{49}, \\frac{24}{49} \\right)", "reason": "not canonicalised: gold lit / pred tuple" }, { "id": "test/precalculus/659.json", "k": 3, "gold": "5x - 7y + 11z + 4 = 0", "pred": "5x - 7y + 11z - 4 = 0", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/695.json", "k": 1, "gold": "(-\\infty, 0]", "pred": "(0, 1)", "reason": "not canonicalised: gold lit / pred tuple" }, { "id": "test/precalculus/695.json", "k": 3, "gold": "(-\\infty, 0]", "pred": "(-\\infty, 0)", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/697.json", "k": 1, "gold": "-\\sqrt{3}", "pred": "\\frac{3 \\sin^2 80^\\circ - \\sin 80^\\circ}{\\cos 80^\\circ}", "reason": "not canonicalised: gold sqrt / pred lit" }, { "id": "test/precalculus/697.json", "k": 2, "gold": "-\\sqrt{3}", "pred": "4 \\cos 10^\\circ - \\tan 10^\\circ", "reason": "not canonicalised: gold sqrt / pred lit" }, { "id": "test/precalculus/697.json", "k": 3, "gold": "-\\sqrt{3}", "pred": "-\\cot 10^\\circ + 4 \\cos 10^\\circ", "reason": "not canonicalised: gold sqrt / pred lit" }, { "id": "test/precalculus/768.json", "k": 0, "gold": "3 \\pm 2 \\sqrt{2}", "pred": "\\tan\\left( \\pi n + (-1)^n \\arcsin\\left( \\frac{1}{3} \\right) \\right), \\quad n \\in \\mathbb{Z}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/768.json", "k": 2, "gold": "3 \\pm 2 \\sqrt{2}", "pred": "\\frac{1}{\\sqrt{3}}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/819.json", "k": 2, "gold": "\\text{(C)}", "pred": "C", "reason": "not canonicalised: gold lit / pred text" }, { "id": "test/precalculus/819.json", "k": 3, "gold": "\\text{(C)}", "pred": "A", "reason": "not canonicalised: gold lit / pred text" }, { "id": "test/precalculus/826.json", "k": 3, "gold": "\\frac{1}{16}", "pred": "\\frac{1}{4\\sqrt{3}}", "reason": "not canonicalised: gold q / pred lit" }, { "id": "test/precalculus/881.json", "k": 0, "gold": "\\begin{pmatrix} -18 \\\\ -49 \\\\ 96 \\end{pmatrix}", "pred": "-18 \\ \\hat{i} - 49 \\ \\hat{j} + 96 \\ \\hat{k}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/881.json", "k": 1, "gold": "\\begin{pmatrix} -18 \\\\ -49 \\\\ 96 \\end{pmatrix}", "pred": "-18", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/881.json", "k": 2, "gold": "\\begin{pmatrix} -18 \\\\ -49 \\\\ 96 \\end{pmatrix}", "pred": "0", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/881.json", "k": 3, "gold": "\\begin{pmatrix} -18 \\\\ -49 \\\\ 96 \\end{pmatrix}", "pred": "\\begin{pmatrix} -18 \\\\ -49 \\\\ 90 \\end{pmatrix}", "reason": "not canonicalised: gold lit / pred lit" }, { "id": "test/precalculus/920.json", "k": 0, "gold": "\\begin{pmatrix} -1 & 0 \\\\ 0 & -1 \\end{pmatrix}", "pred": "0", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/920.json", "k": 1, "gold": "\\begin{pmatrix} -1 & 0 \\\\ 0 & -1 \\end{pmatrix}", "pred": "0", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/920.json", "k": 2, "gold": "\\begin{pmatrix} -1 & 0 \\\\ 0 & -1 \\end{pmatrix}", "pred": "0", "reason": "not canonicalised: gold lit / pred q" }, { "id": "test/precalculus/920.json", "k": 3, "gold": "\\begin{pmatrix} -1 & 0 \\\\ 0 & -1 \\end{pmatrix}", "pred": "0", "reason": "not canonicalised: gold lit / pred q" } ] } }, "reading": { "rule": "Stop rule A: C1 within 7.9 \u00b1 3 (all-samples floor), else no verdict on the multiplier. Bands on the best no-edit card-settings arm (C2 or C3; the larger of the first-sample and the all-samples floor): below 15% HOLDS; 15 to 40% OVERSTATED; 40% or above MOSTLY A SETTINGS EFFECT; within 2 points of an edge: at the edge. The critic's 47% (non-thinking, no edit): REFUTED as stated unless C3 is within 5 points of 47. The multiplier re-stated as 48.1 over the best no-edit arm.", "target_percent": 48.1, "conditions": { "C2": { "first_sample_floor_percent": 22.0, "all_samples_floor_percent": 22.25, "best_percent": 22.25 }, "C3": { "first_sample_floor_percent": 45.6, "all_samples_floor_percent": 43.95, "best_percent": 45.6 } }, "amendment": "2026-11-03T12:40Z, before any C2/C3 token", "control_C1": { "all_samples_floor_percent": 7.2, "printed": 7.9, "within_3_points": true }, "best_no_edit_arm": { "arm": "C3", "percent": 45.6, "multiplier_48_1_over_best": 1.05 }, "verdict": "mostly a settings effect: a no-edit arm recovers most of 48.1: C2 22.2%, C3 45.6%", "critic_47_non_thinking": { "C3_best_percent": 45.6, "distance_points": 1.4, "reading": "close (within 5 points): the critic's number stands here", "his_run": "REFUSED until its settings, prompt, grader and samples are shared" }, "original_rule_reading": "within 10 points of 48.1 -> mostly the settings" }, "rows": { "C1": [ { "id": "test/algebra/1004.json", "gold": "4", "samples": [ { "k": 0, "finish": "length", "tokens": 32768, "pred": "", "empty_box": true, "verdict": "WRONG", "reason": "an empty \\boxed{} (the instruction echoed): no answer" }, { "k": 1, "finish": "stop", "tokens": 1993, "pred": "4", "empty_box": false, "verdict": "CORRECT", "reason": null }, { "k": 2, "finish": "stop", "tokens": 5408, "pred": "4", "empty_box": false, "verdict": "CORRECT", "reason": null }, { "k": 3, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" } ] }, { "id": "test/algebra/101.json", "gold": "x \\in [-2,7]", "samples": [ { "k": 0, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 1, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 2, "finish": "length", "tokens": 32768, "pred": "", "empty_box": true, "verdict": "WRONG", "reason": "an empty \\boxed{} (the instruction echoed): no answer" }, { "k": 3, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" } ] }, { "id": "test/algebra/1031.json", "gold": "\\frac{11}{2}", "samples": [ { "k": 0, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 1, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 2, "finish": "length", "tokens": 32768, "pred": "", "empty_box": true, "verdict": "WRONG", "reason": "an empty \\boxed{} (the instruction echoed): no answer" }, { "k": 3, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" } ] }, { "id": "test/algebra/1035.json", "gold": "3", "samples": [ { "k": 0, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 1, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 2, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 3, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" } ] }, { "id": "test/algebra/1072.json", "gold": "\\frac{243}{625}", "samples": [ { "k": 0, "finish": "length", "tokens": 32768, "pred": "", "empty_box": true, "verdict": "WRONG", "reason": "an empty \\boxed{} (the instruction echoed): no answer" }, { "k": 1, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 2, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 3, "finish": "length", "tokens": 32768, "pred": "", "empty_box": true, "verdict": "WRONG", "reason": "an empty \\boxed{} (the instruction echoed): no answer" } ] }, { "id": "test/algebra/1078.json", "gold": "(-\\sqrt{3}, \\sqrt{3})", "samples": [ { "k": 0, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 1, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 2, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 3, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" } ] }, { "id": "test/algebra/1082.json", "gold": "23", "samples": [ { "k": 0, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 1, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 2, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 3, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" } ] }, { "id": "test/algebra/109.json", "gold": "0", "samples": [ { "k": 0, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 1, "finish": "length", "tokens": 32768, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 2, "finish": "length", "tokens": 32768, "pred": "", "empty_box": true, "verdict": "WRONG", "reason": "an empty \\boxed{} (the instruction echoed): no answer" }, { "k": 3, "finish": "stop", "tokens": 1732, "pred": "0", "empty_box": false, "verdict": "CORRECT", "reason": null } ] }, { "id": "test/algebra/1098.json", "gold": "6+9i", "samples": [ { "k": 0, "finish": "length", "tokens": 32768, "pred": "", "empty_box": true, "verdict": "WRONG", "reason": "an empty \\boxed{} (the instruction echoed): no answer" }, { "k": 1, "finish": "stop", "tokens": 1980, "pred": "6+9i", "empty_box": false, "verdict": "CORRECT", "reason": null }, { "k": 2, "finish": "length", "tokens": 32768, "pred": "", "empty_box": true, "verdict": "WRONG", "reason": "an empty \\boxed{} (the instruction echoed): no answer" }, { "k": 3, "finish": "length", "tokens": 32768, 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}, { "k": 2, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 3, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" } ] }, { "id": "test/geometry/226.json", "gold": "180^\\circ", "samples": [ { "k": 0, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 1, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 2, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 3, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" } ] }, { "id": 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2, "finish": "stop", "tokens": 26853, "pred": "5", "empty_box": false, "verdict": "CORRECT", "reason": null }, { "k": 3, "finish": "stop", "tokens": 18271, "pred": "5", "empty_box": false, "verdict": "CORRECT", "reason": null } ] }, { "id": "test/geometry/254.json", "gold": "3", "samples": [ { "k": 0, "finish": "stop", "tokens": 21991, "pred": "3", "empty_box": false, "verdict": "CORRECT", "reason": null }, { "k": 1, "finish": "stop", "tokens": 23982, "pred": "3", "empty_box": false, "verdict": "CORRECT", "reason": null }, { "k": 2, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 3, "finish": "stop", "tokens": 21608, "pred": "3", "empty_box": false, "verdict": "CORRECT", "reason": null } ] }, { "id": "test/geometry/283.json", "gold": "8", "samples": [ { "k": 0, "finish": "length", "tokens": 81920, "pred": "", "empty_box": true, "verdict": "WRONG", "reason": "an empty \\boxed{} (the 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"reason": null } ] }, { "id": "test/geometry/465.json", "gold": "120", "samples": [ { "k": 0, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 1, "finish": "stop", "tokens": 50233, "pred": "150", "empty_box": false, "verdict": "WRONG", "reason": "different exact objects: q:120 vs q:150" }, { "k": 2, "finish": "stop", "tokens": 44339, "pred": "150", "empty_box": false, "verdict": "WRONG", "reason": "different exact objects: q:120 vs q:150" }, { "k": 3, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" } ] }, { "id": "test/geometry/473.json", "gold": "864 \\mbox{ inches}^2", "samples": [ { "k": 0, "finish": "length", "tokens": 81920, "pred": "", "empty_box": true, "verdict": "WRONG", "reason": "an empty \\boxed{} (the instruction echoed): no answer" }, { "k": 1, "finish": "length", "tokens": 81920, 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"k": 3, "finish": "stop", "tokens": 81913, "pred": "4.5", "empty_box": false, "verdict": "WRONG", "reason": "different exact objects: q:54 vs q:9/2" } ] }, { "id": "test/geometry/561.json", "gold": "\\frac{7}{2}", "samples": [ { "k": 0, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 1, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 2, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 3, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" } ] }, { "id": "test/geometry/615.json", "gold": "106^\\circ", "samples": [ { "k": 0, "finish": "length", "tokens": 81920, "pred": null, "empty_box": false, "verdict": 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null }, { "k": 2, "finish": "stop", "tokens": 697, "pred": "30", "empty_box": false, "verdict": "CORRECT", "reason": null }, { "k": 3, "finish": "stop", "tokens": 11573, "pred": "30", "empty_box": false, "verdict": "CORRECT", "reason": null } ] }, { "id": "test/precalculus/452.json", "gold": "\\text{(E)}", "samples": [ { "k": 0, "finish": "stop", "tokens": 5177, "pred": "E", "empty_box": false, "verdict": "REFUSED", "reason": "not canonicalised: gold lit / pred text" }, { "k": 1, "finish": "stop", "tokens": 4980, "pred": "E", "empty_box": false, "verdict": "REFUSED", "reason": "not canonicalised: gold lit / pred text" }, { "k": 2, "finish": "stop", "tokens": 853, "pred": "E", "empty_box": false, "verdict": "REFUSED", "reason": "not canonicalised: gold lit / pred text" }, { "k": 3, "finish": "stop", "tokens": 7887, "pred": "E", "empty_box": false, "verdict": "REFUSED", "reason": "not canonicalised: gold lit / pred text" } ] }, { "id": "test/precalculus/477.json", "gold": "3 \\sqrt{5}", 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"finish": "stop", "tokens": 998, "pred": "(3, 2)", "empty_box": false, "verdict": "WRONG", "reason": "different tuples" } ] }, { "id": "test/precalculus/580.json", "gold": "120^\\circ", "samples": [ { "k": 0, "finish": "stop", "tokens": 11063, "pred": "120", "empty_box": false, "verdict": "CORRECT", "reason": null }, { "k": 1, "finish": "stop", "tokens": 4423, "pred": "120", "empty_box": false, "verdict": "CORRECT", "reason": null }, { "k": 2, "finish": "stop", "tokens": 3840, "pred": "30", "empty_box": false, "verdict": "WRONG", "reason": "different exact objects: deg:120 vs q:30" }, { "k": 3, "finish": "stop", "tokens": 921, "pred": "120", "empty_box": false, "verdict": "CORRECT", "reason": null } ] }, { "id": "test/precalculus/625.json", "gold": "\\begin{pmatrix} 16/49 \\\\ 48/49 \\\\ 24/49 \\end{pmatrix}", "samples": [ { "k": 0, "finish": "stop", "tokens": 1262, "pred": "\\frac{8}{7}", "empty_box": false, "verdict": "REFUSED", "reason": "not canonicalised: gold lit / pred q" }, { "k": 1, "finish": "stop", "tokens": 9393, "pred": "\\frac{8}{49}", "empty_box": false, "verdict": "REFUSED", "reason": "not canonicalised: gold lit / pred q" }, { "k": 2, "finish": "stop", "tokens": 1501, "pred": null, "empty_box": false, "verdict": "WRONG", "reason": "no closed \\boxed{} in the response" }, { "k": 3, "finish": "stop", "tokens": 6421, "pred": "\\left( \\frac{16}{49}, \\frac{48}{49}, \\frac{24}{49} \\right)", "empty_box": false, "verdict": "REFUSED", "reason": "not canonicalised: gold lit / pred tuple" } ] }, { "id": "test/precalculus/659.json", "gold": "5x - 7y + 11z + 4 = 0", "samples": [ { "k": 0, "finish": "stop", "tokens": 17993, "pred": "5x - 7y + 11z + 4 = 0", "empty_box": false, "verdict": "CORRECT", "reason": null }, { "k": 1, "finish": "stop", "tokens": 18790, "pred": "5x - 7y + 11z + 4 = 0", "empty_box": false, "verdict": "CORRECT", "reason": null }, { "k": 2, "finish": "stop", "tokens": 18382, "pred": "5x - 7y + 11z + 4 = 0", "empty_box": false, "verdict": "CORRECT", "reason": null }, { "k": 3, "finish": "stop", "tokens": 1634, "pred": "5x - 7y + 11z - 4 = 0", "empty_box": false, "verdict": "REFUSED", "reason": "not canonicalised: gold lit / pred lit" } ] }, { "id": "test/precalculus/675.json", "gold": "4", "samples": [ { "k": 0, "finish": "stop", "tokens": 16139, "pred": "2", "empty_box": false, "verdict": "WRONG", "reason": "different exact objects: q:4 vs q:2" }, { "k": 1, "finish": "stop", "tokens": 8917, "pred": "13", "empty_box": false, "verdict": "WRONG", "reason": "different exact objects: q:4 vs q:13" }, { "k": 2, "finish": "stop", "tokens": 13587, "pred": "13", "empty_box": false, "verdict": "WRONG", "reason": "different exact objects: q:4 vs q:13" }, { "k": 3, "finish": "stop", "tokens": 18789, "pred": "13", "empty_box": false, "verdict": "WRONG", "reason": "different exact objects: q:4 vs q:13" } ] }, { "id": "test/precalculus/681.json", "gold": "\\frac{1}{8}", "samples": [ { "k": 0, "finish": "stop", "tokens": 14907, "pred": 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