Publish the verified benchmark: corrected answers, extra books, synthetic problems

ANSWER_AUDIT.md

@@ -93,16 +93,16 @@ because no model can be scored correct on them.
 |---|---|---|---|
 | `algebra_core.2.068` | `algebra_core` | `(-4;24);\ (-6;-2)` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.2.070` | `algebra_core` | `(x_1;y_1)=(0,6;0,3),\quad (x_2;y_2)=(0,4;0,5)` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.2.205` | `algebra_core` | `(2;1),\ (6;-3),\ \left(6+2\sqrt{3};-2-2\sqrt{3}\right),\ \le` | three independent reads agree on the statement and the printed answer - error of the book: the printed answer  |
+| `algebra_core.2.205` | `algebra_core` | `(2;1),\ (6;-3),\ \left(6+2\sqrt{3};-2-2\sqrt{3}\right),\ …` | three independent reads agree on the statement and the printed answer - error of the book: the printed answer … |
 | `algebra_core.2.240` | `algebra_core` | `(10;1),\ \left(-21/2;53/12\right)` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.2.243` | `algebra_core` | `(1;4),(4;1),(-1;-4),(-4;-1)` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.5.002` | `algebra_core` | `x_1=35^\circ+120^\circ\cdot k,\quad x_2=55^\circ+120^\circ\c` | three independent reads agree on the statement and the printed answer |
+| `algebra_core.5.002` | `algebra_core` | `x_1=35^\circ+120^\circ\cdot k,\quad x_2=55^\circ+120^\circ …` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.039` | `algebra_core` | `x_1=\frac{\pi k}{5},\ x_2=\frac{\pi}{8}(4k+3).` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.121` | `algebra_core` | `z_1=2\arctan3+2\pi k,\quad z_2=-2\arctan7+2\pi k` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.147` | `algebra_core` | `x=\frac{\pi}{12}(6k+1)` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.174` | `algebra_core` | `t=\frac{\pi}{2}(4k+1)` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.5.176` | `algebra_core` | `x_1=\frac{\pi}{6}+\pi k;\quad x_2=(-1)^k\frac{\pi}{8}+\frac{` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.5.221` | `algebra_core` | `x_1=-\frac{\pi}{16}(4k+1),\quad x_2=-\frac{1}{4}\arctan\frac` | three independent reads agree on the statement and the printed answer |
+| `algebra_core.5.176` | `algebra_core` | `x_1=\frac{\pi}{6}+\pi k;\quad x_2=(-1)^k\frac{\pi}{8}+\frac …` | three independent reads agree on the statement and the printed answer |
+| `algebra_core.5.221` | `algebra_core` | `x_1=-\frac{\pi}{16}(4k+1),\quad x_2=-\frac{1}{4}\arctan …` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.227` | `algebra_core` | `t=\arctan\frac{4}{5}+2\pi k` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.259` | `algebra_core` | `x=-\frac{\pi}{8}(4k+1)` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.269` | `algebra_core` | `x=-\frac{\pi}{4}(4k+1)` | three independent reads agree on the statement and the printed answer |
@@ -128,35 +128,35 @@ because no model can be scored correct on them.
 | `falin_algebra.1069` | `falin_algebra` | `\left(\frac{5}{3};-\frac{7}{3}\right)` | no assignment of the printed tuple (\frac{5}{3}; -\frac{7}{3}\right) satisfies the system |
 | `falin_algebra.p137.1083` | `falin_algebra` | `\left(\frac{1}{5}; \frac{1}{81}\right)` | no assignment of the printed tuple (\frac{1}{5};  \frac{1}{81}\right) satisfies the system |
 | `falin_algebra.1123` | `falin_algebra` | `\{(8\log_5 2-6\log_2 5;\,8\log_2 5-12\log_5 2)\}` | no assignment of the printed tuple (8\log_5 2-6\log_2 5; \,8\log_2 5-12\log_5 2) satisfies the system |
-| `falin_algebra.p370.598` | `falin_algebra` | `(-\infty;\, -\tfrac{5+\sqrt{21}}{2}) \cup (\tfrac{-5+\sqrt{2` | claimed point x=-5.79129 gives F=961.17, which violates the inequality |
+| `falin_algebra.p370.598` | `falin_algebra` | `(-\infty;\, -\tfrac{5+\sqrt{21}}{2}) \cup (\tfrac{-5+\sqrt …` | claimed point x=-5.79129 gives F=961.17, which violates the inequality |
 | `falin_algebra.p382.914` | `falin_algebra` | `x\leq 0` | x=0.275 satisfies the inequality but is missing from the book's answer |
 | `falin_algebra.p383.957` | `falin_algebra` | `x \leq 0` | claimed point t=-10 gives F=2.99024, which violates the inequality |
 | `falin_algebra.p390.1020` | `falin_algebra` | `(-1; 2]` | claimed point x=-0.85 gives F=-2.2992, which violates the inequality |
 | `shabunin.p183.Example 3` | `shabunin` | `(1;2), (-1;0)` | no assignment of the printed tuple (1; 2) satisfies the system |
 | `shabunin.p190.Example 2` | `shabunin` | `(1;2;3),\ (-1;-2;-3)` | no assignment of the printed tuple (1; 2; 3) satisfies the system |
-| `shabunin.p194.Пример 8` | `shabunin` | `(2;\sqrt[3]{3}; \sqrt[3]{9}),\ \left(\frac{1}{\sqrt[3]{2}}; ` | no assignment of the printed tuple (2; \sqrt[3]{3};  \sqrt[3]{9}) satisfies the system |
+| `shabunin.p194.Пример 8` | `shabunin` | `(2;\sqrt[3]{3}; \sqrt[3]{9}),\ \left(\frac{1}{\sqrt[3]{2}}; …` | no assignment of the printed tuple (2; \sqrt[3]{3};  \sqrt[3]{9}) satisfies the system |
 | `shabunin.p222.Пример 2` | `shabunin` | `(1; 3); \left(\frac{9}{4}; 4\right)` | no assignment of the printed tuple (1;  3) satisfies the system |
 | `kozko_params.p163.3` | `kozko_params` | `0 < x \leqslant 1/2;\ x \geqslant \log_2 3` | claimed point x=2.58496 gives F=-24.8292, which violates the inequality |
 | `kozko_params.2003-2-3` | `kozko_params` | `[3/7; 1) \cup (3; +\infty)` | claimed endpoint 0.428571 gives F=-1.1818182, which violates the inequality |
 | `kozko_params.p172.6` | `kozko_params` | `(1; 18 - 12\sqrt{2}]` | a=500.545 satisfies the inequality but is missing from the book's answer |
 | `kozko_params.p173.6` | `kozko_params` | `(1; 8 - 4\sqrt{3}]` | a=500.565 satisfies the inequality but is missing from the book's answer |
 | `kozko_params.p176.Задача 3` | `kozko_params` | `[(-1-2\sqrt{29})/5;\,2]` | claimed point x=-2.81962 gives F=0.68419, which violates the inequality |
-| `kozko_params.p188.4` | `kozko_params` | `(x; y) = (0; \sqrt{3}); (0; -\sqrt{3}); \left(\sqrt{\frac{3}` | no assignment of the printed tuple (x;  y) satisfies the system |
-| `kozko_params.p189.4` | `kozko_params` | `(x;y) = (0;\sqrt{2});\ (0;-\sqrt{2});\ \left(\sqrt{\frac{2}{` | no assignment of the printed tuple (x; y) satisfies the system |
-| `kozko_params.p195.3` | `kozko_params` | `\left\{\left(-\frac{1}{2}; \log_9 \frac{9}{2}\right); \left(` | no assignment of the printed tuple (-\frac{1}{2};  \log_9 \frac{9}{2}\right) satisfies the system |
-| `kozko_params.p237.7` | `kozko_params` | `\left(\dfrac{\pi}{4}+2\pi m;\ \dfrac{3\pi}{4}+2\pi k\right);` | no assignment of the printed tuple (\dfrac{\pi}{4}+2\pi m; \ \dfrac{3\pi}{4}+2\pi k\right) satisfies the syste |
+| `kozko_params.p188.4` | `kozko_params` | `(x; y) = (0; \sqrt{3}); (0; -\sqrt{3}); \left(\sqrt{\frac …` | no assignment of the printed tuple (x;  y) satisfies the system |
+| `kozko_params.p189.4` | `kozko_params` | `(x;y) = (0;\sqrt{2});\ (0;-\sqrt{2});\ \left(\sqrt{\frac{2} …` | no assignment of the printed tuple (x; y) satisfies the system |
+| `kozko_params.p195.3` | `kozko_params` | `\left\{\left(-\frac{1}{2}; \log_9 \frac{9} …` | no assignment of the printed tuple (-\frac{1}{2};  \log_9 \frac{9}{2}\right) satisfies the system |
+| `kozko_params.p237.7` | `kozko_params` | `\left(\dfrac{\pi}{4}+2\pi m;\ \dfrac{3\pi}{4}+2\pi k …` | no assignment of the printed tuple (\dfrac{\pi}{4}+2\pi m; \ \dfrac{3\pi}{4}+2\pi k … |
 | `kozko_params.ВАРИАНТ 2004 (июль), социологический факультет, 1` | `kozko_params` | `[-5; -3].` | claimed endpoint -5 gives F=0.66666667, which violates the inequality |
 | `kozko_params.p271.2` | `kozko_params` | `(-\infty; 1/4]` | claimed point x=-0.75 gives F=0.275412, which violates the inequality |
 | `kozko_params.p274.1` | `kozko_params` | `2` | claimed integer 2 gives F=9, which violates the inequality |
-| `kozko_params.ВАРИАНТ 2005 (июль), географический факультет, 1` | `kozko_params` | `1. (x;y) = (-\pi/2 \pm \pi/3 + 2\pi k;\ 2\pi m),\ k,m \in \m` | no assignment of the printed tuple (x; y) satisfies the system |
-| `kozko_params.p280.4` | `kozko_params` | `(-\infty;\, 1-\sqrt{14}] \cup [-\sqrt{17}/3;\, -2) \cup (1;\` | x=-2.19 satisfies the inequality but is missing from the book's answer |
+| `kozko_params.ВАРИАНТ 2005 (июль), географический факультет, 1` | `kozko_params` | `1. (x;y) = (-\pi/2 \pm \pi/3 + 2\pi k;\ 2\pi m),\ k,m \in …` | no assignment of the printed tuple (x; y) satisfies the system |
+| `kozko_params.p280.4` | `kozko_params` | `(-\infty;\, 1-\sqrt{14}] \cup [-\sqrt{17}/3;\, -2) \cup (1; …` | x=-2.19 satisfies the inequality but is missing from the book's answer |
 | `kozko_params.p281.1` | `kozko_params` | `x=-2` | claimed solution 'x=-2' fails the equation |
 | `kozko_params.p289.2` | `kozko_params` | `(-\infty;2]` | claimed endpoint 2 gives F=-0.17157288, which violates the inequality |
 | `kozko_params.p290.2` | `kozko_params` | `(-\infty; 0]` | claimed point x=-10 gives F=0.00537474, which violates the inequality |
 | `kozko_params.Задача 1 (Вариант 2006, апрель)` | `kozko_params` | `[-2; (7+\sqrt{21})/21)` | claimed point x=6.14955 gives F=-0.294805, which violates the inequality |
 | `kozko_params.p293.Задача 2` | `kozko_params` | `[-3; (5+\sqrt{21})/2)` | claimed endpoint -3 gives F=-5, which violates the inequality |
-| `gelfand_trig.p146.24.14` | `gelfand_trig` | `(x;y) = \left(\frac{\pi}{2} + \pi(k+n); -\frac{\pi}{2} + \pi` | no assignment of the printed tuple (x; y) satisfies the system |
-| `gelfand_trig.p147.24.14` | `gelfand_trig` | `(x;y) = \left(\frac{\pi}{2} + \pi(k+n); -\frac{\pi}{2} + \pi` | no assignment of the printed tuple (x; y) satisfies the system |
+| `gelfand_trig.p146.24.14` | `gelfand_trig` | `(x;y) = \left(\frac{\pi}{2} + \pi(k+n); -\frac{\pi}{2} + …` | no assignment of the printed tuple (x; y) satisfies the system |
+| `gelfand_trig.p147.24.14` | `gelfand_trig` | `(x;y) = \left(\frac{\pi}{2} + \pi(k+n); -\frac{\pi}{2} + …` | no assignment of the printed tuple (x; y) satisfies the system |
 
 ## Printed answers only suspected to be wrong
 
@@ -168,83 +168,83 @@ out of the scored split as well.
 
 | id | source | printed answer | what the engine found |
 |---|---|---|---|
-| `algebra_core.1.023` | `algebra_core` | `0.5a^3(a-1)` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.027` | `algebra_core` | `-4` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.028` | `algebra_core` | `\frac{2}{\sqrt[3]{r^2}}\left(r^2-\sqrt{r^4-16}\right)` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.039` | `algebra_core` | `y^2` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.041` | `algebra_core` | `-4` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.050` | `algebra_core` | `2\sqrt[6]{a^5/a}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.053` | `algebra_core` | `\sqrt{6x}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.054` | `algebra_core` | `\sqrt[3]{20x}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.059` | `algebra_core` | `-1` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.063` | `algebra_core` | `a^{1/3}+b^{1/3}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.067` | `algebra_core` | `1` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.068` | `algebra_core` | `\frac{1}{a\left(\sqrt[m]{a}-\sqrt[n]{a}\right)}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.069` | `algebra_core` | `6` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.080` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.084` | `algebra_core` | `4p-\sqrt{4p^2-1}` | numeric difference over 3 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.085` | `algebra_core` | `\sqrt{a^2-1}` | numeric difference over 4 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.086` | `algebra_core` | `\frac{1}{\sqrt{a}+\sqrt{2}}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.089` | `algebra_core` | `(1-a)/\sqrt{a}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.098` | `algebra_core` | `\sqrt[3]{x+y}-\sqrt[3]{x-y}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.100` | `algebra_core` | `x+y` | numeric difference over 3 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.101` | `algebra_core` | `2` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.120` | `algebra_core` | `3/5` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.121` | `algebra_core` | `31/3` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.122` | `algebra_core` | `\sqrt[12]{32}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.123` | `algebra_core` | `0.1` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.124` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.135` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.136` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.137` | `algebra_core` | `\frac{a+b}{ab}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.142` | `algebra_core` | `-\frac{\sqrt{6}}{2}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.161` | `algebra_core` | `1) \frac{x^2+5x-3}{x^4}; 2) \frac{(x+2)(x+3)}{x^4}; 3) \frac` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.184` | `algebra_core` | `\frac{1}{x-\sqrt{2x+1}}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.213` | `algebra_core` | `\frac{z^2}{z^2+z+1}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.217` | `algebra_core` | `\sqrt{a^2-1}` | numeric difference over 4 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.222` | `algebra_core` | `-\frac{\sqrt{x-2}}{x+2}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.224` | `algebra_core` | `\sqrt{a}\left(\sqrt{2a+1}-\sqrt{a}\right)` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.226` | `algebra_core` | `2.4` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.237` | `algebra_core` | `2` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.241` | `algebra_core` | `1` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.286` | `algebra_core` | `m/2` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.322` | `algebra_core` | `1) m-n; 2) n-m; 3) m-n` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.323` | `algebra_core` | `2x^2-a^2 if x<-\|a\|; -a^2 if x>\|a\|` | branch '2x^2-a^2' differs numerically - reported as suspected, not as a refutation: the difference can come fr |
-| `algebra_core.1.324` | `algebra_core` | `b-4a if a\in[0,\sqrt{2}); 2(a-1)^2 if a\in[\sqrt{2},+\infty)` | branch '2(a-1)^2' differs numerically - reported as suspected, not as a refutation: the difference can come fr |
-| `algebra_core.1.325` | `algebra_core` | `5/(2\sqrt{x}) if x\in(0,4); (2x-3)/(2\sqrt{x}) if x\in[4,+\i` | branch '5/(2\\sqrt{x})' differs numerically - reported as suspected, not as a refutation: the difference can c |
-| `algebra_core.1.328` | `algebra_core` | `\frac{2-x}{2} if x\in(-\infty,-2); -\frac{x^2+2x+8}{2x} if x` | branch '\\frac{2-x}{2}' differs numerically - reported as suspected, not as a refutation: the difference can c |
-| `algebra_core.1.329` | `algebra_core` | `-x if x\in(0,1); x if x\in(1,\infty)` | branch '-x' differs numerically - reported as suspected, not as a refutation: the difference can come from the |
-| `algebra_core.1.330` | `algebra_core` | `\frac{x-1}{x} if x\in(-\infty,0)\cup[1,\infty); \frac{1-x}{x` | branch '\\frac{x-1}{x}' differs numerically - reported as suspected, not as a refutation: the difference can c |
-| `algebra_core.1.331` | `algebra_core` | `-\frac{z+1}{z} if z\in(-\infty,-1)\cup(0,1); \frac{z+1}{z} i` | branch '-\\frac{z+1}{z}' differs numerically - reported as suspected, not as a refutation: the difference can  |
-| `algebra_core.2.368` | `algebra_core` | `x=2` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.4.080` | `algebra_core` | `\tan\frac{m+n}{2}\alpha` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.4.107` | `algebra_core` | `\tan4\alpha` | numeric difference over 5 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.4.117` | `algebra_core` | `\tan^6\alpha` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.4.257` | `algebra_core` | `\tan^4\frac{\alpha}{2}` | numeric difference over 5 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.4.300` | `algebra_core` | `\frac{4\sin^2\left(\frac{\pi}{4}-4\alpha\right)}{\sin8\alpha` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.4.381` | `algebra_core` | `a) (\cos 2\alpha)_1=-3/5; b) (\cos 2\alpha)_2=4/5` | sides differ numerically - reported as suspected, not as a refutation: the difference can come from the readin |
-| `algebra_core.4.382` | `algebra_core` | `a) 4/5; b) 3/5` | sides differ numerically - reported as suspected, not as a refutation: the difference can come from the readin |
-| `algebra_core.4.412` | `algebra_core` | `-\cos^32x` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.4.488` | `algebra_core` | `A=B=\|\cos\alpha\cos\beta\cos\gamma\|` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.154` | `algebra_core` | `x = \frac{2\pi}{3}(3k \pm 1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.155` | `algebra_core` | `x_1=\frac{\pi}{2}(2k+1),\quad x_2=(-1)^k\frac{\pi}{6}+\pi k` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.156` | `algebra_core` | `t_1=(-1)^k\frac{\pi}{6}+\pi k,\quad t_2=\frac{\pi}{2}(4k+1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.158` | `algebra_core` | `x=\frac{\pi}{6}(6k\pm1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.186` | `algebra_core` | `x_1=2\pi k,\ x_2=\frac{\pi}{2}(2k+1),\ x_3=\frac{\pi}{4}(4k-` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.197` | `algebra_core` | `x_1=\frac{\pi k}{3}; x_2=\frac{\pi}{12}(2k+1).` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.263` | `algebra_core` | `t=\frac{\pi}{3}(3k\pm1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.301` | `algebra_core` | `t_1 = 360^\circ \cdot k; \quad t_2 = 90^\circ (4k+1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.302` | `algebra_core` | `t_1=90^\circ\cdot k;\quad t_2=\pm15^\circ+90^\circ\cdot k` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.311` | `algebra_core` | `x=2\pi k.` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.337` | `algebra_core` | `t=\pi k` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.467` | `algebra_core` | `x=\frac{\pi}{2}(4k+1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.490` | `algebra_core` | `x_1=\arccos\left(\sqrt5-2\right)+2\pi k,\quad x_2=\pi(2k+1).` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.7.045` | `algebra_core` | `890` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.7.201` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.8.055` | `algebra_core` | `[0, 4).` | the book's answer excludes the upper endpoint 4, but it satisfies the inequality - reported as suspected, not  |
-| `algebra_core.10.145` | `algebra_core` | `x is an integer.` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.11.078` | `algebra_core` | `a>4` | the book's answer excludes the lower endpoint 4, but it satisfies the inequality - reported as suspected, not  |
-| `algebra_core.11.252` | `algebra_core` | `0.5\ln 2-1.5` | book says \(0{,}5\ln 2-1{,}5\), computed -128.0 - reported as suspected, not as a refutation: the difference c |
+| `algebra_core.1.023` | `algebra_core` | `0.5a^3(a-1)` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.027` | `algebra_core` | `-4` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.028` | `algebra_core` | `\frac{2}{\sqrt[3]{r^2}}\left(r^2-\sqrt{r^4-16}\right)` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.039` | `algebra_core` | `y^2` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.041` | `algebra_core` | `-4` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.050` | `algebra_core` | `2\sqrt[6]{a^5/a}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.053` | `algebra_core` | `\sqrt{6x}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.054` | `algebra_core` | `\sqrt[3]{20x}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.059` | `algebra_core` | `-1` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.063` | `algebra_core` | `a^{1/3}+b^{1/3}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.067` | `algebra_core` | `1` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.068` | `algebra_core` | `\frac{1}{a\left(\sqrt[m]{a}-\sqrt[n]{a}\right)}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.069` | `algebra_core` | `6` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.080` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.084` | `algebra_core` | `4p-\sqrt{4p^2-1}` | numeric difference over 3 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.085` | `algebra_core` | `\sqrt{a^2-1}` | numeric difference over 4 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.086` | `algebra_core` | `\frac{1}{\sqrt{a}+\sqrt{2}}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.089` | `algebra_core` | `(1-a)/\sqrt{a}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.098` | `algebra_core` | `\sqrt[3]{x+y}-\sqrt[3]{x-y}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.100` | `algebra_core` | `x+y` | numeric difference over 3 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.101` | `algebra_core` | `2` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.120` | `algebra_core` | `3/5` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.121` | `algebra_core` | `31/3` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.122` | `algebra_core` | `\sqrt[12]{32}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.123` | `algebra_core` | `0.1` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.124` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.135` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.136` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.137` | `algebra_core` | `\frac{a+b}{ab}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.142` | `algebra_core` | `-\frac{\sqrt{6}}{2}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.161` | `algebra_core` | `1) \frac{x^2+5x-3}{x^4}; 2) \frac{(x+2)(x+3)}{x^4}; 3) …` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.184` | `algebra_core` | `\frac{1}{x-\sqrt{2x+1}}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.213` | `algebra_core` | `\frac{z^2}{z^2+z+1}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.217` | `algebra_core` | `\sqrt{a^2-1}` | numeric difference over 4 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.222` | `algebra_core` | `-\frac{\sqrt{x-2}}{x+2}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.224` | `algebra_core` | `\sqrt{a}\left(\sqrt{2a+1}-\sqrt{a}\right)` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.226` | `algebra_core` | `2.4` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.237` | `algebra_core` | `2` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.241` | `algebra_core` | `1` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.286` | `algebra_core` | `m/2` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.322` | `algebra_core` | `1) m-n; 2) n-m; 3) m-n` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.1.323` | `algebra_core` | `2x^2-a^2 if x<-\|a\|; -a^2 if x>\|a\|` | branch '2x^2-a^2' differs numerically - reported as suspected, not as a refutation: the difference can come fr … |
+| `algebra_core.1.324` | `algebra_core` | `b-4a if a\in[0,\sqrt{2}); 2(a-1)^2 if a\in[\sqrt{2},+\infty)` | branch '2(a-1)^2' differs numerically - reported as suspected, not as a refutation: the difference can come fr … |
+| `algebra_core.1.325` | `algebra_core` | `5/(2\sqrt{x}) if x\in(0,4); (2x-3)/(2\sqrt{x}) if x\in[4,+ …` | branch '5/(2\\sqrt{x})' differs numerically - reported as suspected, not as a refutation: the difference can c … |
+| `algebra_core.1.328` | `algebra_core` | `\frac{2-x}{2} if x\in(-\infty,-2); -\frac{x^2+2x+8}{2x} if x …` | branch '\\frac{2-x}{2}' differs numerically - reported as suspected, not as a refutation: the difference can c … |
+| `algebra_core.1.329` | `algebra_core` | `-x if x\in(0,1); x if x\in(1,\infty)` | branch '-x' differs numerically - reported as suspected, not as a refutation: the difference can come from the … |
+| `algebra_core.1.330` | `algebra_core` | `\frac{x-1}{x} if x\in(-\infty,0)\cup[1,\infty); \frac{1-x} …` | branch '\\frac{x-1}{x}' differs numerically - reported as suspected, not as a refutation: the difference can c … |
+| `algebra_core.1.331` | `algebra_core` | `-\frac{z+1}{z} if z\in(-\infty,-1)\cup(0,1); \frac{z+1}{z} i …` | branch '-\\frac{z+1}{z}' differs numerically - reported as suspected, not as a refutation: the difference can … |
+| `algebra_core.2.368` | `algebra_core` | `x=2` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.4.080` | `algebra_core` | `\tan\frac{m+n}{2}\alpha` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.4.107` | `algebra_core` | `\tan4\alpha` | numeric difference over 5 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.4.117` | `algebra_core` | `\tan^6\alpha` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.4.257` | `algebra_core` | `\tan^4\frac{\alpha}{2}` | numeric difference over 5 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.4.300` | `algebra_core` | `\frac{4\sin^2\left(\frac{\pi}{4}-4\alpha\right)} …` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.4.381` | `algebra_core` | `a) (\cos 2\alpha)_1=-3/5; b) (\cos 2\alpha)_2=4/5` | sides differ numerically - reported as suspected, not as a refutation: the difference can come from the readin … |
+| `algebra_core.4.382` | `algebra_core` | `a) 4/5; b) 3/5` | sides differ numerically - reported as suspected, not as a refutation: the difference can come from the readin … |
+| `algebra_core.4.412` | `algebra_core` | `-\cos^32x` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.4.488` | `algebra_core` | `A=B=\|\cos\alpha\cos\beta\cos\gamma\|` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.154` | `algebra_core` | `x = \frac{2\pi}{3}(3k \pm 1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.155` | `algebra_core` | `x_1=\frac{\pi}{2}(2k+1),\quad x_2=(-1)^k\frac{\pi}{6}+\pi k` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.156` | `algebra_core` | `t_1=(-1)^k\frac{\pi}{6}+\pi k,\quad t_2=\frac{\pi}{2}(4k+1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.158` | `algebra_core` | `x=\frac{\pi}{6}(6k\pm1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.186` | `algebra_core` | `x_1=2\pi k,\ x_2=\frac{\pi}{2}(2k+1),\ x_3=\frac{\pi}{4}(4k- …` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.197` | `algebra_core` | `x_1=\frac{\pi k}{3}; x_2=\frac{\pi}{12}(2k+1).` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.263` | `algebra_core` | `t=\frac{\pi}{3}(3k\pm1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.301` | `algebra_core` | `t_1 = 360^\circ \cdot k; \quad t_2 = 90^\circ (4k+1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.302` | `algebra_core` | `t_1=90^\circ\cdot k;\quad t_2=\pm15^\circ+90^\circ\cdot k` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.311` | `algebra_core` | `x=2\pi k.` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.337` | `algebra_core` | `t=\pi k` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.467` | `algebra_core` | `x=\frac{\pi}{2}(4k+1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.5.490` | `algebra_core` | `x_1=\arccos\left(\sqrt5-2\right)+2\pi k,\quad x_2=\pi(2k+1).` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.7.045` | `algebra_core` | `890` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.7.201` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from … |
+| `algebra_core.8.055` | `algebra_core` | `[0, 4).` | the book's answer excludes the upper endpoint 4, but it satisfies the inequality - reported as suspected, not … |
+| `algebra_core.10.145` | `algebra_core` | `x is an integer.` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d … |
+| `algebra_core.11.078` | `algebra_core` | `a>4` | the book's answer excludes the lower endpoint 4, but it satisfies the inequality - reported as suspected, not … |
+| `algebra_core.11.252` | `algebra_core` | `0.5\ln 2-1.5` | book says \(0{,}5\ln 2-1{,}5\), computed -128.0 - reported as suspected, not as a refutation: the difference c … |
 | `falin_algebra.269` | `falin_algebra` | `x = \dfrac{-3 + \sqrt{17}}{2}.` | sides differ numerically |
 | `falin_algebra.540` | `falin_algebra` | `\{\tfrac{2}{5};\, 10\}.` | the two sides of the identity differ at every tested point |
 | `falin_algebra.p81.622` | `falin_algebra` | `(-\infty; -2] \cup (-1; 0) \cup (0; +\infty).` | the book's answer excludes the upper endpoint 0, but it satisfies the inequality |
@@ -254,7 +254,7 @@ out of the scored split as well.
 | `falin_algebra.926` | `falin_algebra` | `[-18;-3] \cup (0;2).` | the book's answer includes the upper endpoint -3, where equality holds |
 | `falin_algebra.980` | `falin_algebra` | `3.` | integer 2 satisfies the inequality but is not listed |
 | `falin_algebra.1023` | `falin_algebra` | `4017` | integer 4014 satisfies the inequality but is not listed |
-| `falin_algebra.1185` | `falin_algebra` | `S = \frac{\pi}{8}. The figure is the union of two sectors in` | sides differ numerically |
+| `falin_algebra.1185` | `falin_algebra` | `S = \frac{\pi}{8}. The figure is the union of two sectors in …` | sides differ numerically |
 | `falin_algebra.1529` | `falin_algebra` | `k = 3` | integer 4 satisfies the inequality but is not listed |
 | `falin_algebra.p195.1542` | `falin_algebra` | `\frac{3 - \sqrt{7}}{2}` | numeric difference over 2 point(s) |
 | `falin_algebra.p384.965` | `falin_algebra` | `(2 - \log_2^2 3;\, 2]` | the book's answer excludes the lower endpoint -0.512106, but it satisfies the inequality |
@@ -263,12 +263,12 @@ out of the scored split as well.
 | `kozko_params.p18.30` | `kozko_params` | `a \in (0; 1/54)` | the book's answer excludes the upper endpoint 0.0185185, but it satisfies the inequality |
 | `kozko_params.p188.1` | `kozko_params` | `[-7; -2) \cup (-2; -1].` | the book's answer excludes the upper endpoint -2, but it satisfies the inequality |
 | `kozko_params.198_2` | `kozko_params` | `207` | value differs ((1.063057394823077+0j) vs (207+0j)) |
-| `kozko_params.ВАРИАНТ 2004 (май), факультет почвоведения, 2 — Задача 3` | `kozko_params` | `x \in (-\infty; \log_2 3) (listed answer: x \in (\log_6 2; +` | the book's answer excludes the upper endpoint 1.58496, but it satisfies the inequality |
+| `kozko_params.ВАРИАНТ 2004 (май), факультет почвоведения, 2 — Задача 3` | `kozko_params` | `x \in (-\infty; \log_2 3) (listed answer: x \in ( …` | the book's answer excludes the upper endpoint 1.58496, but it satisfies the inequality |
 | `kozko_params.p263.3` | `kozko_params` | `x \in [1; 2) \cup (2; \sqrt{5})` | the book's answer excludes the upper endpoint 2.23607, but it satisfies the inequality |
 | `kozko_params.p266.Задача 1` | `kozko_params` | `(0;\, (5 - \sqrt{17})/2)` | the book's answer excludes the upper endpoint 0.438447, but it satisfies the inequality |
 | `kozko_params.p266.Задача 5` | `kozko_params` | `a \in [\pi/2;\, 3\pi/2 - 3] \cup (5\pi/2 - 6;\, 7\pi/2 - 9]` | the book's answer excludes the lower endpoint 20.5708, but it satisfies the inequality |
 | `prasolov_planimetry.6.37` | `prasolov_planimetry` | `AB \cdot CD + AD \cdot BC = AC \cdot BD` | the two sides of the identity differ at every tested point |
-| `prasolov_planimetry.13.31` | `prasolov_planimetry` | `\boldsymbol{e}_1 \sin\alpha + \boldsymbol{e}_2 \sin\beta + \` | the two sides of the identity differ at every tested point |
+| `prasolov_planimetry.13.31` | `prasolov_planimetry` | `\boldsymbol{e}_1 \sin\alpha + \boldsymbol{e}_2 \sin\beta + …` | the two sides of the identity differ at every tested point |
 | `prasolov_planimetry.31.45` | `prasolov_planimetry` | `a + c = 0` | the two sides of the identity differ at every tested point |
 
 ## Reproducing the audit