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int64 -30,985
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32,286 | a^{c/2}\cdot a^{c/2} = a^c |
39,192 | A\cdot O = O = O\cdot A |
-18,496 | 5 \times r + 5 \times (-1) = 8 \times (5 \times r + 4) = 40 \times r + 32 |
510 | ((-1) + k)! = \left((-1) + k\right) (k + 2(-1))! |
18,497 | 2^{\frac13} + 4^{1/3} = 2^{2/3} + 2^{\frac{1}{3}} |
3,692 | q x + x t = x\cdot (q + t) |
12,245 | \frac{1}{2} = 3/4 \cdot \frac13 \cdot 2 + \dfrac{1}{4} \cdot 0 |
-4,294 | \dfrac{1}{x\cdot 9} = 1/(9\cdot x) |
-635 | e^{\frac{17}{12} \cdot \pi \cdot i \cdot 3} = \left(e^{17 \cdot \pi \cdot i/12}\right)^3 |
21,615 | (1 - x + x^2)^{3n} \left(1 + x\right)^{3n} = ((1 - x + x^2) (1 + x))^{3n} = (1 + x^3)^{3n} |
-5,488 | \frac{t\cdot 2}{(t + (-1))\cdot \left(t + 4\cdot (-1)\right)} = \frac{2\cdot t}{t^2 - t\cdot 5 + 4}\cdot 1 |
39,883 | \sin\left(-a\right) = -\sin(a) |
15,526 | 4x^3 - c^3 = 2xc + 2 |
11,474 | u = x^2\cdot \alpha\Longrightarrow \sqrt{\frac{u}{\alpha}} = x |
5,468 | 1 + 3 \cdot x^1 + 5 \cdot x^2 + \dotsm = \frac{2 \cdot x}{(x + (-1))^2} - \frac{1}{x + \left(-1\right)} = \frac{x + 1}{(x + \left(-1\right))^2} |
15,922 | \frac{a^f}{a^d} = a^{f - d} |
7,388 | \left(5 + 7 \cdot \left(-1\right)\right) \cdot (3 + 5) = -16 |
-194 | \dfrac{7!}{6! (6 (-1) + 7)!} = \binom{7}{6} |
9,947 | \mathbb{E}(x) \mathbb{E}(C) = \mathbb{E}(Cx) |
20,651 | \left\lfloor{y^2 + (-1)}\right\rfloor = (-1) + \left\lfloor{y \cdot y}\right\rfloor |
11,368 | \sin(Z + \alpha) = \cos{\alpha} \cdot \sin{Z} + \sin{\alpha} \cdot \cos{Z} |
12,319 | f^l = f^{l + \left(-1\right)} \cdot f |
-7,381 | 4/13 \cdot 5/14 = \frac{10}{91} |
36,521 | 2! \times \binom{4}{2} = 2 \times 6 = 12 |
4,493 | 12/10\cdot (-\dfrac{15}{10} + 3) = 1.8 |
10,847 | 1/16 + \dfrac19 = \frac{9}{144} + \frac{1}{144} \cdot 16 = 25/144 |
30,977 | K = K\cdot e\Longrightarrow e \in K |
15,867 | 6^3 - 5^2 \cdot 5 = 216 + 125\cdot (-1) = 91 |
32,788 | \frac{3*\pi}{4}*1 = \pi - \dfrac{\pi}{4} |
-10,642 | \frac{9}{25 + s \cdot 15} \cdot \frac14 \cdot 4 = \frac{36}{100 + s \cdot 60} |
3,278 | \tfrac{1}{32} = \frac{1/2}{2}*1/8 |
1,326 | \left(n + 1\right)! = (n + 1)\times n! < (n + 1)\times n^n = n^{n + 1} + n^n \lt n^{n + 1} + n^{n + 1} = 2\times n^{n + 1} < (n + 1)^{n + 1} |
27,496 | \sin(\pi\cdot y) = 2\cdot \cos(\pi\cdot y/2)\cdot \sin\left(\pi\cdot y/2\right) |
-9,357 | -p*20 + 50 = -p*2*2*5 + 2*5*5 |
8,644 | \sin(\pi) \cdot \cos(0) \cdot 2 = 0 |
4,389 | 71 = f \cdot 2 + g_1 \Rightarrow g_1 = 71 - 2 \cdot f = 71 - 2 \cdot (-4) = 71 + 8 = 79 |
19,390 | 0 = -k + k \times x^2 - x^2 + 1 \Rightarrow (k + (-1)) \times ((-1) + x \times x) = 0 |
27,111 | \left(-(x + 1) + x - 3 \cdot (x + \left(-1\right)) + 2 \cdot (2 \cdot (-1) + x) = 2 + x\Longrightarrow x + 2 = 2 \cdot (-1) - x\right)\Longrightarrow x = -2 |
17,487 | 8 = 3 \cdot (2^{\beta + (-1)} + 3 \cdot (-1)) - 2^{\beta + \left(-1\right)} + (-1) = 2^{\beta} + 8 \cdot (-1) |
9,445 | 4^n + n^4 = 2^n \cdot 2^n + (n^2)^2 = (n^2 + 2^n)^2 - 2 \cdot 2^n \cdot n^2 |
17,223 | (\frac{3}{16} + 3/16)^{77} = \left(6/16\right)^{77} |
45,687 | 1 + 0 = 1 - 1 + 1 |
32,603 | x \cdot E_\pi = x \cdot E_\pi |
4,980 | \sin^2(\vartheta) = \left(-\cos(\vartheta*2) + 1\right)/2 |
-1,364 | \frac{\frac12\times 9}{(-2)\times 1/5} = -\frac{5}{2}\times 9/2 |
5,914 | \left(q - \tfrac12\right)^2 + \frac34 = q^2 - q + 1 |
9,639 | (a\cdot b)^2 = b \cdot b\cdot a \cdot a |
4,875 | \sum_{i=1}^x \left(i + 1\right)\cdot D_i^2\cdot ((-1) + i) + \sum_{i=1}^x D_i^2 = \sum_{i=1}^x i^2\cdot D_i^2 |
26,820 | \left((-6) + 9 \cdot B = 3\Longrightarrow 3 + 6 = 9 \cdot B\right)\Longrightarrow B = 1 |
5,177 | 8\cdot z = 5\cdot z + 3\cdot z |
24,544 | -2 + 2\cdot \left(-1\right) + 2\cdot (-1) = (-3)\cdot 2 |
-152 | \dfrac{1}{4! \cdot 2!} \cdot 6! = 15 |
39,097 | \left(a - x\right)^2 = -(-g + h)^2\Longrightarrow (-g + h)^2 + (-x + a)^2 = 0 |
-30,575 | -3\cdot (x \cdot x + 5\cdot \left(-1\right)) = 15 - x^2\cdot 3 |
-19,578 | 3/8\cdot 8/7 = \frac{1/7}{8\cdot \frac13}8 |
26,822 | \frac34 + \frac34 = \frac{3}{2} |
-3,653 | \frac{18\cdot p^4}{21\cdot p^5}\cdot 1 = 18/21\cdot \tfrac{1}{p^5}\cdot p^4 |
17,012 | \frac{1}{24} \cdot 18 = 3/4 |
-4,158 | x \cdot x/6 = x^2/6 |
3,729 | \frac{X^2}{4} + (-1) = (X + 2)\cdot \left(X + 2\cdot (-1)\right)/4 |
40,038 | 0.99 = (-1)*0.01 + 1 |
10,760 | 2\cdot \beta + 1 + 2\cdot x + 1 = (x + \beta + 1)\cdot 2 |
21,944 | 2^{66} + (-1) = (1 + 2^{33})*(2^{33} + (-1)) |
29,890 | \dfrac{1}{(x + \left(-1\right))^2}*(x + (-1)) = \frac{1}{x + (-1)} |
3,051 | x - y < 2\Longrightarrow y \gt 2 \times (-1) + x |
12,869 | \left(c^3 = h^3 \Rightarrow c^9 = h^9\right) \Rightarrow c^2 = h^2 |
10,118 | \sin{\beta}\cdot \sin{x}\cdot 2 = -\cos(x + \beta) + \cos(x - \beta) |
274 | {\frac12 \choose j} = \dfrac{1}{2 \cdot (1/2 + \left(-1\right)) \cdot \left(\frac12 + 2 \cdot (-1)\right) \cdot \cdots \cdot (1/2 - j + 1) \cdot j!} |
20,917 | \cos\left(e + b\right) = -\sin{e} \cdot \sin{b} + \cos{b} \cdot \cos{e} |
10,768 | d > c \Rightarrow c \cdot c = c\cdot c < c\cdot d < d\cdot d = d^2 |
-9,122 | -20\cdot s = -s\cdot 2\cdot 2\cdot 5 |
7,542 | (y*f) * (y*f) = (y*f)^2 |
-25,818 | \dfrac{5}{4\cdot 10} = 5/40 |
20,452 | z \cdot z = (z + (-1)) \cdot (z + (-1)) + z + z + (-1) |
-404 | \frac{51}{2}\cdot \pi - 24\cdot \pi = \pi\cdot \frac32 |
-1,375 | \frac{7}{5}\cdot (-\frac81) = \frac{\frac{1}{5}\cdot 7}{1/8\cdot (-1)} |
12,170 | \sqrt{\sqrt{3}\cdot 2 + 4} = \sqrt{(\sqrt{3} + 1)^2} |
620 | (4 + 2 + (-1))\cdot (4 + \left(-1\right) + 2 + \left(-1\right)) = 5\cdot 4 = 20 |
-611 | -\pi \cdot 10 + \frac{143}{12} \cdot \pi = 23/12 \cdot \pi |
16,924 | \frac{1}{2} (12 + 12 + 12 (-1) + 12 (-1)) = 0 |
1,317 | 1/20881492632000 = \frac{8!}{26!} \cdot 12! |
35,189 | 1/(b\cdot x) = \frac{1}{b\cdot x} |
4,302 | x + f \cdot f\cdot M\cdot 2 = M\cdot f^2 + x + f^2\cdot M |
9,536 | 0 = 1 + x + x \cdot x + \cdots + x^{r + (-1)} = \dfrac{1}{x + (-1)}\cdot \left(x^r + (-1)\right) \Rightarrow 1 = x^r |
25,279 | \cos(-\delta + \pi) = -\cos(\delta) |
-22,200 | \left(t + 6\right)\cdot (4\cdot \left(-1\right) + t) = 24\cdot \left(-1\right) + t^2 + 2\cdot t |
39,538 | \cos{z}\cdot \sin{z}\cdot 2 = \sin{z\cdot 2} |
-16,954 | -8 = 20\cdot z^2 + 4\cdot z - 8\cdot \left(-5\cdot z\right) - -8 = 20\cdot z^2 + 4\cdot z + 40\cdot z + 8 |
36,377 | |l^2| = |l|^2 = |l| |
-20,079 | -1/4 \cdot \dfrac{(-4) \cdot q}{q \cdot (-4)} = \frac{4 \cdot q}{\left(-16\right) \cdot q} |
-17,040 | -p = -p\cdot (-p) + -p\cdot 6 = p^2 - 6\cdot p = p \cdot p - 6\cdot p |
21,573 | y = \frac{1}{2}\cdot (4 \pm \sqrt{16 + 20\cdot (-1) + 4\cdot y}) = (4 \pm \sqrt{4\cdot y + 4\cdot (-1)})/2 = 2 \pm \sqrt{y + (-1)} |
36,153 | 144 = (h + d)^2 = h^2 + d^2 + 2 \cdot h \cdot d = 100 + 2 \cdot h \cdot d |
-28,407 | x^2 - 14 \cdot x + 58 = x^2 - 14 \cdot x + 49 + 9 = \left(x + 7 \cdot \left(-1\right)\right)^2 + 9 = (x \cdot (-7))^2 + 3^2 |
13,468 | (3*f + 2007)^2 = (3*(f + 669))^2 = 9*(f + 669)^2 |
3,135 | (y + 1)^{l + k} = (1 + y)^k \cdot (y + 1)^l |
42,219 | 1 - f = 0 \implies 1 = f |
-5,911 | \dfrac{-12 m + 12 (6 (-1) + m) + (m + 2 \left(-1\right)) \cdot 6}{(m + 6 (-1)) (m + 2 (-1)) \cdot 12} = \frac{\left(6 (-1) + m\right) \cdot 12}{(2 (-1) + m) \left(6 \left(-1\right) + m\right) \cdot 12} + \frac{6}{\left(2 (-1) + m\right) (m + 6 (-1)) \cdot 12} (2 \left(-1\right) + m) - \frac{m \cdot 12}{12 \left(m + 2 (-1)\right) (m + 6 (-1))} |
-28,995 | 0 = \dfrac12 \cdot \left(-3 + 3\right) |
41,041 | \frac14 = \frac18 + 1/8 |
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