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int64 -30,985
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-11,524 | -9 + 10 + 21 i = 1 + i*21 |
-13,536 | 7 + 7*3 = 7 + 21 = 7 + 21 = 28 |
35,250 | \sin^2\left(x\right) = \sin^2\left(x\right) |
-13,652 | 5 + \tfrac{1}{8}32 = 5 + 4 = 9 |
7,032 | -\frac{1}{13^{1/2}}*5*k + 13^{1/2}*k = \frac{8*k}{13^{1/2}} |
-5,689 | \dfrac{y*2}{(1 + y)*(6*\left(-1\right) + y)} = \frac{2*y}{6*(-1) + y * y - y*5} |
-2,911 | -(4 \cdot 13)^{1/2} + (16 \cdot 13)^{1/2} = -52^{1/2} + 208^{1/2} |
32,506 | \left(B^t\right)^t = B = \frac{1}{B^t} |
-21,908 | -\frac95 + \frac{9}{3} = -\dfrac{27}{5 \cdot 3} \cdot 1 + \frac{9 \cdot 5}{3 \cdot 5} = -\frac{27}{15} + 45/15 = -\frac{1}{15} \cdot \left(27 + 45\right) = \frac{18}{15} |
3,653 | n + 6\cdot n^2 = n\cdot (1 + n\cdot 6) |
33,861 | x^{\left(k + (-1)\right) \cdot 2} = x^{2 \cdot k + 2 \cdot \left(-1\right)} |
6,044 | \frac{y}{y + 2} = \frac{1}{y + 2}\cdot (y + 2 + 2\cdot (-1)) = 1 - \frac{2}{y + 2} |
2,378 | 4 \cdot l_2 \cdot l_2 = l_1^2 \cdot 4 + 100 \cdot l_1 + 76\Longrightarrow (2 \cdot l_2) \cdot (2 \cdot l_2) = (2 \cdot l_1)^2 + 2 \cdot l_1 \cdot 2 \cdot 25 + 625 + 76 + 625 \cdot (-1) |
22,931 | 2\cdot z \cdot z + z\cdot 6 + 3 = (\frac{5}{2} + z)\cdot (2\cdot z + 1) + \dfrac12 |
-19,472 | \frac{1}{5\cdot \frac12}\cdot \dfrac{7}{4} = \dfrac74\cdot \tfrac15\cdot 2 |
33,285 | \dfrac25 = \dfrac25 |
-19,305 | \frac{5 / 4}{1/5 \cdot 3} \cdot 1 = \dfrac{5}{3} \cdot \frac14 \cdot 5 |
4,041 | \sqrt{-x^2 + 1} = \dfrac{(-1) \cdot x}{\sqrt{1 - x^2}} |
23,902 | \frac{1}{5} + \frac13 + 1/4 = \frac{1}{60}47 |
-20,160 | \frac{24}{-12\cdot y + 36\cdot (-1)} = \frac{6}{-3\cdot y + 9\cdot \left(-1\right)}\cdot \frac44 |
17,457 | \frac{9}{64} = \frac{1}{4} \cdot \frac{9}{4}/4 |
23,834 | 100\cdot x^2 = 16\cdot (16 + x^2) \Rightarrow 84\cdot x^2 = 256 |
15,657 | z z - z*2 + 1 = 1 + z z - z - z |
10,985 | \cos{\pi*2}*3 = 3 |
29,045 | \frac{1}{z^6} = (\tfrac{1}{z})^6 |
4,792 | \frac{m}{m + u} + (-1) = \dfrac{u*(-1)}{u + m} |
21,443 | k = \left\{2, 1, k, \ldots\right\} |
12,401 | \frac{1}{n \cdot n + n} = 1/n - \frac{1}{n + 1} |
-6,480 | \dfrac{3*x}{x * x + x*13 + 40} = \dfrac{x*3}{\left(5 + x\right)*(x + 8)} |
10,968 | f^K\cdot f^x = f^{x + K} |
3,638 | 9\cdot \sqrt{10 + (-1)} = 27 |
918 | \frac{\frac{1}{2^l} \cdot l}{-\dfrac{1}{2^l} + 1} = \frac{l}{2^l + (-1)} |
27,057 | \frac{2}{e^{\left(-1\right) (\left(-2\right)*1.0*10^{-10})*1000}} = 2*0.999999 = 1.99999 |
13,945 | b^x = \left(\dfrac{1}{b}\right)^{-x} = \left(\tfrac1b\right)^{-x} |
27,994 | \mathbb{E}(X^4) = \mathbb{E}(X^3)*\mathbb{E}(X) |
38,939 | x^{A + 1} = x*x^A |
26,832 | (2^5 + \left(-1\right)) \cdot \frac{(-1) + 2^{15}}{(2^5 + \left(-1\right)) \cdot (2^3 + (-1))} \cdot ((-1) + 2^2 \cdot 2) = \left(-1\right) + 2^{15} |
28,476 | \binom{6+3-1}{3-1}=\binom{8}{2}=\frac{8\cdot7}{2\cdot 1}=28 |
50,022 | 60 = 17*3 + 9 |
35,625 | 6 (-1) + x^3 - x = 0 \implies x = 2 |
12,611 | {k \choose x}^2 = {k \choose x} {k \choose -x + k} |
-6,348 | \frac{3}{12 \cdot (-1) + 2 \cdot t} = \frac{1}{2 \cdot \left(t + 6 \cdot (-1)\right)} \cdot 3 |
17,374 | \frac{1}{\arctan{x}}\cdot x = (1 - x^2/3 + \frac{x^4}{5} - x^6/7 + \dotsm)^{-1} |
-5,530 | \frac{3}{3*x + 30*(-1)} = \frac{1}{3*(x + 10*\left(-1\right))}*3 |
-7,839 | \frac{-1 + i \times 32}{-5 \times i + 4} = \frac{-1 + 32 \times i}{4 - i \times 5} \times \frac{4 + 5 \times i}{i \times 5 + 4} |
7,896 | 61 = 7^2 + 3 * 3 + 1^2 + 1^2 + 1^2 = 5^2 + 5 * 5 + 3^2 + 1^2 + 1^2 |
20,103 | 2^m = 2^{\left(-1\right) + m}*x^m \Rightarrow 2 = x^m |
-10,395 | \tfrac{20}{20} \cdot \frac{5}{2 \cdot (-1) + q \cdot 3} = \dfrac{100}{q \cdot 60 + 40 \cdot (-1)} |
1,120 | (E_2 \cdot E_1 - E_1 \cdot E_2) \cdot E_1 = -E_2 \cdot E_1^2 + E_1 \cdot E_2 \cdot E_1 |
50,692 | u_1 = -u_1 |
33,914 | -1 = 239 239 - 2*13^4 |
-10,340 | \frac{180}{180*x + 120} = \frac{20}{20}*\frac{9}{9*x + 6} |
20,092 | (x + (-1))^2 = (x + \left(-1\right))*(x + (-1)) = x*(x + (-1)) - x \pm 1 |
27,612 | -i = 1 \Rightarrow 1 \times 1 = (-i)^2 = -1 |
3,574 | det\left(I + A\cdot B\right) = det\left(I + A\cdot B\right) |
11,603 | 2\cdot (-z\cdot 2 - 2\cdot y) = 3\cdot y - z\cdot 7 + z\cdot 3 - 7\cdot y |
-1,453 | -\dfrac{14}{20} = (\left(-14\right)*1/2)/(20*1/2) = -\dfrac{1}{10}*7 |
-20,216 | \dfrac{1}{-y \cdot 45 + 72 \cdot (-1)} \cdot (56 + y \cdot 35) = -\frac19 \cdot 7 \cdot \dfrac{8 \cdot (-1) - 5 \cdot y}{8 \cdot (-1) - 5 \cdot y} |
12,370 | \left(z + 2\cdot \tau\right)^2 = 4\cdot (z\cdot \tau)^2 - 24\cdot z\cdot \tau + 49 = 4\cdot z\cdot \tau\cdot (z\cdot \tau + 6\cdot \left(-1\right)) + 49 |
4,979 | \sin(\pi/2 + x) = \sin(\frac{\pi}{2} - -x) = \cos(-x) = \cos(x) |
37,295 | 2^{\tfrac12} = 2^{\frac{1}{2}} |
33,084 | \sin^2{\frac{4*\pi}{7}} - \sin^2{\frac{2*\pi}{7}} = 2*\sin{\pi/7}*\cos{\frac{3*\pi}{7}} \gt 0 |
-12,111 | 8/15 = \dfrac{x}{12 \cdot \pi} \cdot 12 \cdot \pi = x |
26,929 | 1 + z = \frac{(-1) + z^2}{(-1) + z} |
28,782 | (1 + y * y - y)*(1 + y) = 1 + y^3 |
22,039 | \left(h^2 + h\cdot f + f^2\right)\cdot (-f + h) = -f^3 + h^3 |
29,289 | F^1 = \dfrac1F |
-20,878 | \frac{-70 \cdot x + 21 \cdot \left(-1\right)}{7 \cdot \left(-1\right) + 7 \cdot x} = \frac{1}{x + (-1)} \cdot (-10 \cdot x + 3 \cdot \left(-1\right)) \cdot \frac77 |
9,409 | \left(a_2 \cdot a_1\right)^6 = a_1^2 \cdot a_1^2 \cdot a_1^2 \cdot (a_2^3)^2 |
-26,648 | 100 \cdot (-1) + Z^8 \cdot 81 = \left(9 \cdot Z^4\right)^2 - 10^2 |
2,684 | 3/28 = \frac174 \cdot 0 + 3 \cdot 1/7/4 |
30,928 | e^{\ln\left(D\right)} = D |
8,533 | \left(x + 1\right) \cdot \left(x + 2\right) = x \cdot x + 3 \cdot x + 2 \gt 2 \cdot x |
17,926 | x = -k \cdot k \cdot k + \dfrac{r}{3 \cdot k} \Rightarrow 0 = k^6 + k \cdot k^2 \cdot x - \dfrac{r^3}{27} |
-24,658 | 2/18 = \dfrac{2}{2 \times 9} |
26,253 | -\frac{1}{7} \cdot 2 = -2/7 |
32,226 | |49\cdot (-1) + x \cdot x| = |x + 7\cdot (-1)|\cdot |x + 7| |
-27,759 | \frac{\text{d}}{\text{d}y} (2 \tan(y)) = 2 \frac{\text{d}}{\text{d}y} \tan(y) = 2 \sec^2\left(y\right) |
13,619 | -\sin(x) \sin\left(z\right) + \cos(x) \cos(z) = \cos(x + z) |
-7,936 | (100 - 105 \cdot i - 40 \cdot i + 42 \cdot \left(-1\right))/29 = \frac{1}{29} \cdot \left(58 - 145 \cdot i\right) = 2 - 5 \cdot i |
-504 | (e^{\frac{13}{12}\cdot \pi\cdot i})^{16} = e^{16\cdot i\cdot \pi\cdot 13/12} |
-13,782 | 2 + 5 \times 6 = 2 + 30 = 32 |
-17,403 | 1.173 = 117.3/100 |
21,235 | 100! = 97 \cdot 95! \cdot 96 \cdot 98 \cdot 99 \cdot 100 |
22,870 | ((\tfrac54)^n + (-1)) \cdot 4^n = 5^n - 4^n |
30,013 | (z + 1)\cdot (z + 3\cdot (-1)) = z^2 - 2\cdot z + 3\cdot \left(-1\right) |
19,238 | (-b + h) \cdot (h + b) = h^2 - b^2 |
7,212 | e^{|-z + x| + 1} = e^1 e^{|x - z|} |
22,043 | \frac{1}{4} 3 = \frac14 3 |
28,727 | 2\cdot (2\cdot (-1) + 2^{n + 1}) = 2^{2 + n} + 4\cdot (-1) |
2,115 | z/\vartheta = \frac{z}{\vartheta} |
3,189 | \left(k + 1\right)! = (k + 1) \cdot k! > (k + 1) \cdot 2^k |
13,278 | 0 = y'' + 2 + 4\cdot (-1)\Longrightarrow y'' = 2 |
4,649 | x*g_i = g_i*x |
13,744 | \frac{\frac{1}{(1 - x)^2}}{1 - x}\cdot 1 = \frac{1}{(1 - x)^3} |
4,886 | -x^2 + (x + k)^2 = k \cdot (k + x \cdot 2) |
1,556 | {x \choose r} = \frac{x!}{r! \cdot (x - r)!} |
-7,710 | (8 - 4 i - 16 i + 8 (-1))/20 = (0 - 20 i)/20 = -i |
6,649 | y^2 \cdot 9 + x^2 - 6 \cdot x \cdot y = 16\Longrightarrow 16 = (-3 \cdot y + x)^2 |
34,868 | 2 = \frac{1}{4} \cdot 4 + 7/7 |
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