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int64 -30,985
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8,016 | \binom{4}{1}\cdot \binom{4}{1}\cdot \binom{2}{1}\cdot \binom{10}{1} + 8 = 328 |
-10,609 | \frac{1}{12 \cdot x + 8} \cdot 12 = \frac{3}{x \cdot 3 + 2} \cdot \frac{4}{4} |
-24,673 | 21 i - 92 = -5 + 20 i - 87 + i |
5,556 | \binom{6 + 4 + \left(-1\right)}{4 + (-1)} = 84 |
22,888 | \left(6 = 2*(z + y) \Rightarrow 3 = z + y\right) \Rightarrow -z + 3 = y |
18,012 | bx^k/b = (b\frac{x}{b})^k |
4,634 | \int\limits_0^∞ y^2 \cdot e^{(\left(-1\right) \cdot y^2)/2}\,\mathrm{d}y = \int\limits_0^∞ (-e^{\dfrac12 \cdot \left(\left(-1\right) \cdot y \cdot y\right)})\,\mathrm{d}y |
-16,378 | 3 \sqrt{25*7} = \sqrt{175}*3 |
11,876 | (\pi \cdot \left(-3\right))/4 = \frac{\pi}{4}5 - \pi \cdot 2 |
-9,378 | -2*5*11 - t*2*5*7 = -t*70 + 110*(-1) |
18,669 | \left(x + 3*(-1)\right)*\left(x + 5\right) - (x + 4)*(x + 5*(-1)) = x^2 + 2*x + 15*(-1) - x * x - x + 20*(-1) = 3*x + 5 |
26,303 | (4 - \sqrt{15})^{1/3} (4 + \sqrt{15})^{\frac{1}{3}} = 1 |
34,595 | A^x \cdot B = B \cdot A^x |
10,926 | 64 = x \cdot x - y^2 = (x + y) \cdot \left(x - y\right) |
18,163 | \sin{z}*\cos{z} = \frac12*\sin{z*2} |
26,102 | a_m + a_{m + (-1)} + \dots + a_2 + a_1 = a_1 + a_2 + \dots + a_{m + (-1)} + a_m |
-1,505 | 7/8 \cdot \frac18 \cdot 7 = \tfrac{7 \cdot 1/8}{\frac17 \cdot 8} |
30,805 | 66 = 12!/(10!*2!) |
4,547 | 20\cdot x^3 + 17\cdot (-1) = 77\cdot (-1) + (3 + x^3)\cdot 20 |
29,226 | \frac{2}{3} \cdot x = (x + 1)/3 + \frac13 \cdot (x + (-1)) |
-26,406 | \frac{1}{729*9^{12}} = 9^{-3 + 12 (-1)} = \frac{1}{205891132094649} |
32,976 | z^{t + s} = z^t z^s |
-26,739 | \sum_{n=1}^\infty \frac{\left(n + 5\right)*(-5)^n}{n * n*5^n} = \sum_{n=1}^\infty \frac{\left(-1\right)^n*5^n}{n^2*5^n}*(n + 5) = \sum_{n=1}^\infty (-1)^n*\frac{1}{n^2}*\left(n + 5\right) |
17,140 | (g \cdot f)^2 = g^2 \cdot f^2 |
20,326 | f \cdot x^3 = f \cdot x^3 |
22,299 | \cos(x\cdot 2) = 1 - 2 \sin^2(x) |
5,318 | w_2^3 = (3 + 2^{1/3})^3 = 29 - 27 \cdot w_2 + 9 \cdot w_2^2 \cdot w_2 |
41,512 | \frac{1}{1!*1!*1!}3! = 6 |
17,843 | \dfrac{1}{9^2 + 11 \left(-1\right)}9\cdot 8/9 = 4/35 \approx 0.114285714285714 |
-27,335 | \frac{\cos^2(x) \cdot 3}{-\sin(x) \cdot 2 + 2} = \left(1 + \sin(x)\right) \cdot 3/2 |
-23,252 | 4/5\cdot \dfrac{2}{7} = 8/35 |
-20,078 | \dfrac{4}{4} (-r*5 + 4(-1))/\left(\left(-4\right) r\right) = \tfrac{16 (-1) - r*20}{(-16) r} |
21,830 | 3 - \frac12 = \frac{6}{2} - \dfrac12 = 5/2 |
25,536 | k + 2 \cdot k + 3 \cdot k + \dotsm + k^2 \approx k \cdot k \cdot k = k^3 |
19,475 | 2240 + 1876 \cdot (-1) + 324 + 240 + 96 \cdot (-1) + 4 + 4 \cdot (-1) = 832 |
22,117 | 2 \times n^2 + 4 \times n + 1 = (1 + n) \times (n + 1) + n \times \left(2 + n\right) |
33,814 | t r = t r |
17,276 | Y\cdot L\cdot b + a\cdot L\cdot V = \left(b\cdot Y + V\cdot a\right)\cdot L |
-20,889 | \frac{4 - 10\cdot k}{-k\cdot 2 + 20} = 2/2\cdot \frac{1}{-k + 10}\cdot (-k\cdot 5 + 2) |
17,054 | (w \cdot w + 3(-1)) (2(-1) + w^2) = w^4 - w^2 \cdot 5 + 6 |
-3,399 | \sqrt{7}*\left(5 + 3 + (-1)\right) = 7\sqrt{7} |
-18,360 | \frac{x^2 + x*8 + 9 (-1)}{x^2 - x} = \frac{(x + (-1)) (9 + x)}{x*(x + (-1))} |
-3,757 | \dfrac{96}{120\cdot z^3}\cdot z^3 = 96/120\cdot \dfrac{1}{z^3}\cdot z^3 |
8,607 | (n^2 - n + 1) \times (n + 1) = n \times n \times n + 1 |
24,648 | \frac{\pi\cdot 7}{8} = -\pi/8 + \pi |
40,574 | 0(-1) + 1 = 1 |
17,683 | 3^{1 / 2} - 2^{\frac{1}{2}} + 2^{1 / 2} + 3^{1 / 2} = 3^{\frac{1}{2}}*2 |
22,833 | xb d = xbd |
-5,540 | \frac{5}{3 \cdot (q + 2)} = \frac{5}{3 \cdot q + 6} |
-22,760 | \frac{1}{56}*84 = 28*3/(28*2) |
5,250 | 1 + 2^0 + 2^1*\dotsm*2^{n + \left(-1\right)} + 2^n = 2*2^n = 2^{n + 1} |
-22,231 | (4 + n)\times \left(6\times (-1) + n\right) = 24\times (-1) + n^2 - 2\times n |
8,111 | {k \choose g} + {k \choose g + 1} = {k + 1 \choose g + 1} |
17,695 | ((-1) + z^2) \cdot ((-1) + z^2) = (1 + z) \cdot ((-1) + z) \cdot (z + 1) \cdot (z + (-1)) |
1,374 | a\cdot b\cdot d = (a\cdot b + 1)\cdot d = (a\cdot b + 1)\cdot d + 1 = a\cdot b\cdot d + d + 1 |
2,388 | a^{k_1 + k_2} = a^{k_1} a^{k_2} |
26,544 | {8 \choose 2} = \dfrac{8*7}{2} = 28 |
19,626 | |1/y - 1/3| = \frac{1}{3y}|y + 3(-1)| < \dfrac{1}{6}|y + 3(-1)| |
-10,899 | 88/4 = 22 |
19,453 | -\sin{x}\cdot i + \cos{x} = \sin{-x}\cdot i + \cos{-x} |
-16,700 | -3 = -3 (-2 x) - 21 = 6 x - 21 = 6 x + 21 \left(-1\right) |
22,126 | \frac{1}{1 + l} + 1 = \frac{2 + l}{1 + l} |
-22,328 | (9 + q) \cdot \left(q + 7\right) = 63 + q^2 + 16 \cdot q |
26,084 | -1 = 0/8 - 1 + 0 + 0/2 + 0/4 |
6,717 | 1 - \cos{4*x} = 2*\sin^{22}{x} = 8*\sin^2{x}*\cos^2{x} = 8*\left(1 - \cos{x}\right)*\left(1 + \cos{x}\right)*\cos^2{x} |
13,220 | \left(4 \lt \sqrt{17} \Rightarrow -\sqrt{17} - 1 < -5\right) \Rightarrow -1 > (-1 - \sqrt{17})/4 |
-13,351 | \frac{1}{1 + 4}*50 = 50/5 = 50/5 = 10 |
-2,090 | \frac{1}{6}\pi - \frac{4}{3}\pi = -\frac{7}{6}\pi |
14,655 | 1/6 = \tfrac{1}{6^2} \cdot 6 |
19,847 | 135.966 = 2.666\times 51 |
7,229 | 1 = \lim_{n \to \infty}(1 + \frac1n) = \lim_{n \to \infty}\left(1 + \frac{1}{n}\cdot 2\right) |
43,298 | 110334 = 2\times 3\times 7\times 2627 |
-27,832 | d/dx (-3\cot(x)) = -3d/dx \cot(x) = 3\csc^2(x) |
-20,867 | \frac{80}{8 \cdot x + 80} \cdot x = \frac{1}{8} \cdot 8 \cdot \frac{10 \cdot x}{10 + x} |
-1,897 | \pi\cdot \dfrac{1}{6}\cdot 7 + \frac{\pi}{12} = 5/4\cdot \pi |
17,922 | \frac{14}{9} + 4\sqrt{10}/9 = \frac19(\sqrt{10}\cdot 4 + 14) |
38,663 | \|z\| = \|z*z\| = |z|*\|1\| |
45,493 | 2 + 2 * 2 + 2 * 2 * 2 + \ldots + 2^x = 2*\left(1 + 2 + 2 * 2 + \ldots + 2^{x + (-1)}\right) = 2*\frac{2^x + (-1)}{2 + (-1)} = 2^{x + 1} + 2*\left(-1\right) |
-22,961 | 8\cdot 10/(7\cdot 10) = 80/70 |
-3,565 | \tfrac1m \frac{10}{3} = \frac{10}{3 m} |
27,298 | ( g_1 g_2, e_2 e_1) = ( g_1 g_2, e_1 e_2) |
6,279 | \sin^2{y} = \frac{1}{5}\cdot 4 + \frac{1}{5}\cdot (\sin{y} - \cos{y}\cdot 2)\cdot (\cos{y}\cdot 2 + \sin{y}) |
21,155 | \dfrac{1 - x^2}{1 - x} = x^0 + x^1 |
11,918 | (x^{\dfrac{1}{2}} \cdot W^{1/2})^2 = W \cdot x |
47,729 | 2*\operatorname{atan}(\frac{1}{\phi^{\dfrac{3}{2}}}) = \operatorname{atan}(\tfrac{2*\phi^{\frac12*3}}{\phi^3 + \left(-1\right)}) = \operatorname{atan}\left(\phi^{\frac{1}{2}}\right) |
29,837 | c_1 \left( 1, 0\right) + c_2 ( 1, 1) = ( c_1 + c_2, c_2) = \left\{0\right\} \Rightarrow c_1 = c_2 = 0 |
16,121 | -\frac{108}{2^7} + 1 = \dfrac{20}{2^7} |
20,998 | -a^2 + b^2 = (-a + b)*\left(b + a\right) |
-1,809 | \pi*\frac{2}{3} - \pi/12 = 7/12*\pi |
27,159 | \left(x + \frac1x = 1 \Leftrightarrow 0 = 1 + x^2 - x\right) rightarrow x^2 \cdot x + 1 = (x + 1)\cdot (x^2 - x + 1) = 0 |
9,242 | \frac{1}{1 + 2\cdot q}\cdot (q + 3\cdot (-1)) = \frac{-3/q + 1}{2 + 1/q} |
33,222 | b \cdot b + a^2 - a \cdot b \cdot 2 = (a - b)^2 |
-25,483 | -3 \cdot \sin{y} + 8 \cdot y = d/dy (4 \cdot y^2 + 3 \cdot \cos{y}) |
18,590 | \sin{\frac{1}{2}\left(\pi*(-3)\right)} = 1 |
51,377 | 1 + 1/2 + 1/4 + 1/4 + \dfrac18 + \frac{1}{8} + \frac18 + 1/8 + \dotsm = 1/2 + 1 + \frac12 + 1/2 |
18,665 | 3 \cdot 37 = (10^{\dfrac{1}{2}} + 11) (11 - 10^{\frac{1}{2}}) |
-22,987 | \frac{32}{24} = \dfrac{32}{3 \cdot 8}1 |
16,004 | {x \choose m} = \frac{x!}{m! \cdot (-m + x)!} |
-4,148 | 96\cdot x^3/(12\cdot x) = x^3/x\cdot \dfrac{1}{12}\cdot 96 |
-3,341 | \sqrt{3} \cdot (4 + 2 \cdot (-1)) = 2 \cdot \sqrt{3} |
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