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int64 -30,985
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-5,666 | \frac{1}{6 + 2*i} = \frac{1}{2*(i + 3)} |
15,168 | h_x + c_x = c_x + h_x |
-18,606 | 3g + 5\left(-1\right) = 6*\left(3g + 4(-1)\right) = 18 g + 24 (-1) |
38,118 | 3249*(-1) + 10000 = 6751 |
-29,425 | \frac{8 \cdot 4}{5 \cdot 3} = \tfrac{32}{15} |
14,817 | \left(\cos{z} = i \cdot \sin{z} \Rightarrow 0 = \cos{z} - i \cdot \sin{z}\right) \Rightarrow e^{-i \cdot z} = 0 |
23,390 | 1008 = 3^2\times 2^4\times 7 |
-24,170 | \tfrac{66}{7 + 4} = \frac{1}{11} \cdot 66 = \tfrac{66}{11} = 6 |
-5,936 | \frac{4}{k^2 - 5 \cdot k + 36 \cdot (-1)} = \frac{1}{(9 \cdot (-1) + k) \cdot (k + 4)} \cdot 4 |
40,322 | (-13)\cdot (-1) + 22 = 35 |
-11,966 | 1/20 = r/(20\cdot \pi)\cdot 20\cdot \pi = r |
33,752 | a \cdot a = 25 \Rightarrow 25^{1/2} = (a \cdot a)^{1/2} |
-264 | \frac{8!}{\left(3 (-1) + 8\right)!*3!} = {8 \choose 3} |
27,765 | 8y = 90 \implies y = 45/4 = 11.25 |
28,892 | 2^{2\cdot 3^{2 + 2(-1)}} = 4 = 3^{2 + (-1)} + 1 + 0\cdot 3^2 |
42,207 | e^{-10/500} = e^{-\frac{1}{50}} |
-5,780 | \dfrac{1}{m\cdot 5 + 15} = \frac{1}{(3 + m)\cdot 5} |
50,373 | \int\limits_0^\infty \frac{u^2}{2\cdot u^{\alpha + 1}}\,du = \int_0^\infty u^{1 - \alpha}\,du = \frac{u^{2 - \alpha}}{2 - \alpha} |
21,284 | \frac{5}{2} = 3/2 + 1 |
3,251 | ac + bc = (b + a) c |
3,612 | 27 - 2\times 7 = 13 |
1,498 | 7^2 + (-2)^2 = 49 + 4 = 53 = s^2 \Rightarrow s = \sqrt{53} |
2,702 | \left(q = -\sin{z} + \tan{z}\Longrightarrow \frac{2 \cdot z^3}{4 - z^2} = q\right)\Longrightarrow 2 \cdot z^3 + z \cdot z \cdot q - q \cdot 4 = 0 |
37,462 | |2 - y| = |-(y + 2\cdot \left(-1\right))| = |y + 2\cdot (-1)| |
14,567 | 50 = \frac{1}{2}*(1 + 99) |
15,372 | 2*\left(h_2/2 + \frac{h_1}{2}\right) = h_1 + h_2 |
12,989 | \frac{1}{2}\cdot 3 - \sqrt{5}/2 = (3 - \sqrt{5})/2 |
12,538 | 150 = 3 \cdot (30 + 20) |
-18,299 | \frac{1}{8\cdot (-1) + a^2 + a\cdot 7}\cdot (a\cdot 8 + a^2) = \frac{a}{\left(8 + a\right)\cdot (a + (-1))}\cdot (8 + a) |
34,621 | \frac{\binom{71}{11}}{\binom{80}{20}} = \frac{17}{23471690} |
27,068 | E^{12} + (-1) = \left(E^6 + \left(-1\right)\right) \cdot (1 + E^6) |
-25,794 | \frac{1}{48}*11 = \tfrac{11}{12*4} |
-26,448 | (2(-1) + 3m)\cdot 20 = 20 \left(-40/20 + \frac{m}{20}60\right) |
5,106 | 4\cdot x^2 + 9\cdot z^2 = 180 \Rightarrow x^2/45 + z^2/20 = 1 |
26,861 | (4 - y)^2 + y^2 - (-y + 4)\times 2 - 2\times y + 2\times (-1) = 0 \Rightarrow y^2 - 4\times y + 3 = \left(y + (-1)\right)\times (y + 3\times (-1)) = 0 |
20,881 | \frac{\text{d}}{\text{d}x} (y^3 \cdot 4) = \frac{\text{d}y}{\text{d}x} y^2 \cdot 12 |
19,366 | |z| > 1 rightarrow 1 \gt 1/|z| |
36,150 | 6*8*(4 + 1) = 240 |
45,848 | 150 = 6 + 144 |
28,687 | \frac{1}{30}1000 = 100/3 |
29,293 | -(\frac{\pi}{14} \cdot \cot\left(\frac{19}{24} \cdot \pi\right) - \pi \cdot \cot(\frac{7}{12} \cdot \pi)/24) = \pi/24 \cdot (\cot(\frac{1}{12} \cdot 7 \cdot \pi) - \cot(\frac{1}{24} \cdot 19 \cdot \pi)) = \cdots = \dfrac{1}{24} \cdot \pi |
14,592 | {1\over2}\cdot{1\over2}\cdot{1\over2}={1\over8}=.001 |
13,151 | c_1\cdot a + a\cdot c_2 = (c_1 + c_2)\cdot a |
15,899 | \frac{1}{z \cdot 1/x} = \frac{x}{z} |
13,184 | d * d + g*d*2 + g * g = (g + d)^2 |
8,402 | \dfrac{1}{10^2} \times 2017 = 20.17 |
28,143 | (K + \left(-1\right)) \cdot (K + (-1)) - 2 \cdot (-1) + K = 3 + K^2 - K \cdot 3 |
792 | x_i\cdot z_j = z_j\cdot x_i |
39,230 | 1 - \sin{2\times F}\times \tan{F} = 1 - 2\times \sin^2{F} = \cos{2\times F} |
13,522 | y z = 0\Longrightarrow 0 = z\text{ or }y = 0 |
11,206 | (\alpha + 1) \times (\alpha + 1) = \alpha^2 + 1 = \alpha + 1 + 1 = \alpha |
2,249 | \frac{2}{0} = \frac{1 + 1}{1 + (-1)} |
15,374 | (x + 1)^{x + 1} = (x + 1)^x*(x + 1) |
17,346 | w_1/(w_2) = w_1*\frac{1}{w_2}/1 |
-2,345 | 9/20 - \frac{1}{20} \cdot 3 = \frac{1}{20} \cdot 6 |
-26,629 | (4*x - 7*y)*(x*4 + y*7) = (x*4)^2 - (7*y)^2 |
-20,639 | \tfrac{1}{12\times (-1) - 4\times r}\times \left(-r + 3\times (-1)\right) = \frac14\times 1 |
10,961 | D^4 + 16 (-1) = D^2 * D^2 - 4^2 = \left(D^2 + 4\right) (D^2 + 4(-1)) = \left(D^2 + 4\right) (D + 2) \left(D + 2(-1)\right) |
-20,302 | \frac{1}{1}*1 = \dfrac{4 - 4*s}{4 - 4*s} |
3,261 | \dfrac{\sin{x}}{1 + \cos{x}} = \frac{1}{\sin{x}} \cdot (1 - \cos{x}) |
14,265 | \left(6 (-1) + 3 z^3 - z^2\cdot 2 + z\cdot 9 = 0 \Rightarrow 0 = 3\cdot (3 z + 2 (-1)) + (3 z + 2 \left(-1\right)) z^2\right) \Rightarrow 0 = (3 z + 2 \left(-1\right)) (z^2 + 3) |
2,478 | \frac{81201}{56660} = 1 + \frac{1}{56660}24541 |
8,060 | c + 2 = n \Rightarrow c = 2 (-1) + n, 4 \left(-1\right) + n = 2 \left(-1\right) + c |
12,690 | x\cdot 3 = c rightarrow c^2 = 9\cdot x^2 = 3\cdot 3\cdot x^2 |
27,033 | 1900 = 5^2 \cdot 2 \cdot 2 \cdot 19 |
9,272 | \frac{1}{\left(-r + x\right)!\cdot r!}\cdot x! = \frac{1}{r!\cdot \left(x - r\right)!}\cdot x! |
36,332 | 3^5 + 10 \cdot 10 - 7^3 = 0 |
9,848 | a \cdot d - b \cdot c = a \cdot d - c \cdot 0 + 0 \cdot d - b \cdot c = a \cdot d - b \cdot c |
15,251 | {20 \choose 2}*{20 \choose 2}*\dotsm*{20 \choose 2} = {20 \choose 2}^{10} |
20,338 | 5(-1) + 11 r = r*\left(9 - 2r\right) + r^2*2 + r*2 + 5(-1) |
31,914 | 21\cdot y^{5/2} = y \cdot y\cdot 21\cdot y^{1/2} |
30,596 | s \cdot (s + 1)/2 = 1 + 2 + 3 + \dots + s |
-20,125 | 9/9 \times \dfrac{1}{8 \times x + 2 \times (-1)} \times (8 \times (-1) - x \times 5) = \frac{1}{72 \times x + 18 \times (-1)} \times (-x \times 45 + 72 \times (-1)) |
20,536 | 1 = 1/24 + 1/2 + 1/4 + 1/8 + \tfrac{1}{12} |
10,949 | -(-x + 51) + 50 + x = 2 \cdot x + (-1) |
37,361 | \vartheta + z - z = z - z + \vartheta |
3,734 | i = s*g*a = s*a*g |
3,718 | \left(-1\right) + 3^{12} = (-1) + (3^2)^6 |
8,751 | A^2 x = 0 \Rightarrow A x = 0 |
9,027 | 2^{n*2} = \frac{2^{-n * n}}{2^{-n^2 - n*2}} |
-8,043 | \left(27 + 21\cdot i + 9\cdot i + 7\cdot (-1)\right)/10 = (20 + 30\cdot i)/10 = 2 + 3\cdot i |
28,076 | 2 |x| = \frac{\mathrm{d}}{\mathrm{d}x} (x |x|) |
6,612 | s*w_1 + e*w_2 + h*w_3 = (s - e + h - h)*w_1 + (e - h)*(w_2 + w_1) + h*(w_1 + w_2 + w_3) |
47,723 | 30*12 = 360 |
30,433 | 3 \cdot 3 = (-3)^2 |
-3,648 | \frac{n^4}{n^3} \cdot \frac{1}{144} \cdot 120 = \frac{n^4 \cdot 120}{n^3 \cdot 144} |
-2,704 | \sqrt{11}\cdot \left(4 + 1\right) = \sqrt{11}\cdot 5 |
30,303 | \mathbb{E}[X \cdot B] = \mathbb{E}[X] \cdot \mathbb{E}[B] |
-3,354 | (4 + 3 + 2) \cdot \sqrt{13} = \sqrt{13} \cdot 9 |
15,169 | \left(-1\right) + x^3 = \left(x \cdot x + x + 1\right) (x + (-1)) |
32,592 | 1 = \cot(x*2) \Rightarrow \tan(x*2) = 1 |
-9,242 | 45\cdot q + 117\cdot (-1) = 3\cdot 3\cdot 5\cdot q - 3\cdot 3\cdot 13 |
15,716 | 1050 = 210\cdot (4 + 1) |
24,234 | \dfrac{1}{-a + d} \cdot (\frac{1}{x + a} - \dfrac{1}{x + d}) = \frac{1}{(x + a) \cdot (x + d)} |
-26,019 | \left(24 - 28 \cdot i - 6 \cdot i + 7 \cdot (-1)\right)/17 = \left(17 - 34 \cdot i\right)/17 = 1 - 2 \cdot i |
52,119 | 4^5=1024 |
14,065 | y^3 + 3y^2 + 6 = (y + 1)^3 - 3y + (-1) + 6 = \left(y + 1\right)^3 - 3\left(y + 1\right) + 8 |
7,179 | f_1 X\cdot 2 L + f_2 L\cdot 2C = 2(Xf_1 + Cf_2) L |
25,452 | \dfrac{1}{2} \cdot π + π \cdot m = 4 \cdot x \Rightarrow \frac{π}{8} + m \cdot π/4 = x |
23,730 | i*48 + 240 = (i*3 + 3*i + 30)*16/2 |
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