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int64 -30,985
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26,684 | \frac{\dfrac13*2*x}{\dfrac{\sqrt{1463}}{108}*2} = 36/(\sqrt{1463})*x |
7,688 | 1/y = \overline{y}*1/\overline{y}/y = \dfrac{\overline{y}}{|y|^2} |
18,878 | \tfrac{5}{21} = \frac{1}{{7 \choose 2}}\left({2 \choose 2} + {2 \choose 2} + {3 \choose 2}\right) |
-20,287 | -\dfrac{1}{r + 4} \cdot 9 \cdot 4/4 = -\frac{1}{r \cdot 4 + 16} \cdot 36 |
3,714 | \dfrac{n!}{\left(n - -r + n\right)!\cdot (n - r)!} = \frac{n!}{(n - r)!\cdot r!} |
36,020 | \frac{1}{15 + 2 + 7}*15 = \frac{15}{24} |
11,641 | 3 \cdot (-1) + 31 + 21 \cdot (-1) + 19 \cdot \left(-1\right) + 17 + 13 + 11 \cdot (-1) + 7 + 5 \cdot (-1) = 9 |
-8,335 | -12 \div -3 = 4 |
24,360 | 5 = (4^2 + 3^2)^{\frac{1}{2}} |
12,003 | x = \operatorname{asin}(s) = s + \dfrac{s^3}{2}*1/3 + 3/(2*4)*\frac{1}{5}*x^5 |
8,154 | -i = \sin(\frac{\pi*3}{2}) i + \cos(3\pi/2) |
5,736 | \left(\dfrac14\right)^{\frac{1}{2}} = 1/2 \gt \frac14 |
3,611 | a_{i \cdot i} = -a_{i \cdot i}\Longrightarrow 0 = a_{i \cdot i} |
25,919 | n^7 - n = n^7 - n^5 + n^5 - n^3 + n^3 - n = (n^4 + n^2 + 1)\cdot (n \cdot n \cdot n - n) |
24,610 | \tfrac{89}{55} = 1 + \frac{34}{55} |
30,192 | 20683 = 10^3 + 27^2 \cdot 27 = 19^3 + 24^3 |
-6,253 | \dfrac{t}{2*(9 + t)*(5*(-1) + t)}*2 = \frac{t}{(9 + t)*(t + 5*\left(-1\right))}*\frac{2}{2} |
-1,634 | -\pi*3/4 = \pi - \pi \frac74 |
17,849 | y^{1/3} = y^{2/6} |
-1,082 | \frac{4}{24} = 4\cdot \frac{1}{4}/(24\cdot 1/4) = 1/6 |
6,054 | y^3 + y^2 + y*2 + 0 = (0 + y) (y^2 + y + 2) |
6,068 | n \leq 4 \cdot (\sqrt{n + (-1)} + (-1))^2 = 4 \cdot \left(n + (-1) - 2 \cdot \sqrt{n + (-1)} + 1\right) = 4 \cdot n - 8 \cdot \sqrt{n + \left(-1\right)} |
-2,273 | \frac{1}{12}*2 = -1/12 + \tfrac{1}{12}*3 |
8,704 | \cos(-y + z) = \cos(y)\times \cos(z) + \sin(z)\times \sin\left(y\right) |
15,385 | R_\lambda \cdot R_x = R_x \cdot R_\lambda = \dfrac{R_x - R_\lambda}{\lambda - x} |
13,165 | 1729 = 10^3 + 9^2 \cdot 9 = 12^3 + 1 \cdot 1 \cdot 1 |
1,128 | u_x + h\cdot u_W = 1 = \left( 1, h\right)\cdot ( u_x, u_W) |
2,939 | |7\cdot (-1) + 2| = 5 |
-10,589 | 9 = 8 \cdot x + 12 + 28 \cdot (-1) = 8 \cdot x + 16 \cdot \left(-1\right) |
46,551 | 3*1/3 = 1 |
19,809 | \frac1y + \frac{1}{y} - \frac{1}{y^2} = \frac{2}{y} - \dfrac{1}{y \times y} < \frac{1}{y}\times 2 |
51,602 | \frac{n!}{n^n} = 2/n\cdot \dotsm\cdot (n + (-1))/n\cdot \frac{n}{n}/n \leq 1/n |
19,187 | \int\limits_{-h_1}^{h_1} h_2\,\text{d}z = 2\cdot \int_0^{h_1} h_2\,\text{d}z |
-6,471 | \tfrac{1}{\left(z + 5\right) (2(-1) + z)}4 = \frac{1}{z^2 + 3z + 10 (-1)}4 |
2,292 | \frac{a_m \dfrac{1}{a_m}}{1/\left(a_m\right) + 1} = \frac{a_m}{1 + a_m} |
18,593 | 1/(D\cdot t) = 1/(t\cdot D) |
34,139 | g*z + z*f = z*\left(f + g\right) |
27,764 | 1 + \dfrac{1}{2}\cdot (5^{\tfrac{1}{3}} - 1) = \dfrac{1}{2} + 5^{\frac{1}{3}}/2 |
11,488 | \|\omega \cdot x\| = \|\omega \cdot x - V \cdot x + V \cdot x\| \leq \|\omega \cdot x - V \cdot x\| + \|V \cdot x\| |
15,398 | \sin{4\cdot π/3} = -\sin{\frac{π}{3}} |
21,686 | x_r \rho_r = ((x_r + \rho_r)^2 - (x_r - \rho_r) (x_r - \rho_r))/4 |
32,713 | 3 + q^2 + (-1) = 2 + q^2 |
-7,597 | \frac{-6\cdot i - 9}{-i\cdot 2 - 3} = \frac{-6\cdot i - 9}{-2\cdot i - 3}\cdot \dfrac{i\cdot 2 - 3}{-3 + 2\cdot i} |
26,377 | (x + 1)*(-x*3 + (1 + x)^2) = 1 + x^3 |
-22,248 | x^2 - 12x + 20 = (x - 10)(x - 2) |
5,510 | \frac{1}{2^{(-1) + n}} = \frac{1}{2^n}*(2 + 0*(-1)) |
-5,852 | \dfrac{5}{x\cdot 3 + 12} = \dfrac{1}{3\cdot (x + 4)}\cdot 5 |
-7,394 | \frac{5}{39} = \tfrac{4}{13}\cdot \frac{1}{12}\cdot 5 |
18,405 | 6 = 2.3 = \left(1 + (-5)^{1 / 2}\right)*\left(1 - (-5)^{1 / 2}\right) |
-20,506 | -1/5*\dfrac{(-10)*k}{(-10)*k} = \dfrac{10*k}{k*(-50)} |
-23,817 | 7 + \frac{1}{3} \cdot 21 = 7 + 7 = 14 |
17,973 | \sin(\cos^{-1}(d)) = (1 - d * d)^{1/2} |
10,877 | \frac1y x = \tfrac{1}{y*1/x} |
14,158 | (-\sqrt{m} \cdot y + z) \cdot (\sqrt{m} \cdot y + z) = z^2 - y^2 \cdot m |
24,678 | 1 = -(-\cosh{x} + \sinh{x}) \cdot (\sinh{x} + \cosh{x}) \Rightarrow 5 \cdot (\sinh{x} + \cosh{x}) = 1 |
13,945 | f^y = (1/f)^{-y} = (\frac1f)^{-y} |
737 | b = e b e = \frac{b}{e} e |
-15,722 | \dfrac{{(a^{-3})^{-2}}}{{a^{5}y^{5}}} = \dfrac{{a^{6}}}{{a^{5}y^{5}}} |
7,399 | 56 = -3 \cdot 62 + 242 |
6,706 | (x - b)^2 = s - \tfrac{1}{s} \Rightarrow \sqrt{s - \frac{1}{s}} = |x - b| |
9,041 | c\frac1cb = bc/c |
14,991 | c\cdot b < b^2 + c^2 - b\cdot c\Longrightarrow b^3 + c^3 > b\cdot c\cdot (b + c) = b^2\cdot c + b\cdot c^2 |
7,075 | \frac{3\cdot 17}{17\cdot 4} = \frac{51}{68} |
17,935 | 25 + 20 (-1) = 5 |
32,657 | -(n + \left(-1\right)) * (n + \left(-1\right)) + n^2 = (-1) + n*2 |
16,976 | y' = 1 + x + z + x \cdot z = 1 + x + (1 + x) \cdot z \Rightarrow -(1 + x) \cdot z + y' = x + 1 |
-2,888 | 5 \cdot 3^{\frac{1}{2}} = 3^{1 / 2} \cdot \left(1 + 4\right) |
15,213 | A' + x = A'\times x |
11,296 | x^2 + v^2\cdot 3 = \left(x + v\right)^2 + \left(-x + v\right) (v + x) + (-x + v)^2 |
22,691 | -1/2 + x = \left((-1) + 2*x\right)/2 |
658 | \frac{x^m - j^m}{x - j} = x^{(-1) + m} + \cdots + x \cdot x\cdot j^{3\cdot (-1) + m} + j^{2\cdot (-1) + m}\cdot x + j^{m + (-1)} |
17,565 | 4 = \left(7\times \left(-1\right) + \sqrt{65}\right)\times (\sqrt{65} + 7)/2/2 |
2,955 | c*d + G*c = (d + G)*c |
30,119 | x^2 - y^2 = (x+y)(x-y) |
-26,657 | \left(4y + 3\right) (2 + 3y) = 6 + y^2*12 + 17 y |
-11,081 | (x + 10 \cdot (-1))^2 + h = (x + 10 \cdot (-1)) \cdot (x + 10 \cdot (-1)) + h = x \cdot x - 20 \cdot x + 100 + h |
51,618 | -7 = 1 + 8 \cdot (-1) |
13,371 | x*4 - 2*y = 4 \implies 2*x - y = 2 |
-20,962 | \dfrac{5}{9} \times \dfrac{-10}{-10} = \dfrac{-50}{-90} |
29,748 | \frac{9900}{2} \times 1 = 4950 |
3,324 | (x + 1)^n = (x + 1)^2\cdot \left(1 + x\right)^{2\cdot \left(-1\right) + n} |
2,869 | |A| = B\Longrightarrow A^2 = |A| |A| = B B = B^2 |
13,918 | 8 + y^3 = (y + 2) \cdot (y^2 - y \cdot 2 + 4) |
10,960 | (-\sqrt{y} + 1) \cdot (1 + \sqrt{y}) = 1 - y |
-1,993 | -\frac{\pi}{12} + \pi\cdot 19/12 = 3/2\cdot \pi |
48,010 | \sqrt{x} \sqrt{x} = x |
3,331 | c*h/g = \frac{c}{g}*h |
3,422 | e^{-\int_t^V q*p\,\mathrm{d}p} = e^{-\int_t^V p*q\,\mathrm{d}p} |
-20,313 | \frac{1}{28 + 20 \cdot t} \cdot \left(t \cdot \left(-20\right)\right) = \frac{1}{4} \cdot 4 \cdot \dfrac{1}{7 + t \cdot 5} \cdot (\left(-5\right) \cdot t) |
7,039 | \cos\left(-a + \pi/2\right) = \sin(a) |
-18,331 | \frac{t^2 + t \cdot 4 + 32 \cdot (-1)}{t^2 - t \cdot 4} = \frac{(8 + t) \cdot (t + 4 \cdot \left(-1\right))}{t \cdot (4 \cdot (-1) + t)} |
-14,823 | 320 \div 4 = 80 |
24,726 | 13/204 = \frac{13}{52} \times \dfrac{1}{51} \times 13 |
12,243 | (a - h)*(a^n + h*a^{(-1) + n} + \dotsm + a*h^{(-1) + n} + h^n) = a^{n + 1} - h^{n + 1} |
20,568 | (\frac12*(1 + 1) + \frac{2}{1} + 2/1)/3 = 5/3 |
19,804 | 2^4 + 2^2 + 2^2 = 2 \cdot 2 \cdot 2 + 2^3 + 2 \cdot 2^2 |
5,013 | 1*2 \ldots*((-1) + l) l*(l + 1) = (1 + l)! |
13,428 | h^2 + b^2 + h \cdot b \cdot 2 = (h + b) \cdot (h + b) |
-10,737 | -3 = 12 - 8r + 10 \left(-1\right) = -8r + 2 |
21,835 | 4^{10} = 2^{20} = 1048576 < 1.05*10^6 |
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