id
int64 -30,985
55.9k
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437k
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|---|---|
-2,014 |
π \cdot \frac{1}{12} \cdot 11 = -\frac{π}{6} + π \cdot 13/12
|
19,024 |
0 = 1 + x^2 - x \implies 0 = 1 + x * x * x
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10,882 |
c\cdot a + 0\cdot b = c\cdot (0\cdot b + a)
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-10,559 |
8/(y\cdot 25)\cdot 3/3 = \frac{1}{y\cdot 75}\cdot 24
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19,739 |
2*3 = (-\sqrt{-5} + 1)*(1 + \sqrt{-5})
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16,677 |
\cos\left(2\pi - x\right) = \cos(2\pi - x) = \cos\left(-x\right)
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22,927 |
8 + 5*(-1) = 3 = 3
|
14,165 |
\frac{1}{10}6 = 0.6
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-9,272 |
-y \cdot y \cdot 55 = -y \cdot y \cdot 5 \cdot 11
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5,026 |
0 = 5 \cdot \tan^4{\frac{\pi}{10}} - \tan^2{\frac{\pi}{10}} \cdot 10 + 1
|
41,111 |
2016 = \frac{2017}{1/2016 + 1}
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-21,594 |
-0.5 = \sin{\pi*\frac16*11}
|
-28,792 |
\int x^9\,dx = \dfrac{x^{9 + 1}}{9 + 1} + Y = x^{10}/10 + Y
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-9,604 |
0.01\cdot (-70) = -70/100 = -0.7
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9,445 |
4^x + x^4 = \left(2^x\right)^2 + (x^2)^2 = (x^2 + 2^x)^2 - 2\cdot 2^x\cdot x^2
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-4,725 |
\frac{1}{10\cdot \left(-1\right) + J^2 + 3\cdot J}\cdot (2\cdot J + 25\cdot (-1)) = -\frac{3}{J + 2\cdot (-1)} + \frac{1}{5 + J}\cdot 5
|
-19,046 |
\dfrac{4}{9} = \frac{1}{81\cdot \pi}\cdot A_x\cdot 81\cdot \pi = A_x
|
5,941 |
Var(\bar{B}) = \mathbb{E}((\bar{B} - F*\bar{B})^2) = \mathbb{E}(\bar{B}^2) - (F*\bar{B})^2
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26,179 |
\dfrac{{3 \choose 3}*{7 \choose 0}}{{10 \choose 3}}*1 = 1/120
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31,465 |
q + q = q\cdot 2
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13,852 |
\dfrac{1}{\frac1Z} = Z
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-9,286 |
-n \cdot 49 + 21 = 3 \cdot 7 - n \cdot 7 \cdot 7
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23,763 |
-\tfrac{1}{-(Z + 2) + 1} = \tfrac{1}{1 + Z}
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13,517 |
\alpha^{13}=\alpha\cdot\alpha^3\cdot\alpha^9
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-2,108 |
\pi/6 = -5/12\cdot \pi + \pi\cdot \frac{1}{12}\cdot 7
|
960 |
-(4/5)^5 + 1 = \dfrac{2101}{3125}
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-1,646 |
0 + 13/12*\pi = 13/12*\pi
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36,617 |
(\frac{1}{1 + s} - e^s)/(2\times s) = \left(\frac{1}{1 + s} + (-1) + 1 - e^s\right)/(2\times s) = -\dfrac{1}{2\times (1 + s)} - \frac{1/s}{2}\times (e^s + (-1))
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33,155 |
2 \cdot x + x \cdot x = (\left(-1\right) + x)^2 + 4 \cdot x + (-1)
|
4,194 |
\dfrac{1}{\pi*54} = 4*1/27/(8*\pi)
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3,083 |
(2*z + 3)^2 + 9*(-1) = 12*z + 4*z^2
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18,769 |
6^x = 36\cdot 9.75^{x + 2\cdot \left(-1\right)}\cdot 6^x = 6 \cdot 6\cdot (9 + \frac{3}{4})^{x + 2\cdot (-1)}
|
302 |
68 \cdot (-1) + 5 \cdot t^2 = 0 \Rightarrow t = \sqrt{68/5}
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11,113 |
-\frac12 + \sqrt{13}/2 = \tfrac12\cdot (\sqrt{13} - 1)
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35,778 |
x = 2*x - x
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13,706 |
\dfrac{1}{1 - x}(1 - x^4) = 1 + x + x^2 + x^3
|
710 |
-3x * x + 3x + 6 = -3(x^2 - x + 2(-1)) = -3((x - \tfrac{1}{2})^2 - \frac94)
|
15,416 |
\sqrt{-6} = \alpha\cdot x\Longrightarrow \alpha, x
|
2,304 |
e^{x + a} = e^a\cdot e^x
|
15,329 |
l + 1 + l = 2l + 1
|
26,375 |
\tan(\frac{x}{2}) = \frac{\sin\left(x\right)}{1 + \cos(x)} = \dfrac{1}{\sin(x)}\cdot \left(1 - \cos\left(x\right)\right)
|
-15,811 |
6*\frac{4}{10} - 9*6/10 = -\frac{1}{10}30
|
7,730 |
\frac{1}{2} ((x + g)^2 - g^2 + x^2) = g x
|
5,094 |
\dfrac{1}{d + b} \cdot (a + c) = \frac{b}{d + b} \cdot \dfrac{1}{b} \cdot a + \tfrac{c}{d} \cdot \tfrac{d}{b + d}
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30,790 |
n = \left\{1, 3, 2, n, \ldots\right\}
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-5,972 |
\frac{1}{t \cdot t + 11 \cdot t + 30} \cdot t = \frac{1}{(6 + t) \cdot (t + 5)} \cdot t
|
6,761 |
16/225 = \frac{2}{15}\cdot \frac{8}{15}
|
37,985 |
7 = 1 + 2 \cdot 2 + 1 + 1^2
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-20,763 |
\frac{1}{-12} \cdot (6 \cdot r + 54 \cdot (-1)) = \frac{1}{-2} \cdot (9 \cdot (-1) + r) \cdot 6/6
|
4,710 |
\tfrac{1}{(27 \cdot 27)^{\frac{1}{3}}\cdot (16 \cdot 16^2)^{1/4}} = \frac{1}{27^{2/3}\cdot 16^{\dfrac{1}{4}\cdot 3}}
|
29,068 |
y*\left(-z\right) = -z*y
|
-16,003 |
0 = \frac{4}{10}*9 - 6*\frac{6}{10}
|
48,114 |
2 = 14^g = 2^g\cdot 7^g
|
-642 |
e^{8\cdot \frac{\pi}{3}\cdot i} = (e^{\frac{\pi}{3}\cdot i})^8
|
14,430 |
(\sigma + x)^2 = \sigma^2 + \sigma*x*2 + x^2
|
21,887 |
z^{u + \sigma} = z^u z^\sigma
|
33,369 |
\sum_{l=1}^3 A_l = \sum_{l=1}^3 A_l
|
-17,518 |
31 = 73 + 42*(-1)
|
-20,720 |
-\frac{2}{1} \times \frac{-a \times 5 + 5}{-a \times 5 + 5} = \dfrac{a \times 10 + 10 \times (-1)}{5 - a \times 5}
|
37,809 |
2^{x + 1} = 2*2^x
|
20,558 |
-2 \times \sin^2{x} + 1 = \cos{2 \times x}
|
-5,341 |
5.7 \times 10^{2 + (-1)} = 5.7 \times 10^1
|
11,396 |
5\cdot 2^1/2 = \frac14\cdot 20
|
21,825 |
5/9 = -1/9 + \dfrac{2}{3}
|
22,808 |
x^{x^{x^{x^{\dotsm}}}} = 2 \Rightarrow x^2 = 2
|
9,113 |
A^2x = 0 \implies Ax = 0
|
993 |
1 = x\cdot z\cdot y\Longrightarrow x = 1, 1 = y, 1 = z
|
17,291 |
1 - \dfrac{1}{\lambda + 1} = \dfrac{1}{1 + \lambda} \lambda
|
15,450 |
0 = \lim_{n \to \infty} |a_n|\Longrightarrow 0 = \lim_{n \to \infty} a_n
|
10,440 |
\binom{m + 3 + (-1)}{3 + (-1)} = \binom{m + 2}{2} = (m + 2)\cdot (m + 1)/2
|
-2,947 |
\sqrt{2} \cdot 8 = \sqrt{2} \cdot (1 + 2 + 5)
|
30,710 |
482\cdot \frac{1}{2} = 241
|
40,501 |
\frac{0^2}{0} = 0^{2 + (-1)}
|
4,038 |
\cos(2 \cdot z + 3 \cdot z) = \cos(5 \cdot z)
|
-10,579 |
-\frac{3}{6\cdot (-1) + 9\cdot n} = -\dfrac{1}{n\cdot 3 + 2\cdot (-1)}\cdot \frac{3}{3}
|
33,282 |
15 = 60/4
|
10,453 |
\cos^2\left(x\right) - \sin^2\left(x\right) = \cos(x*2)
|
25,026 |
1/9 + \frac19 = \dfrac{2}{9}
|
15,461 |
\tan\left(π/2 - \zeta\right) = \cot{\zeta}
|
-9,356 |
50 (-1) + p \cdot 10 = -5 \cdot 2 \cdot 5 + 2 \cdot 5 p
|
42,798 |
\tan(z) = \dfrac{1}{\cos(z)}\times \sin(z)
|
30,906 |
h*2 + (-1) = h \implies h = 1
|
13,290 |
k \times 2 + 2 = (k + 1) \times 2
|
-15,545 |
\frac{1}{\tfrac1s \cdot x^2 \cdot x} \cdot s^9 = \frac{s^9}{x^3} \cdot 1/(1/s) = \dfrac{s^{9 - -1}}{x \cdot x^2} = \frac{1}{x \cdot x \cdot x} \cdot s^{10}
|
24,287 |
H^{j + 1} z^{j + 1} = H^j H z^{j + 1} = (j + 1) H^j z^j
|
22,293 |
x^{1/2} \cdot T = T \cdot x^{1/2}
|
13,776 |
(h^2 + 1 - h)*(1 + h) = h * h^2 + 1
|
352 |
\sum_{d=1}^x \mathbb{E}[\alpha_d * \alpha_d] = \mathbb{E}[\sum_{d=1}^x \alpha_d^2]
|
11,814 |
\left(8(-1) + t\right) \left(4\left(-1\right) + t\right) = t^2 - 12 t + 32
|
-2,274 |
\frac{1}{12} \cdot 4 = -5/12 + \tfrac{9}{12}
|
11,919 |
\left(\left(2\cdot x + 2\cdot (-1) = \frac{x}{2} rightarrow 4\cdot x + 4\cdot (-1) = x\right) rightarrow 3\cdot x = 4\right) rightarrow x = 4/3
|
25,106 |
(x - z) \cdot (x^{l + (-1)} + x^{2 \cdot (-1) + l} \cdot z + x^{3 \cdot (-1) + l} \cdot z^2 + \ldots + x \cdot z^{l + 2 \cdot (-1)} + z^{l + (-1)}) = -z^l + x^l
|
19,936 |
\frac17*14 = \frac{7*2}{7}
|
5,080 |
-k + X = m \Rightarrow m + k = X
|
-4,762 |
\frac{1}{12 \cdot (-1) + x^2 - x} \cdot (-x \cdot 6 + 10) = -\dfrac{4}{x + 3} - \frac{2}{x + 4 \cdot (-1)}
|
4,863 |
\cos(b) \cdot \sin(a) + \cos(a) \cdot \sin(b) = \sin(a + b)
|
11,349 |
\frac{1}{5 \cdot (-1) + 10} \cdot 180 = 36
|
817 |
yb + c = 0 rightarrow y = -\frac{c}{b} = \frac{\frac12}{b}b = \dfrac12
|
35,539 |
\sin\left(e + b\right) = \cos{b}*\sin{e} + \sin{b}*\cos{e}
|
24,144 |
2^{l + 5(-1)} = 2^{l + 6(-1)}*2
|
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