id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
15,592 |
s \cdot t^2 = s \cdot t \cdot t = t^3 \cdot s \cdot t = t \cdot t \cdot t \cdot s \cdot t = t^2 \cdot t \cdot t^3 \cdot s = t^6 \cdot s = t^2 \cdot s
|
3,411 |
\pi\cdot 3/16 - \frac{\pi}{16} = \pi/8
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-20,817 |
\left(7*(-1) - n*3\right)/(-8)*\frac{1}{3}*3 = \dfrac{1}{-24}*(-n*9 + 21*(-1))
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-17,864 |
71 + 6\times (-1) = 65
|
-19,616 |
\frac{45}{6} = 5\cdot 9/(6)
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-1,091 |
-\frac{1}{30}*9 = ((-9)*\frac13)/(30*1/3) = -3/10
|
31,304 |
(2 + 1 + 1 + 2 + 2 + 1 + 1 + 2)/8 = \frac{3}{2}
|
27,439 |
x + 1 + (x + 2) \cdot \cdots + 2 \cdot x = x + x + \cdots + x
|
11,388 |
\frac{2}{49} = 2\cdot 1/7/7
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-1,911 |
π/4 - \dfrac54\cdot π = -π
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1,731 |
\dfrac{5!}{2!} \cdot 4!/3! \cdot 6 = 1440
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15,153 |
\sqrt{1 + 4\cdot \sigma \cdot \sigma} < \sqrt{1 + 4\cdot \sigma + 4\cdot \sigma \cdot \sigma} = \sqrt{(1 + 2\cdot \sigma)^2} = 1 + 2\cdot \sigma
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-12,804 |
\frac17*5 = \frac{15}{21}
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25,297 |
f\times b = b\times f
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-19,667 |
\frac{14}{5}1 = \frac{14}{5}
|
3,657 |
3*v + 3*x = 4*x \Rightarrow v*3 = x
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-22,845 |
25/20 = \dfrac{25}{5\cdot 4}1
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-4,473 |
\frac{y \cdot 3 + 16 \cdot (-1)}{12 \cdot \left(-1\right) + y^2 + y} = \frac{4}{y + 4} - \tfrac{1}{y + 3 \cdot (-1)}
|
2,817 |
36/6\cdot 2 = 12
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-6,036 |
\dfrac{(7 + y)\cdot 10}{10\cdot \left(7 + y\right)\cdot (y + 8\cdot \left(-1\right))} = \dfrac{1}{(8\cdot (-1) + y)\cdot 2}\cdot 2\cdot \frac{5\cdot (7 + y)}{(y + 7)\cdot 5}
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2,122 |
D\frac{XB}{B} = XBD/B
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8,498 |
\cos(4x) = 2\cos^{22}(x) + \left(-1\right) = \cdots = 8\cos^4(x) - 8\cos^2(x) + 1
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20,741 |
\mathbb{E}(X^2) = \mathbb{E}(X)^2 + \mathbb{E}((X - \mathbb{E}(X))^2)
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-20,820 |
\frac{3 \cdot r}{3 \cdot r} \cdot (-3/10) = \frac{1}{30 \cdot r} \cdot ((-9) \cdot r)
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-2,590 |
3\cdot \sqrt{3} = \sqrt{3}\cdot (1 + 3\cdot (-1) + 5)
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17,408 |
\cot(-\frac{\pi}{7} + \frac{\pi}{2}) = \cot{\frac{\pi}{14} \times 5}
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7,339 |
x = \cos(\sin{x}) \gt \cos{x}
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11,825 |
(\vartheta + (-1)) \cdot (\vartheta + (-1)) + \left(-1\right) = -\vartheta\cdot 2 + \vartheta \cdot \vartheta
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21,376 |
3^z*2^{z + 1} = 6^z*2
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36,638 |
( x * x, x*z) = ( x^2, x) \cap \left( x^2, z\right) = x \cap ( x^2, z)
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-6,093 |
\frac{2}{3 \times x + 24} = \frac{2}{\left(x + 8\right) \times 3}
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22,032 |
(s^2 - s)/2 = -(\binom{s}{2} + s) + s^2
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29,168 |
\tau\times \sigma = \sigma^i\times \sigma = \sigma\times \sigma^i = \sigma\times \tau
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21,996 |
\tfrac{121}{11\cdot (10 + 1)} = 121/121 = 1
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7,028 |
\frac{x^2}{49} = \frac{y^2}{1} = z^2/9 = \dfrac{1}{9} \cdot \left(x + y - z\right)^2
|
-1,171 |
5/3 \cdot \frac67 = \tfrac{\frac17 \cdot 6}{3 \cdot 1/5}
|
-6,514 |
\frac{1}{(9 + a) (3\left(-1\right) + a)} = \frac{1}{a \cdot a + 6a + 27 (-1)}
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25,315 |
x! = ((-1) + x)*x*(x + 2*(-1))*\cdots*3*2
|
2,791 |
\cos^2(x) = \frac12 \times (\cos(2 \times x) + 1)
|
-10,496 |
9/x \cdot 3/3 = \tfrac{27}{3 \cdot x}
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35,658 |
\csc{2\cdot x} = \frac{1}{\sin{2\cdot x}} = \frac{1}{2\cdot \sin{x}\cdot \cos{x}}
|
16,326 |
I = (I - \alpha\cdot A)\cdot \left(I - 0.4\cdot A\right) = I - \left(0.4 + \alpha - 0.4\cdot \alpha\right)\cdot A
|
-22,899 |
\frac{1}{80}\cdot 56 = \frac{7\cdot 8}{8\cdot 10}
|
13,945 |
h^y = \left(1/h\right)^{-y} = (1/h)^{-y}
|
6,528 |
A + (z \cdot z + \left(-1\right)) \cdot A = A \cdot (1 + z^2 + (-1))
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40,068 |
45/47*\frac{1}{46} 44 = 990/1081 \approx 0.91582
|
-20,735 |
(6 \cdot (-1) - 7 \cdot z)/(-6) \cdot \frac{1}{2} \cdot 2 = \dfrac{1}{-12} \cdot (12 \cdot (-1) - z \cdot 14)
|
35,320 |
\cot{\theta} = \tan(\frac{\pi}{2} - \theta)
|
13,981 |
z_1^2 + z_2^2 + z_3^2 = (z_3 + z_1 + z_2)^2 - \left(z_2 z_1 + z_3 z_1 + z_3 z_2\right)*2
|
-1,615 |
\pi*11/6 = 2\pi - \frac{1}{6}\pi
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-1,255 |
\frac79 \times \frac{5}{8} = \frac{5 \times 1/8}{1/7 \times 9}
|
12,751 |
\dfrac{x^2}{y^2} = 2/1 \implies x^2 = 2,y^2 = 1
|
41,568 |
\|a - g\| \|a - g\| = ( a - g, a - g) = \left( a, a - g\right) - ( g, a - g)
|
25,681 |
\operatorname{atan}\left(-1\right) = ((-1) \pi)/4
|
12,418 |
-\alpha\times m + n\times \alpha = (-m + n)\times \alpha
|
-3,562 |
\frac{k}{k * k}*\frac{110}{33} = \frac{110*k}{33*k^2}
|
24,055 |
\tan^{-1}(-1/4) = -\tan^{-1}(\frac14)
|
18,761 |
(-1) + x^3 = (x + (-1)) (x \cdot x + x + 1)
|
8,525 |
yx^n/y = (y\frac{x}{y})^n
|
3,126 |
x^2 + \lambda^2 + z^2 = (x + 2 \cdot \left(-1\right))^2 + (\lambda + 4 \cdot \left(-1\right)) \cdot (\lambda + 4 \cdot \left(-1\right)) + (z + 3 \cdot (-1)) \cdot (z + 3 \cdot (-1)) = (x + 10 \cdot (-1))^2 + (\lambda + 8 \cdot (-1))^2 + (z + 9 \cdot (-1))^2
|
10,998 |
x^2 - 2 \cdot x + 3 \cdot (-1) = 0\Longrightarrow (x + 3 \cdot \left(-1\right)) \cdot (1 + x)
|
16,540 |
-(m + l) = -m - l
|
-20,783 |
2/(-12) = -1/6\cdot (-2/\left(-2\right))
|
27,149 |
x_F + x_X = x_X + x_F
|
12,315 |
a + b = -2\Longrightarrow -8 = a - b
|
13,384 |
5 + x + x^2 + \ldots\cdot \ldots = 5 + \frac{x}{-x + 1}
|
8,409 |
y \cdot 303 = y \cdot (3939 - 6 \cdot 606)
|
25,589 |
25 = \sqrt{\left(5 + 20*\left(-1\right)\right)^2 + \left(10 + 30*(-1)\right)^2}
|
10,674 |
\binom{n}{1} + \binom{n}{2} + \binom{n}{n + 2\cdot (-1)} = n \cdot n
|
887 |
b + r*n + a + p*n = (p + r)*n + a + b
|
12,382 |
2/2 = -\frac{3}{\left(-1\right) \left(a + 3\right)} = 1/(3a)
|
44,003 |
0.0*\overline{9}*\ldots = 0 + \frac{9}{(10^1 + (-1))*10 * 10^2} = 9/(9*1000) = \dfrac{1}{1000}
|
11,420 |
a*c*b*3 + (a * a + b^2 + c^2 - b*a - b*c - a*c)*(a + b + c) = a^3 + b^3 + c^3
|
17,152 |
1/x = \tan(\frac{π}{2} - \arctan(x)) = \cot(\arctan(x))
|
16,931 |
i\cdot \pi\cdot 2 = \pi\cdot i\cdot 2
|
22,457 |
h^2*4 - h^2*3 = h^2
|
16,780 |
\frac{9^8}{e^9}\cdot 9/\left(9\cdot 8!\right) = \frac{\frac{1}{e^9}}{9!}\cdot 9^9
|
8,638 |
s_1^2 + s_1 \cdot s_2 + s_2^2 + 3 \cdot (-1) = s_1 + s_2 = 0\Longrightarrow s_2 \cdot s_1 = -3
|
-29,038 |
2^7\times 2^3 = 2^{10}
|
-20,764 |
\frac{7\cdot s + 49}{28 + 7\cdot s} = \frac{7 + s}{s + 4}\cdot 7/7
|
43,066 |
35 + 11 \times (-1) = 24
|
19,139 |
\sin(A + B) = \cos(B)\cdot \sin\left(A\right) + \cos(A)\cdot \sin(B)
|
-7,589 |
(2 - 14*i - 6*i + 42*\left(-1\right))/10 = (-40 - 20*i)/10 = -4 - 2*i
|
6,690 |
\cos(x) = t \Rightarrow \operatorname{acos}\left(t\right) = x
|
4,300 |
\frac{\mathrm{d}}{\mathrm{d}x} \tan^{-1}\left(x\right) = \frac{1}{1 + x \cdot x}
|
-26,543 |
-25 x^2 + 9 = \left(3 - 5x\right) (3 + 5x)
|
15,412 |
h\cdot U = U = U\cdot h
|
-922 |
0 + \dfrac{0}{10} + 7/100 + 1/1000 + \frac{7}{10000} = 717/10000
|
6,708 |
-d^2 + g^2 = (g + d)\cdot (-d + g)
|
30,571 |
3*(-\dfrac{1}{n + \frac13} + 1/n) = \frac{1}{n*(1/3 + n)}
|
-16,409 |
2\times \sqrt{25}\times \sqrt{3} = 2\times 5\times \sqrt{3} = 10\times \sqrt{3}
|
29,423 |
\binom{e + x}{e} = \binom{x + e}{x}
|
5,708 |
0 = s^3 - 6 \cdot s + 40 \cdot (-1) = (s + 4 \cdot \left(-1\right)) \cdot (s^2 + 4 \cdot s + 10)
|
10,298 |
5 \cdot h_2 + 8 \cdot (-1) = h_1 \cdot 5 + 8 \cdot \left(-1\right) \implies h_1 = h_2
|
28,897 |
\dfrac{9}{11} = \frac{1}{44} \cdot 36
|
4,302 |
2*M*d^2 + x = x + M*d^2 + M*d^2
|
-22,358 |
36\times (-1) + x^2 + x\times 5 = (9 + x)\times (x + 4\times \left(-1\right))
|
36,132 |
\binom{3}{2} \times 0.8^2 \times 0.2 + 0.8 \times 0.8 \times 0.8 = 0.384 + 0.512 = 0.896
|
12,496 |
x\times 0.1 + x = 1.1\times x
|
12,457 |
4(-yz + z^2 + y \cdot y) = (z \cdot 2 - y)^2 + y \cdot y \cdot 3
|
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