id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
14,830 |
\frac{1}{12}(2^6 + 8 \cdot 2^2 + 2 \cdot 2 \cdot 2^2 \cdot 3) = 12
|
20,920 |
\frac{dy}{dx} \cdot y = d/dx (\frac{1}{2} \cdot y^2)
|
10,133 |
r^{n + (-1) + n + \left(-1\right) - 2 \cdot (-1) + n} = r^n
|
32,854 |
\frac12 = \frac{-\dfrac{2}{3} + 1}{2\cdot 1/3}
|
-18,334 |
\frac{9\cdot f + f^2}{f^2 + 81\cdot (-1)} = \frac{(9 + f)\cdot f}{(9 + f)\cdot (9\cdot \left(-1\right) + f)}
|
-20,133 |
\frac{y \cdot 8}{(-1) \cdot 80 \cdot y} = -\frac{1}{10} \cdot \frac{1}{(-8) \cdot y} \cdot (y \cdot (-8))
|
41,568 |
\|a - b\| \cdot \|a - b\| = ( a - b, a - b) = ( a, a - b) - ( b, a - b)
|
15,930 |
(4 + 2 \cdot 5 + 3 \cdot 6) \cdot (3 + 2 \cdot 6 + 3) = 576
|
14,273 |
2x\frac{\mathrm{d}x}{\mathrm{d}x} = \frac{\mathrm{d}}{\mathrm{d}x} x * x
|
3,969 |
6^2 + 4^2 = 14^2 - 12^2
|
13,534 |
\sin\left(2y\right)/2 = \sin(y) \cos(y)
|
18,888 |
(h*a*c*d)^2 = h*a*c*d*d*c*a*h
|
11,745 |
(n + (-1))\cdot (n + 2\cdot \left(-1\right)) - n = n^2 - 4\cdot n + 2 = (n + 2\cdot (-1)) \cdot (n + 2\cdot (-1)) + 2\cdot (-1)
|
34,379 |
(b + c)^4 = b^4 + 4b^3 c + 6b^2 c \cdot c + 4bc \cdot c \cdot c + c^4 = b^4 + c^4 + 4bc \cdot (b \cdot b + c^2) + 6b^2 c^2
|
-27,349 |
0 = x^2 - 29 \cdot x + 198 = (x + 11 \cdot (-1)) \cdot \left(x + 18 \cdot \left(-1\right)\right)
|
18,323 |
r*(x + u) = r u + x r
|
44,486 |
-8 = -4 - 4
|
13,120 |
0 = 1 + y^2 + y \implies 0 = y^3 + (-1)
|
-11,535 |
15 + 8 - i\cdot 2 = -i\cdot 2 + 23
|
11,682 |
-z_0\cdot y_0 + y\cdot z = y\cdot z - y\cdot z_0 + y\cdot z_0 - z_0\cdot y_0
|
-2,052 |
\pi \frac{1}{12}23 - \pi/3 = \frac{1}{12}19 \pi
|
24,969 |
\left(z \cdot z + a\cdot z + b\right)\cdot (g + z) = z \cdot z \cdot z + z^2\cdot (g + a) + (b + a\cdot g)\cdot z + g\cdot b
|
-13,544 |
\dfrac{ -15 }{ (4 - 7) } = \dfrac{ -15 }{ (-3) } = \dfrac{ -15 }{ -3 } = 5
|
4,978 |
r^i\cdot r^x = r^x\cdot r^i
|
34,755 |
3\cdot (-1) + n^2 = (2\cdot (-1) + n)\cdot (n + 2) + 1
|
-18,439 |
\dfrac{1}{p\cdot (p + 10\cdot (-1))}\cdot (3\cdot (-1) + p)\cdot (10\cdot (-1) + p) = \dfrac{1}{p^2 - p\cdot 10}\cdot (30 + p^2 - 13\cdot p)
|
27,144 |
\dfrac{3}{16} = \frac{1}{4^2} \cdot (-1^2 + 2^2)
|
33,866 |
x*9 = x*25 = x
|
568 |
(-g^2 + (g + x) \cdot (g + x) - x^2)/2 = g\cdot x
|
13,759 |
(x/4)^{1/3} + 2\left(-1\right) = (x/4)^{1/3} + 2(-1)
|
-22,298 |
7 \cdot (-1) + x^2 - 6 \cdot x = \left(x + 7 \cdot (-1)\right) \cdot (1 + x)
|
10,493 |
1/3 \cdot 2/36 + \frac{1}{9 \cdot 3} = 1/18
|
-18,335 |
\tfrac{1}{l*(l + 6)}\left(6 + l\right) (l + 10 (-1)) = \frac{l^2 - 4l + 60 \left(-1\right)}{l^2 + l*6}
|
-4,610 |
5*(-1) + z^2 + 4*z = \left((-1) + z\right)*(z + 5)
|
19,121 |
g \pi + y y - \left(g + \pi\right) y = \left(y - g\right) (y - \pi)
|
-30,779 |
x * x*7 + 21 = 7*(x^2 + 3)
|
-24,813 |
\left(-1676\right)\cdot (-1) - 108 = 1568
|
28,890 |
\sin{x} \cdot \cos{c} + \sin{c} \cdot \cos{x} = \sin\left(c + x\right)
|
-4,817 |
3.1*10^{-2 - -4} = 3.1*10^2
|
-8,311 |
(-5) \cdot \left(-4\right) = 20
|
35,449 |
\left(n + (-1)\right)\cdot (1 + n) = n^2 + (-1)
|
-1,677 |
-\frac{\pi}{2} + \pi \frac{5}{6} = \dfrac{\pi}{3}
|
-4,552 |
-\frac{1}{(-1) + x} - \frac{5}{2 + x} = \dfrac{1}{x^2 + x + 2\times (-1)}\times \left(-x\times 6 + 3\right)
|
24,787 |
-2 \cdot \sin\left(x\right) \cdot \cos(x) = -\sin\left(x \cdot 2\right)
|
-1,204 |
1/\left(-9/7*8\right) = \dfrac{\left(-7\right)*\frac19}{8}
|
15,743 |
296 + x^2 \cdot 5 + 64 \cdot x = x \cdot x + \left(x + 4\right)^2 + (x + 6)^2 + \left(x + 10\right)^2 + (12 + x)^2
|
-10,487 |
2 = 12 r + 40 (-1) + 16 \left(-1\right) = 12 r + 56 (-1)
|
36,505 |
146097 = 97 + 400\cdot 365
|
4,715 |
\frac{1}{6^2}\cdot \binom{5}{1} = 5/36
|
-10,496 |
\frac13\cdot 3\cdot 9/h = \frac{1}{3\cdot h}\cdot 27
|
7,561 |
(-1) + \frac{1}{2^m} + 1 = \dfrac{1}{2^m}
|
7,245 |
\nu*f = \nu*f
|
8,635 |
\frac153 = \dfrac1q(p + (-1)) \Rightarrow p = \frac153 q + 1
|
24,404 |
792 + 252 \cdot \left(-1\right) = 540
|
30,616 |
b \cdot 2 = 4 \cdot b/2
|
20,945 |
0 = \frac{\chi}{4} + 3/4 y + z/4\Longrightarrow 0 = \chi + 3y + z
|
24,785 |
\frac{1}{12 \cdot 4} = 1/48
|
4,528 |
\sin(e) = \sin(g) \implies g = e
|
-1,122 |
\frac{56}{18} = 56\cdot 1/2/(18\cdot \frac12) = 28/9
|
19,177 |
(2 \cdot \sqrt{3}) \cdot (2 \cdot \sqrt{3}) = 12
|
6,661 |
2 \cdot v \cdot 3 \cdot x = 6 \cdot v \cdot x
|
-16,335 |
10 \cdot \sqrt{25 \cdot 2} = 10 \cdot \sqrt{50}
|
6,047 |
-d_1 \cdot e_1 + d_2 \cdot e_2 = e_2 \cdot d_2 - d_2 \cdot e_1 + e_1 \cdot d_2 - d_1 \cdot e_1
|
-20,140 |
\frac{1}{y*81 + 27*(-1)}*(y*9 + 54) = \frac{y + 6}{3*(-1) + 9*y}*\frac{1}{9}*9
|
9,652 |
\tfrac{5}{(x + 2\cdot \left(-1\right))\cdot (x + 3)}\cdot (x + (-1))\cdot (x + 2) = \frac{5\cdot x^2 + 5 + 10\cdot (-1)}{(x + 2\cdot \left(-1\right))\cdot (x + 3)} = \dfrac{\frac{1}{x + 2\cdot (-1)}}{x + 3}\cdot (5\cdot x^2 + 5 + 10\cdot \left(-1\right))
|
-30,288 |
\frac{1}{2}*(0 + 80) = 80/2 = 40
|
3,334 |
2ab = a^2 + b^2 - (a - b)^2
|
9,691 |
\lim_{z \to -\infty} -z + z = \lim_{z \to -\infty} (z \cdot z + 5z + 3)^{1/2} + z
|
-25,063 |
\dfrac{1}{8}\times 3\times 2/7 = \frac{6}{56} = \tfrac{3}{28}
|
-2,554 |
\sqrt{11} \sqrt{4} + \sqrt{11} \sqrt{25} = 5 \sqrt{11} + 2 \sqrt{11}
|
19,469 |
\left(2 \cdot (-1) + z\right) \cdot (z + 3) = z^2 + z + 6 \cdot (-1)
|
10,762 |
\frac{1 + m}{m\cdot 2 + 3} = (1 - \frac{1}{2 m + 3})/2
|
11,447 |
\frac{1}{\frac{1}{\sin{t}}*\frac{1}{1/\cos{t}}} = \tan{t}
|
-15,899 |
-7 \cdot 4/10 + 6 \cdot \frac{6}{10} = 8/10
|
-9,326 |
t\cdot 2\cdot 2\cdot 2 = t\cdot 8
|
7,805 |
3/4*\int A^{-\frac13}\,dA = 3/4*\int \dfrac{1}{A^{\dfrac13}}\,dA
|
6,518 |
625/576 = (-7/24) * (-7/24) + 1
|
26,154 |
\frac{\partial}{\partial y} y^{m \cdot 2 + 1} = (1 + 2 \cdot m) \cdot y^{2 \cdot m}
|
40,555 |
\dfrac{1}{3}\cdot 3 = 1 = 3 + 2\cdot \left(-1\right)
|
-20,278 |
\frac{10\cdot (-1) - x\cdot 3}{10 + x\cdot 3} = -1^{-1}\cdot \frac{1}{x\cdot 3 + 10}\cdot (10 + 3\cdot x)
|
30,310 |
\cos^2(w + x/2) = \sin^2\left(\pi/2 + x/2 + w\right)
|
23,426 |
x^6 + \left(-1\right) = (x^3 + (-1))\cdot (x^3 + 1) = (x + (-1))\cdot (x^2 + x + 1)\cdot (x + 1)\cdot (x^2 - x + 1)
|
39,182 |
(A\cdot A^T)^T = \left(A^T\right)^T\cdot A^T = A\cdot A^T
|
11,183 |
\left(2z + (-1) = 0 \implies 1 = 2z\right) \implies z = \frac12
|
27,552 |
e_R*s = e_R*s
|
-20,034 |
\dfrac{1}{45}*(-10*x + 15*(-1)) = \frac{1}{9}*(-2*x + 3*(-1))*\frac55
|
-2,063 |
-\pi \cdot \frac13 \cdot 2 + \frac{5}{12} \cdot \pi = -\frac14 \cdot \pi
|
-2,935 |
10^{1/2} - 9^{1/2}\cdot 10^{1/2} + 25^{1/2}\cdot 10^{1/2} = 10^{1/2}\cdot 5 + 10^{1/2} - 3\cdot 10^{1/2}
|
625 |
|y - x| = |y + x| \implies |-x + y|^2 = |x + y|^2
|
-20,108 |
\tfrac{1}{y*(-35)}(70 - 14 y) = \frac{7}{7} \frac{-2y + 10}{(-5) y}
|
30,996 |
5^2 - 3^2 = 16
|
-5,503 |
\tfrac{4}{r^2 + 12 r + 36} = \frac{1}{(6 + r) (6 + r)} 4
|
-22,381 |
(6 + x) \left(4(-1) + x\right) = x \cdot x + x \cdot 2 + 24 (-1)
|
2,024 |
k^3 + k^2 + k*2 + 1 = k^3 + (k + 1)^2
|
8,994 |
j*5 = m \Rightarrow 3*m = j*15
|
-2,273 |
\dfrac{3}{12} - \tfrac{1}{12} = 2/12
|
-4,334 |
\frac{10}{9} = \frac{10}{9}
|
36,927 |
1/(\beta z) = \frac{1}{z\beta}
|
16,282 |
(x^2 - x + 1)\times (1 + x) = 1 + x^3
|
-6,989 |
2\cdot \dfrac{1}{8}/7 = \frac{1}{28}
|
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