id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-9,211 |
-99 \cdot i + 110 = 2 \cdot 5 \cdot 11 - 3 \cdot 3 \cdot 11 \cdot i
|
24,294 |
\frac{1}{\cos\left(\alpha\right)}\times \sin(\alpha) = \tan(\alpha)
|
-25,371 |
\tan{x} = \frac{\sin{x}}{\cos{x}}
|
-4,538 |
\frac{1}{12*(-1) + x^2 - x}*(3 - 6*x) = -\frac{3}{x + 4*(-1)} - \frac{3}{x + 3}
|
9,639 |
c_1^2 \cdot c_2^2 = (c_1 \cdot c_2)^2
|
18,394 |
\overline{e^{-i\theta}}=\overline{cos\theta-i\sin\theta}=\cos\theta+i\sin\theta=e^{i\theta}
|
8,645 |
\frac{\partial}{\partial x} x^{\alpha} = \alpha\cdot x^{\left(-1\right) + \alpha}
|
14,589 |
\frac{1/b\cdot g}{c\cdot \frac{1}{d}}\cdot 1 = d\cdot g/\left(c\cdot b\right)
|
9,769 |
x^2 - a \cdot a = a^2 - x \cdot x^2 - a^2 = x - a^2
|
32,643 |
(x + 1) (x + (-1)) = (-1) + x^2
|
19,443 |
\dfrac{6*5*4}{216} = \dfrac{5}{9}
|
23,788 |
30 = \left(\frac{9}{40} + 3/40\right)*100
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31,645 |
66 + (-1) + 6(-1) + 6(-1) + 15 \left(-1\right) = 38
|
7,795 |
1 - 2\cdot \sin^2(x) = \cos^2(x) - \sin^2\left(x\right)
|
7,363 |
\pi/4 = -\tan^{-1}(0) + \tan^{-1}(1)
|
588 |
\frac14 + \dfrac{1}{1/3 \cdot 4} = 1
|
-19,063 |
31/45 = E_s/(81\cdot \pi)\cdot 81\cdot \pi = E_s
|
31,624 |
(4x + 2) (x\cdot 4 + 2) = \left(x\cdot 4 + 2\right)^2
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-24,008 |
6 + \tfrac18\times 56 = 6 + 7 = 6 + 7 = 13
|
-20,552 |
-4/9\cdot \frac{6 + W}{W + 6} = \frac{1}{54 + W\cdot 9}\cdot (-4\cdot W + 24\cdot (-1))
|
-10,527 |
\frac{1}{2}\cdot 2\cdot (-\dfrac{1}{z\cdot 2 + 10}\cdot 8) = -\frac{16}{20 + 4\cdot z}
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-7,793 |
\frac{1}{-4}\cdot (-20 + 20\cdot i) = 20\cdot i/(-4) - 20/(-4)
|
1,685 |
\cos\left(3\cdot \pi/4\right) = \cos(5\cdot \pi/4)
|
20,817 |
q \cdot q + (-1) = (q + 1)\cdot (\left(-1\right) + q)
|
-15,061 |
\tfrac{1}{b^5*\frac{1}{x^2}}*b^{10} = \frac{(b^5)^2}{\frac{1}{\frac{1}{b^5}*x^2}}
|
-7,923 |
\frac{1}{32}\cdot (80 + 48\cdot i - 80\cdot i + 48) = \frac{1}{32}\cdot \left(128 - 32\cdot i\right) = 4 - i
|
11,237 |
\dfrac{1}{1 + \tan^2(\operatorname{atan}(y))} = \frac{1}{1 + y^2}
|
6,086 |
2/5\times \frac{1}{7}\times 4 = \frac{8}{35}
|
10,942 |
h*x/h = \frac{h*x}{h}
|
23,321 |
d^n d * d = d^{n + 2} = d^2 d^n
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-9,292 |
12\cdot (-1) - 10\cdot z = -3\cdot 2\cdot 2 - 2\cdot 5\cdot z
|
2,914 |
2\cdot f - v = v\cdot 2 - v\cdot 3 + 2\cdot f
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-8,018 |
\dfrac{1}{29} \left(-24 + 2 i - 60 i + 5 (-1)\right) = (-29 - 58 i)/29 = -1 - 2 i
|
-2,529 |
\sqrt{5} \cdot 2 = (3 + (-1)) \cdot \sqrt{5}
|
6,064 |
\frac{y + \cos\left(y\right)}{-\cos(y) + y} = \frac{\cos(y) \cdot 2}{-\cos(y) + y} + 1
|
37,583 |
\frac1n\times n^2 = n
|
7,397 |
48/(3*4) = 4
|
17,297 |
2 \cdot (2^5 + 3\left(-1\right)) + 2 \cdot \left(2^4 + (-1)\right) + 3 \cdot 2^4 = 58 + 30 + 48 = 136
|
32,101 |
7920 = 11\cdot 10\cdot 9\cdot 8
|
28,578 |
\frac{1}{2}*\left(\cos(s - q) - \cos(s + q)\right) = \sin{q}*\sin{s}
|
-10,393 |
-\frac{1}{20\cdot z + 100}\cdot (16\cdot z + 12\cdot (-1)) = -\frac{3\cdot \left(-1\right) + z\cdot 4}{z\cdot 5 + 25}\cdot 4/4
|
-1,507 |
\frac{1/3\cdot 4}{9\cdot 1/5} = 4/3\cdot \tfrac{1}{9}\cdot 5
|
39,689 |
(-2) + (-1) = -3
|
28,666 |
\sqrt{x} = x^{\frac{1}{2}} = x^{\dfrac36}
|
26,367 |
6^2 \cdot 10^6 \cdot 5 = 3^2 \cdot 2^8 \cdot 5^7
|
33,696 |
\sqrt{z} + \sqrt{f} = \sqrt{(\sqrt{z} + \sqrt{f})^2} = \sqrt{z + f + 2\cdot \sqrt{z\cdot f}}
|
5,864 |
4^{1 + i} = 4*4^i
|
22,598 |
-\frac{1}{2378} \cdot 5 = -\dfrac{5}{2378}
|
10,276 |
\frac{1/a}{b \cdot b} \cdot 1/b \cdot a \cdot a \cdot b^6 = \frac{1}{b^2 \cdot \tfrac{1}{a \cdot a \cdot b^6} \cdot a \cdot b}
|
12,915 |
\cos{n} = \sin{2\cdot n}/\left(2\cdot \sin{n}\right)
|
10,122 |
a^2 + g \cdot a \cdot 2 + g^2 = (g + a)^2
|
-24,188 |
\dfrac{1}{9 + 8}85 = \frac{85}{17} = 85/17 = 5
|
13,287 |
-\frac{1}{d} = 1/(\left(-1\right)\cdot d)
|
31,898 |
(k + 1)^3 = k^3 + 3*k^2 + 3*k + 1 > 3*k * k
|
-5,899 |
\dfrac{1}{n*4 + 24*(-1)}*2 = \frac{2}{4*(n + 6*(-1))}
|
8,452 |
3df = (d + f)^2 - f \cdot f - fd + d^2
|
26,033 |
(\frac{1}{y^2})^2 + (y^2)^2 = (\frac{1}{y \cdot y} + y^2)^2 + 2(-1)
|
33,012 |
\sqrt{a} = a^{\tfrac{1}{2}}
|
20,804 |
-b^3 + a^3 = (a * a + b*a + b^2)*(-b + a)
|
30,849 |
l + 2\cdot (-1) = -(3 + (-1)) + l
|
17,369 |
\frac{1}{\dfrac{1}{3^4}} = \frac{1}{\frac{1}{81}}
|
421 |
\tfrac{1}{-e^{1/y} \cdot \dfrac{1}{y^2}} \cdot ((-2) \cdot \dfrac{1}{y}) = \dfrac{(-2) \cdot y}{(-1) \cdot e^{1/y}} = 2 \cdot y \cdot e^{-1/y}
|
1,870 |
1 + s - t - t*s = (1 - t)*(1 + s)
|
33,875 |
(x \cdot x + xd + d^2) (x - d) = x^3 - d^3
|
4,044 |
n \cdot \tan^{n + (-1)}\left(x\right) = \frac{\partial}{\partial x} \tan^n(x)
|
28,593 |
( x, 0) = \left( x, 1\right) = \left\{( x, 0), \left( x, 1\right)\right\}
|
22,917 |
-2 - \frac{3}{5} = -(3/5 + 2)
|
-5,785 |
\frac{1}{4*z + 20}*2 = \frac{2}{\left(5 + z\right)*4}
|
20,276 |
xy^3=yxy^2
|
28,782 |
\left(1 + x\right)*(1 + x^2 - x) = x^3 + 1
|
-4,690 |
-\frac{3}{4 + x} + \frac{2}{x + (-1)} = \tfrac{-x + 11}{4 \cdot (-1) + x^2 + x \cdot 3}
|
-3,695 |
\frac{1}{q^2}\cdot q\cdot \tfrac{132}{99} = \dfrac{q\cdot 132}{99\cdot q^2}\cdot 1
|
11,350 |
U U^r = U^r U
|
22,346 |
-2*G + G^2 = 0 rightarrow 0 = G,2
|
24,804 |
1/y = \bar{y} = y^2 \cdot y rightarrow 1 = y^4
|
10,145 |
\frac{1}{(1 + (-n + 1)/(2\cdot n))\cdot 2 + 1} = \tfrac{n}{n\cdot 2 + 1}
|
1,578 |
2.519631233*\dotsm/exp(11) = 242753155112819/9634471581445544690955000
|
-4,459 |
(z + 2 \cdot (-1)) \cdot (z + 5) = 10 \cdot (-1) + z \cdot z + 3 \cdot z
|
12,662 |
4^{n + 1} + (-1) = 4\cdot 4^n + \left(-1\right) = 4\cdot (4^n + (-1) + 1) + (-1) = 4\cdot (4^n + (-1)) + 4\cdot 4 + (-1) = 4\cdot \left(4^n + (-1)\right) + 15
|
6,046 |
\frac{\frac{1}{1000}}{100}(701\cdot 100 + 100\cdot 2.35\cdot 299) = 1.40365
|
1,799 |
2/\pi = (\frac{1}{\pi^2}4)^{1/2}
|
19,391 |
28 = 4^2 + 3\cdot 2^2 = 5 \cdot 5 + 3\cdot 1 \cdot 1 = 1^2 + 3\cdot 3 \cdot 3
|
28,882 |
|h\cdot b| = |h\cdot b\cdot h/h| = |b\cdot h|
|
5,772 |
Y - F \cup Z = \overline{Z} \cap \left(Y \cap \overline{F}\right) = Y - F - Z
|
34,049 |
\tfrac19 = 4/36
|
7,480 |
1 - c/x = x/x - \tfrac{c}{x} = \left(x - c\right)/x
|
-18,999 |
1/9 = \frac{A_q}{81*\pi}*81*\pi = A_q
|
2,102 |
g\cdot x\cdot A = g\cdot A\cdot x
|
-20,294 |
\tfrac{8y + 8}{-y \cdot 40 + 32} = \frac{y \cdot 2 + 2}{8 - y \cdot 10} \cdot 4/4
|
-18,969 |
1/4 = A_p/(4*\pi)*4*\pi = A_p
|
7,690 |
1 + (7\cdot k + 1)\cdot 2 = 14\cdot k + 3 \implies 1 = ( 21\cdot k + 4, 14\cdot k + 3)
|
6,396 |
(\dfrac{g}{f} \cdot f)^x = f^{-x} \cdot f^x \cdot g^x
|
26,105 |
a^{b + x + d} = a^x\cdot a^d\cdot a^b
|
6,716 |
\mathbb{E}(-f + Y) = -f + \mathbb{E}(Y)
|
9,074 |
4*m*x + m^2*4 = (x + 2*m)^2 - x^2
|
2,968 |
(1/10)^2 + \frac{1}{10} \cdot \frac{1}{10} + \cdots + \frac{1}{10} \cdot \frac{1}{10} = 1/10 \gt 0.01
|
-30,498 |
3 = \frac{3}{2} \cdot 2^2 + G = 6 + G
|
-3,951 |
\frac{44 a^5}{a^5 \cdot 55}1 = \frac{1}{a^5}a^5 \cdot \tfrac{44}{55}
|
-7,492 |
\frac{1}{10}56 = 28/5
|
-10,362 |
12/12 \cdot \left(-\frac{1}{3 \cdot l} \cdot 6\right) = -\dfrac{1}{l \cdot 36} \cdot 72
|
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