id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
8,567 |
6 \cdot (l_1 \cdot l_2 \cdot 6 + l_2 + l_1) + 1 = (6 \cdot l_2 + 1) \cdot (l_1 \cdot 6 + 1)
|
17,511 |
\frac{1}{4^m} = \dfrac{1}{\left(2^m\right)^2}
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-22,380 |
(4\cdot (-1) + i)\cdot \left(i + 6\cdot (-1)\right) = i^2 - i\cdot 10 + 24
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33,589 |
g*(1 + y) + \left(y + 1\right)*e = (e + g)*(y + 1)
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-25,238 |
d/dy \dfrac{1}{y^4} = -\frac{4}{y^5}
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-23,281 |
-\frac15 + 1 = \frac15\cdot 4
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20,403 |
(y * y + 2*y + 5)^{\frac{1}{2}} = ((y + 1) * (y + 1) + 4)^{1 / 2} = 2*\left(((y + 1)/2)^2 + 4\right)^{\dfrac{1}{2}}
|
-10,512 |
-\frac{1}{4n \cdot n}(n \cdot 12 + 4(-1)) = 4/4 (-\frac{1}{n^2}(n \cdot 3 + (-1)))
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26,763 |
18^{\frac13} = \frac12*12^{\dfrac13} * 12^{\dfrac13}
|
6,187 |
9 \cdot (f + 1) = 9 \cdot f + f + h + x = 10 \cdot f + h + x
|
25,513 |
x^2+2x+1=(x+1)^2
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24,078 |
( f + b, f - b) = m \cdot f + m \cdot b + n \cdot f - n \cdot b = m \cdot f - n \cdot b + n \cdot f + m \cdot b
|
-17,684 |
1 = 55 + 54*\left(-1\right)
|
3,715 |
z*o = o*z = z * z*o^2 = o^2*z^2
|
37,797 |
x - z + z\cdot 2 = x + z
|
27,118 |
\frac{dy}{dx} = \frac{1}{y^2} + 4\cdot (-1) = \dfrac{1}{y^2}\cdot \left(1 - 4\cdot y^2\right)
|
9,119 |
(a^6)^{1 / 2} = (a^3 * a^3)^{1 / 2} = a^3
|
8,639 |
x^{10} + (-1) = (x^5 + (-1)) \times (1 + x^5)
|
23,309 |
10 = \dfrac{1}{2}\cdot (13 + 7)
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-20,414 |
\tfrac{7*p + 42*(-1)}{24*(-1) + 4*p} = \dfrac14*7*\dfrac{1}{p + 6*(-1)}*(p + 6*(-1))
|
-1,076 |
10/56 = \frac{5}{56 \cdot 1/2} \cdot 1 = 5/28
|
-10,579 |
-\dfrac{3}{6 \cdot \left(-1\right) + 9 \cdot l} = -\frac{1}{l \cdot 3 + 2 \cdot (-1)} \cdot \frac33
|
9,112 |
\frac{1}{2 \cdot \pi} \cdot d = \frac{d}{2} \cdot \pi = \frac{d}{2} \cdot \pi
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21,782 |
\frac{\partial}{\partial z} \sum_{l=0}^\infty e^{-l \cdot z} = -\sum_{l=0}^\infty l \cdot e^{-l \cdot z}
|
20,152 |
tzr = rtz
|
22,398 |
\cos\left(\alpha\right)\cdot \sin(\beta) + \sin(\alpha)\cdot \cos(\beta) = \sin(\alpha + \beta)
|
30,927 |
BR A \Rightarrow BRA
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-12,015 |
4/5 = \dfrac{t}{8 \cdot \pi} \cdot 8 \cdot \pi = t
|
25,370 |
s^2+4s+5=(s+2)^2+1^2
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-23,814 |
\frac{1}{5 + 7} \cdot 84 = 84/12 = \frac{84}{12} = 7
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-7,396 |
4/45 = 4\cdot 1/9/5
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-6,415 |
\frac{112 - 7\cdot x}{192 + x^2\cdot 6 - x\cdot 72} = \frac{1}{6\cdot x^2 - 72\cdot x + 192}\cdot (6\cdot x + x\cdot 2 + 8\cdot (-1) - 15\cdot x + 120)
|
10,695 |
(1 - G)/G = \tan^2{x}\Longrightarrow \cos^2{x} = G
|
30,854 |
\cos(x) = \sin(-x + \tfrac{\pi}{2})
|
41,602 |
B^4 + 1 = B^4 - h^2 = (B^2 + h)\cdot (B \cdot B - h)
|
27,505 |
e^{x*y} = 1 + x*y + \dfrac{y^2*x^2}{2!} + ...
|
-22,849 |
72/16 = 2\cdot 36/(2\cdot 8) = \frac{2\cdot 2\cdot 18}{2\cdot 2\cdot 4} = \dfrac{2\cdot 2\cdot 2\cdot 9}{2\cdot 2\cdot 2\cdot 2} = \frac{9}{2}
|
-20,449 |
\frac{7}{4 \cdot (-1) + p} \cdot 4/4 = \frac{28}{4 \cdot p + 16 \cdot \left(-1\right)}
|
5,969 |
(q + (-1)) (q + 1) + 1 = q^2
|
-2,025 |
-\pi + 17/12*\pi = \frac{5}{12}*\pi
|
-10,720 |
-\frac{1}{x*4 + 10}(16 (-1) + x*2) = -\frac{x + 8(-1)}{2x + 5}*2/2
|
-20,184 |
\frac{k\times 30}{20\times (-1) - 40\times k} = \dfrac{6\times k}{4\times (-1) - k\times 8}\times \frac{5}{5}
|
1,047 |
\frac{(1 + 4)*6}{1 + 6} = \frac{1}{7}*30
|
-4,368 |
\dfrac{11}{8 \cdot t^3} = \dfrac{1/8}{t^3} \cdot 11
|
19,193 |
-b \cdot b + a \cdot a = (-b + a) \cdot (a + b)
|
7,102 |
16^{\dfrac{1}{4} \cdot 3} = \left(16^3\right)^{\frac{1}{4}}
|
40,607 |
x^k = x^{k + (-1)}\cdot k
|
-3,413 |
\sqrt{7}\times (2 + 5 + 3) = \sqrt{7}\times 10
|
-6,634 |
\frac{4}{(9 \cdot (-1) + q) \cdot (q + 4)} = \dfrac{4}{q^2 - 5 \cdot q + 36 \cdot (-1)}
|
12,380 |
x\cdot 2 = \pi\Longrightarrow x = \pi/2
|
-11,484 |
8 + 1 - i \cdot 2 = -i \cdot 2 + 9
|
5,998 |
|(5 + z) (z + 5(-1))| = |25 (-1) + z * z|
|
19,479 |
x = r * r \Rightarrow r = \sqrt{x}
|
-24,843 |
997 + 252 \left(-1\right) = 745
|
-20,070 |
z\cdot 8/(\left(-24\right)\cdot z) = (z\cdot (-8))/(z\cdot (-8))\cdot (-\dfrac{1}{3})
|
4,307 |
|-2 \cdot x + 2| = 2 \cdot |x + \left(-1\right)|
|
27,167 |
1.0 = 1 = ... = 1.0 \cdot ...
|
4,816 |
b\cdot a\cdot 2 = 2\cdot -a\cdot (-b)
|
20,189 |
\mathbb{E}[U] + \mathbb{E}[X] = \mathbb{E}[U + X]
|
17,497 |
1/2 = \frac{1}{100} + 49/99 \cdot 99/100
|
26,907 |
\frac66 + 6/5 + 6/4 + 6/3 + \frac{6}{2} + \frac61 = 14.7
|
-15,932 |
57/10 = 7*\frac{1}{10}*9 - \dfrac{1}{10}*6
|
5,291 |
92*1/5/100 = 92/500 = \dfrac{1}{125}*23
|
24,277 |
\frac183 = \frac{\left(-1\right) + 4}{(-1) + 4 + 5}
|
-4,485 |
\dfrac{4\cdot (-1) + 3\cdot x}{x^2 - x\cdot 5 + 6} = -\frac{2}{x + 2\cdot (-1)} + \dfrac{1}{x + 3\cdot (-1)}\cdot 5
|
11,791 |
\cos{z} = \cos(-z + 2\cdot \pi)
|
8,585 |
f_2 \cdot f_1 = \frac{1}{f_2 \cdot f_1} = \frac{1}{f_1 \cdot f_2} = f_1 \cdot f_2
|
4,141 |
250 = 1/(4\cdot \frac{1}{1000})
|
-20,048 |
\frac{1}{9\cdot (-1) + 9\cdot z}\cdot (-5\cdot z + 5) = \tfrac{1}{\left(-1\right) + z}\cdot ((-1) + z)\cdot (-\frac{5}{9})
|
22,530 |
\mathbb{E}\left(x - \theta\right) = \mathbb{E}\left(x\right) - \mathbb{E}\left(\theta\right) = \mathbb{E}\left(x\right) - \theta
|
32,343 |
(0*(-1) + 1)*(b - a) = -a + b
|
13,235 |
Z^{l + 1} = Z*Z^l
|
48,404 |
\sum_{i=0}^m \binom{x + 1}{i} = \sum_{i=0}^m \binom{x + 1}{x + 1 - i} = \sum_{i=m + 1}^{x + 1} \binom{x + 1}{i}
|
-8,004 |
\dfrac{1}{-i\cdot 4 + 4}\cdot \left(24\cdot i - 8\right) = \frac{-8 + i\cdot 24}{4 - i\cdot 4}\cdot \dfrac{1}{4 + 4\cdot i}\cdot \left(i\cdot 4 + 4\right)
|
-22,542 |
\dfrac{7}{8} \times \dfrac{4}{5} = \dfrac{7 \times 4}{8 \times 5} = \dfrac{28}{40} = \dfrac{7}{10}
|
2,520 |
\left(1 - x^2 = u \implies x^2 = 1 - u\right) \implies (1 - u)^{1/2} = x
|
17,756 |
2^{1 / 2} = 1.414213562373\cdot \dotsm
|
-11,978 |
\dfrac{7}{12} = s/(12 π)*12 π = s
|
15,401 |
-d^3 + y^2 \cdot y = (d^2 + y^2 + y\cdot d)\cdot (-d + y)
|
31,693 |
987654321 - 8 \cdot 123456789 = \dfrac{1}{9 \cdot 9} \cdot (1 + 8 \cdot (10^2 + 9 \cdot (-1))) = 9
|
17,226 |
\dfrac{1}{(\dfrac19)^x} = 3^{2 \cdot x}
|
18,941 |
a*b*e = a*b*e = a*b*e
|
-2,839 |
\sqrt{10}\cdot 2 + \sqrt{10} = \sqrt{10} + \sqrt{10}\cdot \sqrt{4}
|
-11,882 |
\tfrac{6.822}{1000} = 6.822*0.001
|
25,232 |
((-1) + n*2)*2n*(n*2 + 2(-1)) \dotsm = (2n)!
|
3,794 |
\frac{52!}{39!*13!} = 52!/\left(13!*39!\right)
|
-17,200 |
\frac{\cos^2{x}}{\cos^2{x}} = \frac{1}{\cos^2{x}}*\left(1 - \sin^2{x}\right)
|
-7,502 |
\dfrac{42}{6} = 7
|
33,361 |
a^2 - x^2 = \left(x + a\right)*\left(-x + a\right)
|
-26,147 |
-2*\cos{4*\pi} - -2*\cos{3*\pi} = -2 + 2*(-1) = -4
|
23,496 |
\sin(-x + t) = \cos(x)\cdot \sin\left(t\right) - \sin(x)\cdot \cos(t)
|
9,778 |
\frac{1}{40}\left(3000 + 2l\right) = 3000/40 + \tfrac{2}{40}l = 75 + l/20
|
9,404 |
x^Y*h*e^Y*x = x^Y*h*e^Y*x = x^Y*h = h^Y*x
|
12,020 |
4 + 4^{2\cdot p + 2} = 4 \cdot 4\cdot 4^{p\cdot 2} + 4
|
113 |
4 \cdot (1! \cdot \binom{9}{1} + \binom{9}{2} \cdot 2! + \ldots + 9! \cdot \binom{9}{9}) = 3945636
|
13,578 |
E[(X - E[X])^2] = -E[X]^2 + E[X^2]
|
-29,356 |
x \cdot (-7) \cdot \left(x + 3 \cdot (-1)\right) = x^2 - 3 \cdot x - 7 \cdot x + 21 = x^2 - 10 \cdot x + 21
|
42,649 |
1000 = 0 + 0*(-1) + 1000
|
23,532 |
2\cdot n = 2\cdot ((-1) + n) + 2
|
20,846 |
\mathbb{E}[T] = \mathbb{E}[\sum_{k=1}^m T_k] = \sum_{k=1}^m \mathbb{E}[T_k]
|
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