id
int64
-30,985
55.9k
text
stringlengths
5
437k
31,739
-(\sqrt{-2 \cdot m})^2 = m \cdot 2
49,005
14 = 28/2
44,518
\frac{1}{\sin(\pi/6*2/2)} \sin(\frac12 (3 + 1) \frac{\pi*2}{6}) \sin(3/2*2 \pi/6 + \pi/6) = 3/2
16,210
\sin\left(z\right) \cos(z) \cdot 2 = \sin\left(z \cdot 2\right)
17,671
x^4 - 2 \cdot x^2 + 8 \cdot \left(-1\right) = (x^2 + (-1))^2 + 9 \cdot \left(-1\right) = (x^2 + (-1) + 3 \cdot \left(-1\right)) \cdot (x^2 + (-1) + 3) = (x + 2 \cdot (-1)) \cdot (x + 2) \cdot (x^2 + 2)
4,876
x^{f - h} = \frac{x^f}{x^h}
7,622
\dfrac{1}{2 \cdot c} \cdot \left(a - b + c\right) = 1/2 + \dfrac{1}{2 \cdot c} \cdot (a - b)
17,228
-w_{yy} a^2 + w_t = 0 \Rightarrow w_t w = a^2 ww_{yy}
13,039
(2 - k)^2 = \left(-(k + 2*(-1))\right) * \left(-(k + 2*(-1))\right) = (-1) * (-1)*(k + 2*\left(-1\right))^2 = \left(k + 2*\left(-1\right)\right) * \left(k + 2*\left(-1\right)\right)
23,218
\left|{Z}\right|^2 = \left|{Z}\right| \left|{Z}\right|
4,844
{180 + 3 \cdot \left(-1\right) + 2 \choose 2} = 15931
12,104
c \cdot b \cdot m = m \cdot b \cdot c
231
\frac{1}{\omega}*(-x * x + (x + \omega)^2) = \omega + 2*x
-22,368
(2(-1) + x) (5(-1) + x) = x^2 - x\cdot 7 + 10
3,737
(b^2 + a^2 + ab) \left(a - b\right) = a \cdot a^2 - b^3
8,994
5 m_2 = m_1 \Rightarrow 3 m_1 = 15 m_2
8,338
m\cdot x\cdot 2 = -m + m\cdot (2\cdot x + 1)
27,526
\sin\left(b + a\right) = \sin\left(a\right) \cdot \cos(b) + \cos(a) \cdot \sin(b)
41,148
2 = (1 + i) * (1 + i) \approx (1 + i)*\left(1 - i\right)
11,441
\int_0^t x t\,dt = x t^2/2
15,783
\sqrt{x} - \dfrac{1}{\sqrt{x}} = (x + \left(-1\right))/(\sqrt{x})
-2,080
\pi/3 = \pi\cdot \frac76 - \pi\cdot \frac{5}{6}
-3,952
8/4*\frac{s^2}{s * s} = \frac{s^2*8}{4*s^2}
26,019
\left(n + 1\right)/n\cdot z = \frac{1}{n\cdot z^n}\cdot z^{n + 1}\cdot (n + 1)
5,503
x^3 + 0\cdot x^2 + 0\cdot x + 0 = (x + 0) \cdot (x + 0) \cdot (x + 0)
-4,336
\frac{1}{t^2\cdot 2} = \tfrac{1}{2t^2}
-1,845
5/3 \cdot \pi + \frac{1}{4} \cdot 7 \cdot \pi = \frac{1}{12} \cdot 41 \cdot \pi
37,239
(y + z)\cdot 3 = y\cdot 3 + 3\cdot z
29,253
z^5 + (-1) = \left(z + (-1)\right) \cdot (1 + z^4 + z^2 \cdot z + z^2 + z)
12,544
{n \choose i}*i = {(-1) + n \choose i + \left(-1\right)}*n
-20,959
-1/2 \cdot \frac{1}{2} \cdot 2 = -\dfrac{1}{4} \cdot 2
-30,239
20 + y^2 - y \cdot 12 = (y + 2 \cdot (-1)) \cdot (y + 10 \cdot (-1))
-1,841
\frac14*π - π*4/3 = -13/12*π
-12,773
8 = 6 (-1) + 14
28,491
\frac{1}{x + (-1)} - \frac1x = \frac{1}{x\cdot ((-1) + x)}
9,376
\dfrac{1}{x + 4} \left(x + (-1)\right) = \frac{x + 4 + 5 (-1)}{x + 4} = 1 - \frac{5}{x + 4}
8,248
2*g + 3 = 5 + 2*(g + (-1)) = (2^3 + 2)/2 + 2*(g + (-1))
594
\left|{C \cdot H + x}\right| = \left|{H \cdot C + x}\right|
-8,490
-\frac{1}{-1} = 1
26,769
A*E*A*E*A*E = \left(E*A\right) * (A*E)^2
7,875
z^{j + n} = z^n*z^j
11,417
5/216 = \tfrac{5\cdot 1/36}{6}
11,970
1 = \dfrac{2^1 - 2^0}{0\cdot (-1) + 1}
-27,508
a^2 \cdot 12 = 2 \cdot 2 \cdot 3 \cdot a \cdot a
20,189
\mathbb{E}\left[U + X\right] = \mathbb{E}\left[U\right] + \mathbb{E}\left[X\right]
21,325
\left(1 + 2^{22} + 2^{11}\right)\cdot \left(2^{11} + \left(-1\right)\right) = (-1) + 2^{33}
13,883
-(f^6)^{30} + \left(f^6\right)^{15} + (f^6)^8 - f^6 = -f^6 - f^{180} + f^{90} + f^{48}
7,858
-(u^2 + x^2 + t^2) + \left(u + x + t\right)^2 = 2\times (t\times u + x\times u + x\times t)
922
|\frac{1}{2\times x\times i + 1}\times (-3\times x + 2\times i)| = \frac{|2\times i - 3\times x|}{|i\times x\times 2 + 1|}
21,560
\sqrt{2 \cdot 2 - x \cdot x} = d \Rightarrow d^2 + x^2 = 2^2
6,168
1 - e^{\frac{1}{\tfrac{1}{10}}\cdot ((-1)\cdot \frac{1}{12})} = 1 - e^{-\frac{10}{12}} \approx 0.5654
-4,279
\frac{n^3}{n^2}\cdot 2/5 = \frac{2}{5n^2}n^3
806
l - (l + 1)/2 = (2 \cdot l - x + 1)/2 = (2 \cdot l - x + 1)/2 + 0 \cdot \left(-1\right)
44,274
0 \approx 0.0001 \cdot \pi/2
-7,026
\frac16 = \frac16
-7,566
\left(-30 + 6 \cdot i + 20 \cdot i + 4\right)/13 = \frac{1}{13} \cdot (-26 + 26 \cdot i) = -2 + 2 \cdot i
16,455
\mathbb{E}[(x_1 \cdot x_2)^2] = \mathbb{E}[x_1^2 \cdot x_2^2] = \mathbb{E}[x_1 \cdot x_1] \cdot \mathbb{E}[x_2^2]
12,350
x^4 + 1 = \left(x - u\right)\cdot (x - u^3)\cdot (x - u^5)\cdot (x - u^7) = (x - u)\cdot \left(x - u^3\right)\cdot \left(x + u\right)\cdot (x + u^3)
9,372
\dfrac12 \times (35 \times \left(-1\right) - 7) = -21
-4,077
\tfrac{s^4}{s \cdot 15} \cdot 18 = s^4/s \cdot \frac{1}{15} \cdot 18
17,194
2 \cdot 2R = 4R
19,683
\sum_{k=1}^\infty \int f_k\,dx = \int \sum_{k=1}^\infty f_k\,dx
-5,972
\frac{t}{t^2 + 11\cdot t + 30} = \dfrac{t}{(t + 5)\cdot \left(t + 6\right)}
-3,922
\frac{66*d^2}{30*d^5} = 66/30*\frac{d^2}{d^5}
5,664
z^B Dz = (z^B Dz)^B = z^B D^B z
-18,635
-\frac{1}{14}29 = -29/14
23,799
\left(\dfrac12\cdot \left(1 - \sin{x}\right) = 1\Longrightarrow \sin{x} = -1\right)\Longrightarrow x = 3\cdot \pi/2
5,076
(1 - x)^{l + 3\cdot (-1)} = (-1)^{l + 3\cdot (-1)}\cdot (x + (-1))^{l + 3\cdot \left(-1\right)} = (-1)^{l + (-1)}\cdot \left(x + (-1)\right)^{l + 3\cdot (-1)}
1,051
20 x^3 + 17 = 20 (3\left(-1\right) + x^3) + 77
24,090
(-i)^3 = -i^3
-10,559
24/(z*75) = \tfrac{8}{z*25}*\dfrac{3}{3}
-9,910
-\tfrac{20}{25} = -0.8
42,178
l + n + 1 + 1 = l + 1 + n + 1
20,017
-\sin^2(y) + \cos^2\left(y\right) = \cos(2y)
19,588
(-1) + 2^{x + (-1)} + (-1) = 2*(-1) + 2^{(-1) + x}
42,423
1 = \left(\frac1e\right)^0
36,698
f + c = f + c
5,339
28/7 = (7 + 1 + 2 + 3 + 4 + 5 + 6)/7
24,928
e^C\cdot e^X = e^{X + C}
-22,092
10/6 = \frac{1}{3}5
2,212
\frac{4}{1 + 16 t^2} = \frac{d}{dt} \arctan(4t)
6,748
\frac{25}{9} = \frac59*5
679
\frac{n!}{2 \times n} = \left(n + (-1)\right)!/2 \geq n
1,877
4 > |y|\Longrightarrow 1 \gt |y|/4
9,141
(-1) + (z + 1)^2 = z^2 + 2\times z
-4,418
(5 \cdot (-1) + y) \cdot \left(y + \left(-1\right)\right) = y^2 - y \cdot 6 + 5
30,312
f\cdot B = B\cdot f
-20,987
\frac{4 + n*10}{7*(-1) - n*9}*\dfrac{7}{7} = \dfrac{28 + 70*n}{49*(-1) - 63*n}
3,791
\overline{a}\times \overline{b} = \overline{b}\times \overline{a}
16,114
(0\left(-1\right) + y)^x = y^x
37,211
6 = 2 \times 2^2 + 2 \times \left(-1\right)
12,648
\dfrac{n!}{k!} = \binom{n}{k} \cdot (-k + n)!
5,277
\tfrac{1}{6} = \frac{10}{60}
-25,362
\dfrac{d}{dx}[\cot(x)]=-\dfrac{1}{\sin^2(x)}
414
\frac{1}{1 + W \cdot x} = \dfrac{1}{(x + \frac{1}{W}) \cdot W}
17,197
\alpha/(\bar{\alpha}) = \alpha \times \alpha/(\alpha\times \bar{\alpha})
26,026
A*I*c = A*c*I
36,124
|-z + 1/\left((-1)\cdot z\right)| = |\frac1z + z|
-15,945
\frac{17}{10} = 5*\dfrac{7}{10} - 6*3/10
8,310
\tfrac{5}{4 \cdot 3 \cdot 2} 8 \cdot 7 \cdot 6 = 70