id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
17,058 |
x = u + \vartheta\Longrightarrow \vartheta = -u + x
|
40,411 |
\mu_n = \mu_n
|
-9,211 |
110 - 99\times k = -k\times 3\times 3\times 11 + 2\times 5\times 11
|
-20,170 |
\frac{1}{48\cdot s}\cdot (24\cdot (-1) + 8\cdot s) = \frac{8}{8}\cdot \frac{1}{s\cdot 6}\cdot (3\cdot (-1) + s)
|
31,997 |
d + g + e = g + e + d
|
2,279 |
\tfrac{x^2}{s + z} = (2x)^2*\frac{1}{s + z}/4 \geq \frac14(4x - s - z)
|
-3,647 |
\frac{q^4}{q^2} = \frac{q\cdot q\cdot q\cdot q}{q\cdot q} = q \cdot q
|
-2,453 |
\sqrt{10} = \left(5 + 4(-1)\right) \sqrt{10}
|
-23,163 |
-5/4 \cdot 2 = -\frac52
|
33,935 |
7 + 2*y = 41/4*\left(28/41 + \frac{1}{41}*8*y\right) + 0
|
-22,394 |
1 = 3 + 2\times (-1)
|
10,368 |
(\left(-1\right) + k)/k = 1 \implies k + \left(-1\right) = k
|
33,766 |
\cos(2\pi + x) = \cos(2\pi) \cos(x) - \sin(2\pi) \sin(x) = \cos(x)
|
-16,591 |
112^{\frac{1}{2}}\cdot 2 = (16\cdot 7)^{\frac{1}{2}}\cdot 2
|
16,016 |
b + x + y = y + b + x
|
38,317 |
n^2 \cdot n \gt 22 n^2 = 3n^2 + 7n^2 + 12 n^2 \gt 3n \cdot n + 7n + 12
|
-26,389 |
(-3)*\left(-3\right)*\left(-3\right)*(-3) = 81
|
21,057 |
k = l + (-1) \implies \left\lfloor{\frac{1}{l}*(k + 1)^2}\right\rfloor = l > l + (-1)
|
7,652 |
txz = tx z
|
-23,158 |
-\dfrac{8}{9} \cdot -\dfrac{2}{3} = \dfrac{16}{27}
|
-20,204 |
\frac{t + 3}{24 + 8t} = \dfrac181
|
5,488 |
\dfrac{4}{3} = \frac{1}{3} 4
|
9,227 |
9 = 1/(\frac{1}{9})
|
16,115 |
\sqrt{5}*h + f*5 = \sqrt{5}*(h + f*\sqrt{5})
|
33,651 |
\frac{1}{(1 + \frac{x^2}{2}\cdot 3)\cdot 2} = \frac{1}{2 + x^2\cdot 3}
|
32,863 |
\frac{1}{i! (-i + n)!}n! = {n \choose i}
|
4,724 |
(c \cdot x)^3 = 3375 \Rightarrow 15 = x \cdot c
|
7,651 |
(-1) + x^2 = \left(x + \left(-1\right)\right)\cdot (x + 1)
|
-6,438 |
\dfrac{1}{20 (-1) + f*2} = \dfrac{1}{2(10 (-1) + f)}
|
3,694 |
\frac{7!}{2!\times 2!\times 3!} = \binom{5}{2}\times \binom{3}{3}\times \binom{7}{2}
|
27,146 |
\operatorname{im}{\left(x\right)} = \sin{m*\pi/n} \Rightarrow e^{\frac{\pi*m}{n}*i} = x
|
8,886 |
k^2 + k = \left(1 + k\right) \cdot \left(1 + k\right) - 1 + k
|
15,032 |
(z \cdot x^2 + y \cdot y \cdot x + z^2 \cdot y)/2 + 3 = 3 + (y \cdot x \cdot y + z \cdot z \cdot y + x \cdot z \cdot x)/2
|
37,978 |
\dfrac{n}{n \cdot n^2} = \tfrac{1}{n^2}
|
-23,014 |
63/56 = 9*7/\left(8*7\right)
|
5,449 |
\left(v_1 + v_2\right)\cdot s = v_2\cdot s + s\cdot v_1
|
17,697 |
\dfrac{1}{e} + e^{-1^{-1}} = \frac2e \lt (1 + \frac1e \times 2)/2
|
23,231 |
1/(\frac{1}{d}\cdot b) = d/b
|
30,894 |
\left(-\infty,\infty\right) = \R
|
27,701 |
x_5 + 1 = \tfrac{1}{1 - x_5}\cdot (-x_5 \cdot x_5 + 1)
|
14,280 |
(1 - \frac12 + \epsilon) = 1/2 + \epsilon
|
-1,831 |
\dfrac{13}{4} \cdot \pi = \pi \cdot \dfrac{17}{12} + \pi \cdot 11/6
|
4,402 |
( \rho(z), y) = \left( \rho(z), \rho(\rho^{-1}(y))\right) = \left( z, \rho^{-1}(y)\right)
|
-29,519 |
5!/3! = \frac16\cdot 120 = 20
|
-9,808 |
-0.45 = -\frac{1}{10} \cdot 4 = -\frac{1}{20} \cdot 9
|
20,124 |
E_1 \cup E_2 = E_2 \cup E_2 = E_2 = E_2 = E_1 \cap E_2
|
16,842 |
\left(b \cdot b + a^2 + a\cdot b\right)\cdot \left(-b + a\right) = a^3 - b^3
|
16,775 |
(n \cdot i)^2 = i \cdot i \cdot n^2
|
29,529 |
\sqrt{\tfrac{4\cdot 6 + (-1)}{6 + 4\cdot (-1)}} = \sqrt{23/2} \lt 4
|
-1,170 |
-8/3 \cdot (-8/9) = \frac{1}{(-1) \cdot 9 \cdot 1/8} \cdot (\tfrac{1}{3} \cdot (-8))
|
24,546 |
-e^e + e^{(-1) + e} e = 0
|
7,852 |
-(-y + x)^2 + (x + y)^2 = y \cdot x \cdot 4
|
23,897 |
\cos^2 A+\cos^2 A=2\cos^2 A
|
29,717 |
-218/45 = -218/45
|
27,670 |
\cot\left(A\right) - \tan(A) = (\cos^2\left(A\right) - \sin^2\left(A\right))/(\sin(A)*\cos(A)) = 2*\cot\left(2*A\right)
|
-9,268 |
-88\cdot z^3 = -z\cdot z\cdot z\cdot 2\cdot 2\cdot 2\cdot 11
|
19,938 |
f + h = \left(f + h\right)^2 = f^2 + f \cdot h + h \cdot f + h^2 = f + f \cdot h + h \cdot f + h
|
32,374 |
\frac{1}{4} = \dfrac{2}{8}
|
2,281 |
\dfrac{1}{15}\times 12\times \tfrac{11}{14} = 22/35
|
-22,844 |
\frac{50}{20} = \frac{5}{2\cdot 10}\cdot 10
|
16,098 |
-z_2*z_1 = z_1*\left(-z_2\right)
|
43,653 |
{21 \choose 9} = {9 + 12 \choose 9}
|
31,892 |
(-w + \sqrt{w})/(\sqrt{w}) + \frac11 \times (1 - \sqrt{w}) = (1 - \sqrt{w}) \times 2
|
5,400 |
y = \left((y + 7*\left(-1\right))^2 + 11*(-1)\right)^2 = (y^2 - 14*y + 38) * (y^2 - 14*y + 38)
|
-9,300 |
-3\cdot 2\cdot 2\cdot 3 - 2\cdot 2\cdot 3\cdot 7\cdot i = -84\cdot i + 36\cdot (-1)
|
2,233 |
-x^2/4 + 1 = \frac14*\left(4 - x^2\right)
|
35,241 |
\overline{x*y} = \overline{y}*\overline{x}
|
28,780 |
4\cdot \binom{8}{4}\cdot 4^4 - 4^5 - \binom{8}{4}\cdot 4 + 4 = 70380
|
14,976 |
\dfrac{z^2}{(-1) + z z} = \frac{1}{(z + (-1)) (z + 1)} z z
|
33,684 |
26 = 3^2 \cdot 3 + (-1)
|
1,770 |
x^2 + z^2 + \left(-1\right) = x^2 + \left(z + 1\right) \left(z + (-1)\right)
|
-7,135 |
2/7 = \frac{6*\frac17}{3}
|
-16,157 |
8\cdot 7\cdot 6 = \frac{8!}{(8 + 3 (-1))!} = 336
|
23,885 |
(i \cdot l_2 \cdot l_1) \cdot (i \cdot l_2 \cdot l_1) = i \cdot i \cdot l_2^2 \cdot l_1^2 = i \cdot l_2 \cdot l_1 \cdot i \cdot l_2 \cdot l_1 \cdot i \cdot l_2 \cdot l_1 = (i \cdot l_2 \cdot l_1)^3
|
-2,281 |
1/15 = \frac{1}{15} \cdot 5 - \dfrac{4}{15}
|
-8,064 |
\frac{1}{5i + 1}(20 i + 30) \frac{1 - i\cdot 5}{1 - i\cdot 5} = \tfrac{1}{1 + i\cdot 5}(30 + 20 i)
|
-4,440 |
\dfrac{9x-6}{x^2-2x-8} = \dfrac{5}{x-4} + \dfrac{4}{x+2}
|
27,576 |
\cos\left(\frac12\cdot \pi - x\right) = \sin(x)
|
2,447 |
\frac{1}{16} = -1/16 + \frac18
|
30,195 |
\left|{I + a\cdot X\cdot C}\right| = \left|{I + a\cdot C\cdot X}\right| = \left|{I + a\cdot X^{\dfrac12}\cdot C\cdot X^{\frac{1}{2}}}\right|
|
-20,140 |
\dfrac{9 \cdot y + 54}{27 \cdot (-1) + 81 \cdot y} = 9/9 \cdot \dfrac{6 + y}{y \cdot 9 + 3 \cdot (-1)}
|
17,271 |
0 = x^{j + (-1)}\times c\times c = x^{j + \left(-1\right)}\times c^2 = x^{j + 2\times (-1)}\times c\times x\times c
|
-26,636 |
-49 \cdot y^2 + 16 \cdot z^2 = \left(4 \cdot z - y \cdot 7\right) \cdot (4 \cdot z + 7 \cdot y)
|
26,486 |
(7 + 9) \cdot 2 = 32
|
-20,636 |
\frac{1}{r \cdot 10 + 30} \cdot (-60 \cdot r + 80 \cdot (-1)) = \frac{10}{10} \cdot \frac{1}{3 + r} \cdot \left(8 \cdot (-1) - 6 \cdot r\right)
|
40,163 |
v*y*x + x'*z + z*y' + z*v = y'*z + x*y*v + z*x'
|
4,807 |
x^2 + z\cdot x\cdot 4 + z \cdot z = -3\cdot (4\cdot x + z)^2 + (2\cdot z + x\cdot 7)^2
|
6,389 |
9\cdot l_2 + 6\cdot l_1 = 3\cdot 3\cdot l_2 + 2\cdot 3\cdot l_1 = 3\cdot (3\cdot l_2 + 2\cdot l_1)
|
24,572 |
\{x_1,x_2\} \Rightarrow \{x_1, x_2\}
|
13,754 |
\sqrt{\dfrac{1}{2 * 2} + \dfrac{1}{2^2}} = 1/\left(\sqrt{2}\right)
|
31,877 |
\dfrac{212}{39} = 5 + \frac{1}{39}\cdot 17
|
2,392 |
\cos\left(3 \cdot x\right) = \cos\left(2 \cdot x + x\right) = \cos\left(2 \cdot x\right) \cdot \cos(x) - \sin(2 \cdot x) \cdot \sin(x)
|
-20,979 |
\frac22 \frac12(5(-1) - z*7) = \frac14(-z*14 + 10 (-1))
|
-19,673 |
\frac{9}{9}\cdot 2 = 18/9
|
8,355 |
x^5 - 55*x + 21 = (x * x - x*3 + 1)*\left(21 + x * x * x + x^2*3 + 8*x\right)
|
5,406 |
n!/x! = ((n + 1) \cdot (n + 2) \cdot \dots \cdot x)^{-1} \lt n^{n - x}
|
23,885 |
(i\cdot l\cdot n)^2 = i^2\cdot l \cdot l\cdot n^2 = i\cdot l\cdot n\cdot i\cdot l\cdot n\cdot i\cdot l\cdot n = \left(i\cdot l\cdot n\right) \cdot \left(i\cdot l\cdot n\right) \cdot \left(i\cdot l\cdot n\right)
|
46,004 |
\frac23*30 = 20
|
23,942 |
x_1 + 4\cdot x_1 + x_2 + x_2\cdot 4 = x_2 + x_1
|
17,725 |
a^n + f*a^{(-1) + n}*{n \choose 1} + \ldots = (a + f)^n
|
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