id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
2,480 |
g + 0 + 0 = ( g, ( 0, 0)) = ( g, 0) = g
|
42,377 |
(10 + (-1))*3 = 27
|
5,524 |
{x \choose 2} - x + 2 \left(-1\right) = 1 + {x + \left(-1\right) \choose 2}
|
1,876 |
\frac{1}{4} + \frac{1}{5}\cdot \vartheta = (5 + 4\cdot \vartheta)/20
|
10,940 |
\frac{1}{1/2 \sqrt{H}}(A_H - \frac{H}{2}) = (2A_H - H)/(\sqrt{H})
|
29,934 |
(3^2 + 2^2)^{1 / 2} = 13^{1 / 2}
|
9,658 |
(z^6 + z^5 + z^4 + z^3 + z^2 + z + 1) ((-1) + z) = (-1) + z^7
|
51,695 |
\frac {30} 3 - 1 = 10 -1 = 9
|
7,615 |
375 = {6 \choose 4} \cdot 5^2
|
1,245 |
z_2 + (-1) = z_1 + (-1) \Rightarrow z_1 = z_2
|
22,989 |
\dfrac{p}{z} + z = q\Longrightarrow \frac{1}{2}*(q \pm \left(-4*p + q^2\right)^{1/2}) = z
|
21,051 |
\frac{dC}{dx} = \frac{4C^2}{4Cx}1 = C/x
|
-20,201 |
5/7 \cdot \frac{1}{(-1) + a} \cdot (a + \left(-1\right)) = \frac{1}{a \cdot 7 + 7 \cdot \left(-1\right)} \cdot (5 \cdot a + 5 \cdot (-1))
|
6,805 |
d d b^2 c c = b c c d b d
|
53,094 |
22 = 10 + 8 + 4
|
-9,628 |
8\% = 8/100 = \tfrac{2}{25}
|
-3,971 |
\frac{1}{n^4}\cdot n = \dfrac{n}{n\cdot n\cdot n\cdot n} = \dfrac{1}{n^3}
|
-19,338 |
\frac{2}{3} \cdot 4/7 = \frac{4 \cdot 1/7}{3 \cdot 1/2}
|
43,045 |
204.68 = 51.17 \cdot 4
|
29,657 |
30 = {5 \choose 4}\cdot {3 \choose 3}\cdot {4 \choose 2}
|
33,138 |
Z_l\cdot Z_k = Z_l\cdot Z_k
|
-15,423 |
\frac{x^2 \cdot 1/y}{(x \cdot y^3) \cdot (x \cdot y^3)} = \tfrac{x^2 \cdot 1/y}{y^6 \cdot x^2}
|
-3,222 |
2^{\frac{1}{2}}*(5 + 3) = 2^{\dfrac{1}{2}}*8
|
-3,620 |
\tfrac{a}{a^5}\cdot 84/120 = \tfrac{84\cdot a}{120\cdot a^5}\cdot 1
|
7,355 |
\frac{m}{\sqrt{1 + m^4}} + 0 \cdot (-1) + 0 - 0 \cdot \dotsm = \frac{m}{\sqrt{m^4 + 1}}
|
20,608 |
i^2 + \left(-1\right) = (i + 1) \cdot \left((-1) + i\right)
|
1,641 |
-i\cdot π = π\cdot i\cdot 2\cdot (-\frac{1}{2})
|
16,359 |
\sin(-H + D) = \sin(D)\cdot \cos(H) - \cos(D)\cdot \sin(H)
|
15,633 |
\sin^{-1}{1/2} = \frac{1}{6} \cdot \pi
|
-15,916 |
\tfrac{5}{10} - \frac{1}{10}\cdot 9\cdot 7 = -\dfrac{1}{10}\cdot 58
|
23,124 |
\frac{x\cdot x^2}{4} + \dfrac{x \cdot x \cdot x}{4}\cdot 1 + C = \dfrac12\cdot x \cdot x \cdot x + C
|
-6,211 |
\tfrac{1}{(3\cdot (-1) + t)\cdot 5} = \frac{1}{15\cdot (-1) + 5\cdot t}
|
-8,015 |
-\frac{4}{-2}i - \frac{4}{-2} = (-i*4 - 4)/\left(-2\right)
|
35,307 |
(b + a) \cdot 3 = b \cdot 3 + 3a
|
22,346 |
0 = D^2 - 2\cdot D\Longrightarrow D = 0, 2
|
40,961 |
d/c \coloneqq d/c
|
19,442 |
11 \times (74 + 7 \times (-1)) + 7 \times \left(-111 + 11\right) = 11 \times 74 + 7 \times (-111) + 77 \times (-1) + 77 = 11 \times 74 - 7 \times 111 = 37
|
38,875 |
1/\left(\dfrac{1}{0}\right) = 1/\left(1/0\right)
|
41,157 |
3^2 + 2 \cdot 2 = 13
|
-10,700 |
\dfrac{3}{3}\cdot \dfrac{9}{6 + 10\cdot x} = \tfrac{27}{18 + 30\cdot x}
|
14,347 |
1/2 = -\frac{1}{1 + 3\cdot (-1)} = -1 + 3\cdot (-1) + 9\cdot (-1) + 27\cdot (-1) - \cdots
|
18,355 |
2\cdot 32\cdot 4^4 + 8\cdot 28\cdot 4^4 = 73728
|
21,876 |
58 = 50 + 1 - 2\cdot (-7) + 1^2 - 2\cdot 2\cdot (-1) + 2\cdot (-7) + 2^2 + 2\cdot \left(-1\right)
|
14,403 |
4^2 + 6^2 + 12^2 = 7 \cdot 7 \cdot 4
|
14,032 |
Y\cdot 2 + X = Y + X + Y
|
19,204 |
\frac{x}{1/d \cdot c} \cdot 1/b = \frac{d \cdot x}{c \cdot b}
|
-20,079 |
\frac{r \cdot (-4)}{r \cdot (-4)} \cdot \left(-\frac14\right) = \frac{r \cdot 4}{(-16) \cdot r}
|
-19,421 |
\dfrac{\frac{1}{5}}{1/6} \cdot 2 = \frac{2}{5} \cdot \frac{6}{1}
|
15,216 |
(x^2 + w*x + w^2)*(-w + x) = -w^3 + x^3
|
-9,346 |
y \cdot 10 + 50 (-1) = 2 \cdot 5 y - 2 \cdot 5 \cdot 5
|
30,352 |
3 = \frac{1}{1 + 3} \cdot (3 + 3^2)
|
-29,318 |
-7*i + 6 = 4 + 2 - i*7
|
11,665 |
Cov[x + C,x - C] = Cov[x,x] - Cov[x, C] + Cov[x,C] - Cov[C,C] = VAR[x] - VAR[C]
|
32,787 |
R_a R_b = R_a R_b
|
8,394 |
229^2 \cdot 229 - 192^3 = 4931101 = 102 \cdot 102 \cdot 102 + 157^3 = 76 \cdot 76 \cdot 76 + 165 \cdot 165^2
|
-23,810 |
\dfrac{63}{5 + 2} = \dfrac{63}{7} = 63/7 = 9
|
-16,940 |
5 = 5*2*a + 5*(-4) = 10*a - 20 = 10*a + 20*(-1)
|
6,300 |
x*d = d^{1 / 2} * d^{1 / 2}*(x^{\frac{1}{2}})^2
|
-5,825 |
\frac{n\cdot 3}{n^2 + n + 42\cdot (-1)}\cdot 1 = \frac{n\cdot 3}{(n + 6\cdot (-1))\cdot (n + 7)}
|
2,580 |
b^2 + a^2 - ab\cdot 2 = (a - b) (a - b)
|
-5,318 |
10^1 \cdot 7.1 = 10^{-4 + 5} \cdot 7.1
|
28,890 |
\sin\left(e + c\right) = \sin{c}*\cos{e} + \cos{c}*\sin{e}
|
23,280 |
a^T ax = a^T ax
|
-20,632 |
\frac{t\cdot (-27)}{72 t} = t\cdot 9/(t\cdot 9) (-3/8)
|
6,265 |
r^2+r-15=0\implies r=\frac{-1\pm\sqrt{61}}{2}
|
6,467 |
i*2 + (-1) = 1 + 2(i + (-1))
|
-19,685 |
\frac{6\times 3}{7} = 18/7
|
-2,684 |
5 \sqrt{5} = (2 + 3) \sqrt{5}
|
44,191 |
64 = 2 \cdot 4 \cdot 8
|
19,660 |
8 \cdot (-1) + x^3 + x \cdot 7 \leq 0 \Rightarrow 1 \geq x
|
18,932 |
z + 2 z + z\cdot 4 + 8 ... = z
|
-21,036 |
8/8 (-7/9) = -\dfrac{1}{72} 56
|
11,713 |
1 - \frac{2}{e^x + 1} = \frac{e^x + (-1)}{e^x + 1} < x/2
|
10,538 |
(1 + z)^{n + (-1)}\cdot (1 + z) = \left(z + 1\right)^n
|
30,186 |
m\cdot 2 + 1 = (1 + m) \cdot (1 + m) - m^2
|
16,849 |
\int \frac{1}{1 + x^2}\cdot \left(1 + x^4 + (-1)\right)\,\mathrm{d}x = \int \frac{1}{1 + x^2}\cdot x^4\,\mathrm{d}x
|
-10,362 |
\frac{12}{12} \cdot (-\dfrac{1}{x \cdot 3} \cdot 6) = -\frac{72}{x \cdot 36}
|
16,405 |
(x + 2*\left(-1\right))*(1 + x) = x * x - x + 2*(-1)
|
8,612 |
u \times x := x \times u
|
-20,622 |
\dfrac{1}{k \cdot 30} \cdot (-40 \cdot k + 20 \cdot (-1)) = \frac{1}{6 \cdot k} \cdot (4 \cdot (-1) - k \cdot 8) \cdot 5/5
|
-22,716 |
60/90 = \frac{2\cdot 30}{2\cdot 45} = \frac{10}{2\cdot 3\cdot 15}\cdot 2\cdot 3 = \frac{2}{2\cdot 3\cdot 5\cdot 3}\cdot 2\cdot 3\cdot 5 = 2/3
|
-4,442 |
x^2-2x-8 = (x-4)(x+2)
|
1,467 |
\frac{3}{7}*(16 + 12) = (30 + 12)*2/7
|
-22,340 |
30 + r^2 - 11 \cdot r = (5 \cdot (-1) + r) \cdot (r + 6 \cdot (-1))
|
1,707 |
\tan\left(E\right) = y \implies \operatorname{atan}(y) = E
|
24,671 |
-2\cdot a + x^2 + x\cdot 2 - a^2 = \left(x - a\right)\cdot 2 + x^2 - a^2
|
29,569 |
3/5\cdot \dfrac{3}{5} = 9/25
|
47,877 |
\cos^2{0} + \sin^2{0} = 1
|
32,339 |
49 = 23 + 2*(b*f + d*b + d*f) \implies 13 = f*b + b*d + d*f
|
-27,624 |
-4 + 5 (-1) + 4 + 5 \left(-1\right) = -4 + 4 + 5 (-1) + 5 (-1) = 0 + 10 (-1) = -10
|
16,012 |
\left(\frac{1}{1 + \frac{5}{13}} \cdot 2\right)^{1/2} = \frac13 \cdot 13^{1/2}
|
23,036 |
|-w\cdot \left(-1\right) + z| = |z + w|
|
34,969 |
a^{54} \cdot a^{54} = a^{108}
|
14,959 |
|B\cdot Y - I\cdot x| = |Y\cdot B - x\cdot I|
|
32,861 |
|x - c| = -(x - c) = c - x
|
-17,403 |
117.3/100 = 1.173
|
-25,372 |
\sec^2\left(y\right) = d/dy \tan(y)
|
34,947 |
y \approx x \Rightarrow x \approx y
|
-29,541 |
34 = 36 + 2 \cdot \left(-1\right)
|
20,347 |
a^n - d^n = (a - d) \cdot (a^{n + (-1)} + d \cdot a^{2 \cdot (-1) + n} + \cdots + d^{2 \cdot \left(-1\right) + n} \cdot a + d^{\left(-1\right) + n})
|
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