id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-19,766 |
1.5 = \tfrac{1}{2} \cdot 3
|
12,133 |
\frac{2}{(1 - x^{k \cdot m \cdot 2})^2} \cdot m \cdot x^{m \cdot k \cdot 2 + (-1)} \cdot k = \frac{\partial}{\partial x} (\frac{1}{-x^{k \cdot m \cdot 2} + 1} \cdot x^{2 \cdot m \cdot k})
|
30,090 |
\tilde{K}\cdot d = 0.036\cdot K/(0.0018\cdot d) = \tfrac{20}{d}\cdot K
|
27,462 |
14 + 6 \cdot (-1) + \left(-1\right) = 7
|
23,883 |
\left(4 \cdot a + a \cdot 6 = 120 \Rightarrow 12 = a\right) \Rightarrow 144 = a^2
|
10,895 |
x_s + x_w = x_s - x_w + x_w*2
|
29,766 |
\frac{\partial}{\partial f} \left(u\cdot x\right) = \frac{\partial}{\partial f} (x\cdot u)
|
-10,520 |
\frac{7 + x}{(-1) + x \cdot 5} \cdot \tfrac55 = \frac{5 \cdot x + 35}{25 \cdot x + 5 \cdot (-1)}
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42,644 |
7! \cdot 7! \cdot 8 = 8! \cdot 7!
|
3,114 |
102 \cdot 4 + 53 \cdot (-1) = 355
|
11,542 |
\frac{1}{\sqrt{3 * 3 + 2^2 + 6^2}}(35 + 7(-1)) = 4
|
44,809 |
14680057 = ((-1) + 2^{21}) \times 7
|
11,447 |
\tan\left(t\right) = \frac{1}{1/\left(\frac{1}{\cos(t)}\right)*1/\sin\left(t\right)}
|
16,314 |
(g + b)^2 = g^2 + 2\cdot b\cdot g + b^2 \Rightarrow g \cdot g + b^2 = (g + b)^2 - g\cdot b\cdot 2
|
-20,799 |
\frac{90 + 10*x}{63 + x*7} = 10/7*\tfrac{x + 9}{x + 9}
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-20,364 |
\frac{1}{2\cdot r}\cdot (5\cdot r + 5\cdot (-1))\cdot \frac77 = (35\cdot \left(-1\right) + 35\cdot r)/(14\cdot r)
|
11,453 |
(y + 1)*\left(y * y - y + 2\right) = (y + 1)*\left(y^2 - y + 1\right) + y + 1 = y^3 + 1 + y + 1 = 6 + y
|
14,169 |
4\cdot (-1) + m = -7 \implies m = -3
|
12,774 |
(-f + h) \cdot (h + f) = h^2 - f \cdot f
|
-23,702 |
\left((-1)*0.73 + 1\right)^6 = 0.27^6
|
23,216 |
|dg| = |d| |g|
|
-17,037 |
2 = 2\cdot (-3\cdot p) + 2\cdot \left(-1\right) = -6\cdot p - 2 = -6\cdot p + 2\cdot \left(-1\right)
|
53,537 |
c = \frac{z}{3 + 10 \cdot k} \Rightarrow c \cdot 3 + k \cdot c \cdot 10 = z
|
9,136 |
\frac{1}{2^{l + (-1)}} = \frac{1 \cdot 2}{2^{l + (-1)} \cdot 2} = \dfrac{2}{2^l}
|
27,017 |
\dfrac{1}{d_2} \cdot f \cdot d_1/x = \tfrac{1/x \cdot d_1}{1/f \cdot d_2}
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-4,214 |
x \cdot 8/7 = \frac{8}{7} \cdot x
|
-1,303 |
\frac{\left(-9\right)*1/7}{1/5} = 5/1 \left(-9/7\right)
|
-15,125 |
\frac{1}{\dfrac{1}{x^{10}\cdot y^6}}\cdot x^5 = \dfrac{1}{\frac{1}{x^{10}}\cdot \frac{1}{y^6}}\cdot x^5
|
940 |
n + 2*(-1) + n + n + (-1) = n*3 + 3*(-1)
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-22,339 |
(1 + f)\cdot (f + 5\cdot \left(-1\right)) = 5\cdot (-1) + f^2 - 4\cdot f
|
28,730 |
2^1 = \frac{4}{2} = 2
|
30,694 |
\frac{\partial}{\partial z} z^n = n\cdot z^{n + \left(-1\right)}
|
22,989 |
c + q/c = r\Longrightarrow \frac{1}{2}*(r ± \sqrt{-4*q + r^2}) = c
|
-15,356 |
\frac{z^8}{f^5\cdot z^5}\cdot f^6 = \dfrac{f^6}{f^5}\cdot \dfrac{1}{z^5}\cdot z^8 = f^{6 + 5\cdot (-1)}\cdot z^{8 + 5\cdot \left(-1\right)} = f\cdot z^3
|
10,212 |
a^2 + ba \cdot 2 + b^2 = (a + b) \cdot (a + b)
|
15,909 |
\binom{5}{3} = 5\cdot 4\cdot 3/\left(3\cdot 2\right) = 10
|
1,522 |
x^l - z^l = (x - z)*(x^{l + (-1)} + x^{l + 2*\left(-1\right)}*z + \dots + x*z^{2*(-1) + l} + z^{\left(-1\right) + l})
|
-11,636 |
-10 + 5 + 27 \cdot i = -5 + 27 \cdot i
|
19,122 |
\sqrt{( x^2, y^3)} = \sqrt{x^2 y^3} = \sqrt{x^2} \sqrt{y^3} = xy = \left[x,y\right]
|
9,756 |
xY^X = (xY)^X = (xIY)^X = Y^X xI
|
13,665 |
(\frac{d*x}{d}*1)^{n + 1} = (x*d/d)^n*x*d/d = x^n*d/d*\frac{x*d}{d}
|
7,557 |
U + V + W = U + V + W
|
-487 |
e^{6\cdot 17\cdot i\cdot \pi/12} = (e^{17\cdot \pi\cdot i/12})^6
|
-17,404 |
1.473 = \frac{147.3}{100}
|
23,150 |
6 = 3\cdot 2 + 7\cdot 0
|
-626 |
-4\pi + \frac{65}{12} \pi = \dfrac{17}{12} \pi
|
42,464 |
e^{i \cdot x} = \cos(x) + i \cdot \sin(x) = \cosh(i) + x \cdot \sinh\left(i\right)
|
3,947 |
(x*n) * (x*n) = (n*x)^2
|
-21,342 |
\tfrac36 = \frac12
|
21,971 |
e = 1/\left(\frac1e\right)
|
12,194 |
\frac{\text{d}x}{\text{d}x} = \frac{\text{d}x}{\text{d}Z}\cdot \frac{\text{d}Z}{\text{d}x} = \frac{\text{d}x}{\text{d}Z}\cdot \frac2Z
|
7,595 |
bp^m = cxp\Longrightarrow bp^{m + (-1)} = xc
|
-18,391 |
\tfrac{42 + k \cdot k + 13 \cdot k}{k^2 + 7 \cdot k} = \frac{(k + 6) \cdot (k + 7)}{(k + 7) \cdot k}
|
15,028 |
\frac12\cdot (\left(-b + a\right) \cdot \left(-b + a\right) + \left(b - c\right)^2 + (c - a)^2) = a^2 + b^2 + c^2 - a\cdot b - c\cdot b - c\cdot a
|
28,988 |
\frac{a^2}{(c-b)}+\frac{b^2}{(c-a)}=\frac{c(a^2+b^2)-a^3-b^3}{(c-b)(c-a)}=\frac{c(a^2+b^2-c^2)}{(c-b)(c-a)}........(3)
|
28,325 |
g - \frac{f}{x} = -f/x + g
|
-1,139 |
\frac{1}{(-4)\cdot 1/9}\cdot ((-9)\cdot \tfrac17) = -\frac94\cdot (-\frac{9}{7})
|
3,743 |
3/4 = \dfrac{1^{-1}}{4} \cdot 3
|
-10,650 |
3/3\cdot (-\frac1r\cdot \left(r\cdot 4 + 7\cdot (-1)\right)) = -(r\cdot 12 + 21\cdot \left(-1\right))/(r\cdot 3)
|
-475 |
e^{8 \cdot i \cdot \pi \cdot 5/3} = (e^{i \cdot \pi \cdot 5/3})^8
|
5,704 |
\frac{1}{z^d + z^{-d}} = \dfrac{z^d}{z^{2\cdot d} + 1} \approx \frac{1}{z^d}
|
24,216 |
-\pi/6 = \arcsin(-\dfrac{1}{2})
|
12,154 |
((2\cdot n)!)! = 2\cdot n\cdot 2\cdot \left(n + (-1)\right)\cdot 2\cdot \left(n + 2\cdot (-1)\right)\cdot \dots\cdot 2 = 2^n\cdot n!
|
15,331 |
\frac{1}{36} = \frac{6}{6^3}
|
14,135 |
2 \cdot \pi/5 \cdot 1.25 = \dfrac{2}{5} \cdot \pi \cdot 5/4 = \frac{\pi}{2}
|
32,719 |
\frac8x = \dfrac8x
|
38,155 |
a*\frac1b/d = a/(b*d) = a*1/b/d = \tfrac{1}{b*d}*a
|
14,063 |
\mathbb{E}[Z_t^2 \cdot Z_{-j + t}^2] = \mathbb{E}[Z_{t - j}^2] \cdot \mathbb{E}[Z_t^2]
|
-10,617 |
3 = 30 \cdot \beta + 30 \cdot (-1) + 15 = 30 \cdot \beta + 15 \cdot (-1)
|
22,302 |
\frac{210}{2}1 = 105
|
20,788 |
15 = -10^0 \cdot 5 + 10^1 \cdot 2
|
2,482 |
\left(y + 2(-1)\right) (2(-1) + y) = (y + 2(-1))^2
|
13,286 |
347720 = \binom{26}{7} - \binom{20}{7} - \binom{20}{6}\cdot 6
|
22,424 |
\dfrac{10}{\dfrac{10}{2} + 1} = 5/3
|
11,006 |
\sin^2(A) + \sin^2(B) + \sin^2\left(H\right) = 2\Longrightarrow 1 - \cos^2(A) + 1 - \cos^2\left(B\right) - \sin^2(H) = 2
|
2,415 |
2 + 8 + 24 + 64 + \dotsm + 2^n\cdot n = 2\cdot (\left(n + (-1)\right)\cdot 2^n + 1)
|
18,098 |
x^{b + (-1)} \cdot b = \frac{\partial}{\partial x} x^b
|
-22,172 |
\frac{1}{7} 9 = 45/35
|
8,846 |
2^{n*3} = (2^3)^n
|
18,073 |
1/(\sqrt{l}) = \frac{l^{3/2}}{l \cdot l}
|
19,235 |
|-x + Q| = |x - Q|
|
34,324 |
2^{200} - 2^{192} \cdot 31 + 2^{198} = (2^{96} \cdot 17) \cdot (2^{96} \cdot 17)
|
36,855 |
166 - 33 + 23 + 4\cdot (-1) = 114
|
-17,984 |
27\cdot (-1) + 64 = 37
|
28,677 |
(1/100 + 1)*10000 = 10000 + \frac{1}{100}*10000
|
26,576 |
\tan(\tan^{-1}\left(\dfrac{b}{g}\right)) = \frac{1}{g} \cdot b
|
29,118 |
\sin\left(x + \pi\cdot 2\right) = \sin(x)
|
13,278 |
0 = 2 + 4(-1) + y''\Longrightarrow 2 = y''
|
8,710 |
x^5 \cdot 6 + 15 \cdot x^4 + x^3 \cdot 20 + x^2 \cdot 15 + 6 \cdot x + 1 = -x^6 + \left(1 + x\right)^6
|
14,391 |
2 = 546 - 32 \cdot 17 = 5 \cdot h_2 - h_1 - 32 \cdot (2 \cdot h_1 - 9 \cdot h_2) = 293 \cdot h_2 - 65 \cdot h_1
|
53,231 |
15 = 6 + 4 + 5
|
-18,634 |
-\frac{1}{4}11 = -\frac{11}{4}
|
15,576 |
B = \begin{array}{rr}1 & 0\\0 & -1\end{array} = \dfrac{1}{B}
|
-7,184 |
\frac17*0 = 0
|
17,758 |
x * x + i = 0 rightarrow x = \left(-i\right)^{1/2}
|
-562 |
e^{3\cdot \frac{\pi\cdot i}{3}\cdot 1} = (e^{\frac{\pi\cdot i}{3}})^3
|
10,159 |
1/5 + y = \tfrac15(y \cdot 5 + 1)
|
-24,199 |
6 + \frac1848 = 6 + 6 = 12
|
28,201 |
\frac{\frac{1}{10^6}}{10^4} (10^6 + (-1)) = 9.99999 \cdot 10^{-5}
|
250 |
i = \sin{\dfrac{\pi}{2}}*i + \cos{\dfrac12*\pi}
|
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