id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
18,098 |
\frac{\partial}{\partial x} x^a = ax^{a + (-1)}
|
28,425 |
g_1 g_1^{g_2} = g_1^{g_2 + 1}
|
39,590 |
\sin(2 \pi + y) = \sin\left(y\right)
|
23,937 |
\dfrac{15}{36} = 1 - 1/36 - 20/36
|
-25,830 |
z^2 + z \cdot 3 + 5 = \dfrac{z^3 - z \cdot 4 + 15 \cdot \left(-1\right)}{z + 3 \cdot (-1)}
|
-2,660 |
\sqrt{16} \cdot \sqrt{11} + \sqrt{11} = \sqrt{11} \cdot 4 + \sqrt{11}
|
8,198 |
E(e^Y) = e^{E(Y)}
|
8,540 |
\frac{\sin{z}}{z^2} = \frac{\sin{z}*\frac1z}{z}
|
26,517 |
4 = \frac12(7 - -1)
|
23,386 |
\dfrac{-1 + 5 \cdot (-1)}{-2 + 4 \cdot (-1)} = -6/(-6) = 1
|
23,007 |
\frac{F/M\cdot M}{M} = \frac{F}{M}
|
7,638 |
\frac{4}{t \cdot 4} = \dfrac{1}{t}
|
-26,456 |
128 - 32 \cdot x + 2 \cdot x^2 = (x^2 + 64 - x \cdot 16) \cdot 2
|
17,276 |
x*(cW + Ud) = Wx c + dxU
|
-23,125 |
-\frac12\cdot \tfrac18\cdot 5 = -5/16
|
38,287 |
105 = 10\cdot (1 + 2 + 3 + 4) + 5
|
18,693 |
( x', y') + ( \psi, y'') + ( x, y) = \left( \psi + x', y' + y''\right) + \left( x, y\right)
|
5,031 |
{\left(-1\right) + i \choose 2} = \frac12 \cdot \left(\left(-1\right) + i\right) \cdot (i + 2 \cdot \left(-1\right))
|
31,936 |
2\cdot \pi\cdot \sigma^2 = \left(\pi\cdot 2\right)^{1/2}\cdot \sigma\cdot \left(\pi\cdot 2\right)^{1/2}\cdot \sigma
|
32,833 |
x^{R*y} = x^{y*R}
|
44,894 |
N \geq 8 \cdot 9 \cdot 5 \cdot 7 \cdot 11 \cdot 13 = 360360 \gt \overline{N}
|
22,507 |
det\left(-G \cdot F + x\right) = det\left(-F \cdot G + x\right)
|
34,017 |
2*(0*(-1) + 1) = 2
|
-10,149 |
0.01 \cdot \left(-64\right) = -\tfrac{64}{100} = -\frac{16}{25}
|
4,857 |
\frac17 \cdot 40 = -2/7 + 6
|
-22,711 |
110/77 = 11\cdot 10/(7\cdot 11)
|
-12,345 |
144^{\frac{1}{2}} = 12
|
12,122 |
\frac{1}{x^l \cdot z^l} \cdot (x^l + z^l) = \frac{1}{x^l} + \frac{1}{z^l}
|
-18,726 |
\left(-1\right) \cdot 0.0359 + 0.0446 = 0.0087
|
21,471 |
\frac{T*k*3}{x} = v * v \Rightarrow \sqrt{3*k*T/x} = v
|
36,277 |
c^2 + z * z + 2*c*z = (c + z)^2
|
23,159 |
1000 = 2^3 \cdot 5^2 \cdot 5
|
1,609 |
35.7/4.4 = \frac{35.7}{4.4}*\dfrac{10}{10} = \tfrac{357}{44}
|
40,551 |
0 = (-1)^3 - 3 \cdot (-1) + 2 \cdot (-1)
|
4,442 |
12 \cdot x^3 + 8 \cdot x^2 - x + (-1) = \left(x + \frac{1}{2}\right) \cdot \left(12 \cdot x^2 + 2 \cdot x + 2 \cdot (-1)\right) = 2 \cdot (x - 1/2) \cdot (6 \cdot x^2 + x + (-1))
|
-10,283 |
\frac{1}{8\times n}\times 6\times \frac33 = \tfrac{1}{n\times 24}\times 18
|
-1,208 |
(1/3*(-4))/7 = 1/(7*(-\dfrac14*3))
|
-5,166 |
\tfrac{1}{100} \cdot 1.1 = 1.1/100
|
38,286 |
\cos(2*x) = 2*\cos^2\left(x\right) + (-1) = 1 - 2*\sin^2(x)
|
-9,269 |
y^3\cdot 4 + 4\cdot y^2 = 2\cdot 2\cdot y\cdot y + y\cdot 2\cdot 2\cdot y\cdot y
|
-2,892 |
50^{1/2} + 32^{1/2} = (25*2)^{1/2} + (16*2)^{1/2}
|
-2,582 |
2 \cdot \sqrt{11} = \sqrt{11} \cdot (5 + 3 \cdot (-1))
|
24,274 |
3 x + 1 = 3 (x + 3 (-1)) + 10 = 3 (x + 3 \left(-1\right)) + 5\cdot 2
|
2,538 |
E^2 = E_\phi^2 + E_z^2 \Rightarrow \sqrt{E_\phi^2 + E_z^2} = E
|
-20,038 |
-5/8*\frac{1}{7*p + 9}*\left(9 + 7*p\right) = \tfrac{1}{72 + p*56}*(-35*p + 45*(-1))
|
-20,551 |
\frac{24 \cdot c}{-8 \cdot c + 16 \cdot (-1)} = \dfrac{3 \cdot c}{2 \cdot (-1) - c} \cdot 8/8
|
-11,505 |
-8 + 0\cdot (-1) - 20\cdot i = -8 - i\cdot 20
|
-1,287 |
8\cdot \frac13/(\frac12\cdot (-7)) = -\tfrac{1}{7}\cdot 2\cdot \frac13\cdot 8
|
-1,644 |
\frac{29}{12}\cdot \pi - 2\cdot \pi = 5/12\cdot \pi
|
11,579 |
(21 + 30 + 10 + 12 + 3)/14 = \frac{1}{14}*76
|
1,880 |
\int x^3 \cdot \sqrt{\left(-x + 2\right) \cdot (2 + x)}\,dx = \int \sqrt{2 \cdot 2 - x^2} \cdot x^3\,dx
|
32,032 |
x^2 - x \cdot 4 + 5(-1) = (x + 2\left(-1\right))^2 + 9\left(-1\right)
|
-20,019 |
\dfrac{p - 10}{7p + 9} \times \dfrac{8}{8} = \dfrac{8p - 80}{56p + 72}
|
24,396 |
-2 \cdot x^2 - 4 \cdot x + 8 \cdot \left(-1\right) + x^3 + 2 \cdot x^2 + 4 \cdot x = 8 \cdot \left(-1\right) + x^3
|
-26,462 |
b^2 + g^2 - 2\cdot g\cdot b = (-b + g)^2
|
16,859 |
n^2\cdot 2 + 3\cdot n + 1 = 1 + n\cdot (3 + n\cdot 2)
|
48,811 |
\dfrac{36}{60}\cdot 30 = 18
|
7,684 |
Z^2 \cdot H^2 = \left(Z \cdot H\right)^2
|
27,301 |
x^a\cdot x^d = x^{a + d}
|
8,586 |
-a \cdot (-\frac1b) = (0 - a) \cdot (0 - 1/b)
|
27,884 |
x^4\cdot 4 = (2\cdot x^2)^2
|
12,170 |
\sqrt{4 + \sqrt{3}\cdot 2} = \sqrt{\left(\sqrt{3} + 1\right)^2}
|
53,625 |
\int \frac{1}{y * y + 4}*y^2\,dy = \int \frac{1}{y^2 + 4}*(y^2 + 4 + 4*(-1))\,dy = \int 1\,dy - 4*\int \frac{1}{y * y + 4}\,dy
|
11,151 |
59 \cdot \left(93 \cdot 31 - 31 \cdot 29\right) = 59 \cdot 31 \cdot 2^6
|
27,478 |
1 = \frac{1}{0!^2} \cdot (2 \cdot 0)!
|
-2,225 |
\frac{1}{17}\cdot 3 = 9/17 - \frac{1}{17}\cdot 6
|
50,889 |
2^{2 k + 1} = \sum_{l=0}^{2 k + 1} \binom{2 k + 1}{l} = \sum_{l=0}^k \binom{2 k + 1}{l} + \sum_{l=k + 1}^{2 k + 1} \binom{2 k + 1}{l}
|
-5,233 |
65.1 \cdot 10^{5 - 2} = 10^3 \cdot 65.1
|
4,462 |
\left(-1\right) + n^2 = ((-1) + n) \cdot (1 + n)
|
27,130 |
1/(f\cdot h) = 1/(h\cdot f) = 1/\left(f\cdot h\right)
|
-3,404 |
\sqrt{7}*\left(1 + 5 + 4\left(-1\right)\right) = \sqrt{7}*2
|
1,529 |
\sin(q + \frac{1}{2} \times \pi) = \cos(\pi/2) \times \sin(q) + \sin(\pi/2) \times \cos(q)
|
27,285 |
\binom{4 + 2}{2} = \binom{4 + 2}{4} = \dfrac{1}{4!\cdot 2!}6! = 15
|
25,029 |
\sum_{i=0}^l g^i = \sum_{i=0}^{l + 1 + (-1)} g^i
|
37,219 |
60 = 5!/2
|
16,609 |
\dfrac{1}{1! \cdot 1! \cdot 1!} \cdot \left(1 + 1 + 1\right)! = 3! = 6
|
3,526 |
-(9 + y)^2\cdot 3 + 12 = 0 \Rightarrow 4 = (9 + y) \cdot (9 + y)
|
32,914 |
(l + 1)! = (l + 1) l! < (l + 1) \frac{1}{2^l}l^l
|
27,957 |
\frac1FF = \frac{F}{F}
|
-10,418 |
-\frac{5}{4 \cdot l} \cdot \frac55 = -\dfrac{1}{l \cdot 20} \cdot 25
|
11,705 |
|x * x| = |x|^2 = (\Re{(x)})^2 + (\Im{(x)})^2
|
12,308 |
(2*j + 1) * (2*j + 1) = 4*j^2 + 4*j + 1 = 4*(j^2 + j) + 1
|
2,728 |
1 + n^3 = (n + 1)*(n^2 - n + 1)
|
48,440 |
377 = 13*29
|
11,479 |
\frac{1}{676} = \frac{1}{52} \cdot 2 \cdot \frac{1}{52} \cdot 2
|
10,027 |
0 = -2 \cdot \gamma + x \implies x = \gamma \cdot 2
|
-1,409 |
7/2\cdot \frac{7}{2} = 7\cdot \frac{1}{2}/\left(2\cdot 1/7\right)
|
33,904 |
e^{i\cdot x\cdot \pi} = \left(e^{i\cdot \pi}\right)^x = \left(-1\right)^x
|
21,136 |
25^{2 + k} = 5^{4 + k \cdot 2}
|
200 |
n*2 + 1 = -n^2 + (1 + n)^2
|
-19,102 |
\frac{1}{15} = A_s/(36 \pi)\cdot 36 \pi = A_s
|
-656 |
(e^{\pi i/12})^{20} = e^{20 \frac{i\pi}{12}}
|
15,087 |
x\cdot e_1 + e_2\cdot y + e_3\cdot z = e_3\cdot z + x\cdot e_1 + y\cdot e_2
|
37,050 |
2 = 9/16\cdot \left(-\frac23\right) + \frac{19}{8}
|
17,939 |
2 + e^{2 \times r} + e^{-2 \times r} = (e^r)^2 + 2 \times e^r \times e^{-r} + (e^{-r})^2 = (e^r + e^{-r})^2
|
-1,727 |
-\pi \frac{1}{6}5 = \frac{\pi}{3} - \dfrac{7}{6} \pi
|
6,732 |
s^4 + 256\times \left(-1\right) = \left(s \times s - 4^2\right)\times \left(s \times s + 4^2\right) = (s + 4\times (-1))\times (s + 4)\times (s^2 + 16)
|
15,190 |
\tfrac{1}{(1 - x^2)^{1/2}} = \frac{d}{dx} \sin^{-1}\left(x\right)
|
4,712 |
\left(y + y^2/2! + \dfrac{1}{3!}*y^2 * y + \dotsm\right)^{-1} = \frac{1}{\left(-1\right) + e^y}
|
-8,405 |
\left(-4\right)*5 = -20
|
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