id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
34,582 |
\cos(x) = 2 \cos^2(x/2) + \left(-1\right) = 1 - 2 \sin^2(x/2)
|
24,800 |
\frac{1/3}{\dfrac{1}{3} \cdot (1 + x)} = \frac{1}{x + 1}
|
30,226 |
y = y/\|y\| \|y\|
|
28,812 |
x^\zeta x^z = x^{z + \zeta}
|
26,198 |
12130303122=2*3^3*7*59*543911
|
380 |
\|\int a\,dz\|^2 = \|I\|^2 = I \cdot I = I \cdot \int a\,dz
|
2,750 |
-g \cdot (-f) = f \cdot g
|
-29,431 |
\frac{3*12}{5} = \frac{36}{5}
|
8,604 |
z * z + 3*z + 2*(-1) = \dfrac{1}{z + 1}*(z^3 + z^2*4 + z + 2*\left(-1\right))
|
-1,380 |
-\dfrac19\cdot 7\cdot (-9/7) = \left(1/7\cdot \left(-9\right)\right)/((-9)\cdot \dfrac{1}{7})
|
-25,665 |
\frac{\text{d}}{\text{d}r} (4*r^3 + r) = 3*4*r * r + 1 = 12*r^2 + 1
|
47,364 |
\frac{1}{0.25}*0.5 = 2
|
-4,553 |
\frac{\epsilon \cdot 7 + 20 \cdot (-1)}{\epsilon^2 - \epsilon \cdot 6 + 8} = \frac{3}{2 \cdot (-1) + \epsilon} + \dfrac{4}{\epsilon + 4 \cdot (-1)}
|
22,973 |
12 = \frac{1}{3} 36
|
-19,485 |
\frac{7}{3}\cdot 7/9 = \dfrac{7\cdot 7}{3\cdot 9} = \frac{49}{27}
|
-18,322 |
\frac{1}{-6*t + t^2}*\left(t^2 + t*3 + 54*(-1)\right) = \frac{1}{t*(t + 6*(-1))}*(6*(-1) + t)*\left(t + 9\right)
|
-11,798 |
\frac{4}{81} = \left(\frac{1}{9}\cdot 2\right) \cdot \left(\frac{1}{9}\cdot 2\right)
|
27,566 |
2/3 \times 2/3 = 4/9
|
23,976 |
\left(AB = C \Rightarrow \dfrac1AC = AB/A\right) \Rightarrow B = C/A
|
16,755 |
pq = (-(q \cdot q + p^2) + (p + q)^2)/2
|
20,199 |
e^{X + Y} = e^X e^Y\Longrightarrow (X,Y) = 0
|
37,623 |
1 + 2 + 3 + \cdots + m = m + 2
|
5,227 |
(\lambda - \sigma) \times (\lambda - \sigma) = \lambda \times \lambda - 2 \times \sigma \times \lambda + \sigma^2
|
1,936 |
z + 1 = \dfrac{\pi}{2} \cdot 3 + \cos(\pi \cdot 3/2) \Rightarrow \pi \cdot 3/2 + 2 \cdot (-1) = z
|
14,452 |
K\times N\times g = N\times g\times K
|
-9,178 |
-z \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times z = -96 \times z^2
|
9,352 |
2*x_i + \left(-1\right) = x_i
|
1,873 |
(a*c)^2 = c^2*a * a
|
13,314 |
\sin(h) = x rightarrow h = \operatorname{asin}(x)
|
37,810 |
\log_e(z) + \log_e\left(y\right) = 0\Longrightarrow 0 = \log_e(z*y)
|
-18,258 |
\frac{z}{(6\cdot (-1) + z)\cdot (6\cdot \left(-1\right) + z)}\cdot (z + 6\cdot \left(-1\right)) = \frac{z^2 - z\cdot 6}{36 + z \cdot z - 12\cdot z}
|
10,964 |
2\cdot \frac34 = \frac{3}{2}
|
-9,345 |
2 \cdot 3 \cdot 5 \cdot m + 2 \cdot 5 = 10 + m \cdot 30
|
-20,718 |
4/4 \cdot (-3 \cdot z + 9 \cdot \left(-1\right))/6 = (36 \cdot (-1) - 12 \cdot z)/24
|
6,561 |
\tfrac{1}{8} = \frac{\frac12}{2} \cdot 1/2
|
-30,899 |
4 = 8\cdot (-1) + 3\cdot 4
|
10,253 |
\frac{r_n - 1/(r_n)}{r_n + (-1)} = 1 + \frac{1 - 1/(r_n)}{r_n + \left(-1\right)} \geq 1 + \frac{1}{2 \cdot (r_n + \left(-1\right))}
|
3,065 |
2 - \dfrac{2}{3 - x} = \frac{1}{3 - x} \cdot (4 - 2 \cdot x) = \dfrac{2}{3 - x} \cdot (2 - x)
|
47,953 |
(-1) + 2^{11} = 23\cdot 89
|
22,219 |
3/8 + 1/8 = \frac{1}{8} \cdot 4 = \frac{1}{2}
|
26,329 |
0 = \left|{(M - x)^R}\right| = \left|{M^R - x}\right|
|
29,070 |
B\cdot X\cdot x = x\cdot B\cdot X
|
14,582 |
(-\alpha + 1)^{i/2} \cdot (1 - \alpha)^{\dfrac{i}{2}} = \left(1 - \alpha\right)^i
|
30,665 |
\frac{1}{18}*2 = 1/(3*6) + \frac{1}{3*6}
|
16,834 |
a + f = 16\Longrightarrow -f + a = 1
|
19,353 |
x^{\frac{1}{2}}*V = x^{\frac{1}{2}}*V
|
24,732 |
\dfrac{1}{l + 2*(-1)} - \dfrac{1}{l + 2} = \frac{1}{l^2 + 4*(-1)}*4
|
-6,098 |
\frac{1}{36 + z*4} 5 = \frac{1}{4 \left(z + 9\right)} 5
|
27,807 |
\frac{1}{x + (-1)}(x^2 + (-1)) = \frac{1}{x + (-1)}\left(x + 1\right) (x + (-1)) = x + 1
|
-10,613 |
4/4\cdot (-\frac{4\cdot z + 3}{3\cdot z + 2}) = -\dfrac{16\cdot z + 12}{8 + z\cdot 12}
|
2,366 |
(2 + x)/(\left(-1\right)*x) = \frac{y}{\left(-1\right)*(y + 4*(-1))}\Longrightarrow y = 2*x + 4
|
31,191 |
-b\cdot (-e) = b\cdot e
|
44,880 |
\frac{(1 - y) \cdot e^y}{y + e^y} = \frac{1 - y}{1 + y \cdot e^{-y}} = (1 - y) \cdot \left(1 - y \cdot e^{-y} + y^2 \cdot e^{-2 \cdot y} - \dotsm\right)
|
13,470 |
(-1) + \tan{\frac12 π} = 1 + \tan{\frac12 π}
|
6,882 |
z^2 = \sqrt{z}\cdot \sqrt{z}\cdot \sqrt{z}\cdot \sqrt{z}
|
-11,646 |
22 i - 15 + 8 = -7 + i*22
|
5,714 |
B = y \cdot k \Rightarrow y = B/k
|
26,416 |
a^{\dfrac1d} = a^{1/d}
|
-14,249 |
(8 + 4 \times 10) - 5 \times 9 = (8 + 40) - 5 \times 9 = 48 - 5 \times 9 = 48 - 45 = 3
|
-25,510 |
\frac{\mathrm{d}}{\mathrm{d}t} (\frac{1}{t + 2} \times 4) = -\dfrac{4}{(t + 2)^2}
|
2,943 |
e^l = e^{1/(\frac1l)}
|
6,767 |
b\times (-a) = -b\times a
|
-522 |
-30 \times \pi + \pi \times 361/12 = \pi/12
|
33,378 |
\sum_{x=1}^n (x + 1) = \sum_{x=1}^n x + \sum_{x=1}^n 1
|
30,624 |
\frac{1}{(3(-1) + 4)!*3!}4! + \frac{1}{2! (6 + 2\left(-1\right))!}6! = 19
|
-605 |
e^{17 \frac{7\pi i}{6}} = \left(e^{\frac{\pi i*7}{6}}\right)^{17}
|
21,554 |
1 + \cdots + t^{1 + n} = \frac{1}{-t + 1}\cdot \left(1 - t^{1 + n} + t^{1 + n}\cdot (-t + 1)\right)
|
-6,201 |
\frac{6}{(t + 2)\cdot (2 + t)}\cdot (t + 2) - \frac{(2 + t)\cdot 2}{(t + 2)\cdot (2 + t)} + \frac{6\cdot t}{(t + 2)\cdot (t + 2)} = \dfrac{6\cdot (2 + t) - 2\cdot \left(2 + t\right) + 6\cdot t}{\left(t + 2\right)\cdot \left(2 + t\right)}
|
5,338 |
\sum_{n=0}^\infty \left(n + 1\right) \cdot x^n = \frac{\partial}{\partial x} \sum_{n=0}^\infty x^n
|
29,870 |
(g_2 + (-1))/2 = \dfrac{1}{-1} \cdot (b + 3 \cdot (-1)) = (g_1 + 4 \cdot (-1))/1 = j \implies 1 + 2 \cdot j = g_2\wedge b = -j + 3\wedge g_1 = j + 4
|
44,045 |
\tan^{-1}\left(0\right) = 0
|
30,440 |
1 - \dfrac194 = 5/9
|
-1,988 |
5/4 \pi - \pi \tfrac{1}{12}19 = -\frac{\pi}{3}
|
-4,700 |
-\frac{1}{y + 2} - \dfrac{1}{5 + y}\cdot 3 = \frac{11\cdot (-1) - y\cdot 4}{y^2 + y\cdot 7 + 10}
|
21,775 |
\left(l + (-1)\right)! \times (l + 1)! = \frac{l + 1}{l + (-1)} \times l! \times l! > l! \times l!
|
-3,562 |
\frac{1}{k^2}*k*110/33 = \dfrac{k}{33*k^2}*110
|
17,690 |
(-1) + d \cdot x = 0\Longrightarrow 1 = d \cdot x
|
-3,690 |
4/3\cdot p^2 = p^2\cdot 4/3
|
15,283 |
\int 1*2 \pi s\,\mathrm{d}s = 2 s s/2 \pi = \pi s^2
|
8,609 |
\binom{l}{k} = \tfrac{1}{\left(l - k\right)!\cdot k!}\cdot l!
|
36,427 |
(1 - p)^4 \cdot p + (1 - p)^5 = (1 - p)^4 \cdot (p + 1 - p) = (1 - p)^4
|
6,830 |
e^{v + u} = e^v \cdot e^u
|
2,810 |
z^r - b^r = (-b + z) (z^{r + (-1)} + z^{r + 2\left(-1\right)} b + ... + b^{r + 2\left(-1\right)} z + b^{(-1) + r})
|
12,995 |
(-f + x)^2 = x^2 - 2\cdot f\cdot x + f^2
|
21,012 |
(d\cdot y)^2 = (d\cdot y)^2
|
9,764 |
\theta^3 + (-1) = (1 + \theta^2 + \theta) ((-1) + \theta)
|
771 |
-d + p = -p*(-\frac1d + 1/p)*d
|
28,116 |
|\frac{5x^2 + 7}{2x^2 - x} - \frac{1}{2}5| = |\frac{1}{2x * x - x}(5x^2 - 5x^2 + \dfrac52 x + 7)| = |\tfrac{1}{2x^2 - x}(\frac{5}{2} x + 7)|
|
-20,724 |
\frac66 \times \dfrac{n + 9 \times (-1)}{4 - 9 \times n} = \frac{1}{-n \times 54 + 24} \times (6 \times n + 54 \times (-1))
|
-26,408 |
\dfrac{1}{z^4}\cdot z^3 = z^{-4 + 3} = 1/z
|
-19,309 |
7/1\cdot \frac{9}{2} = \frac{1}{2}\cdot 9/\left(\frac{1}{7}\right)
|
2,147 |
(1 + 1)^x = \binom{x}{0} + \binom{x}{1} + \binom{x}{2} + ...
|
12,675 |
\left[a_x,b_x\right] \approx [a_y, b_y]\Longrightarrow \left[a_x, b_x\right] \approx [a_y,b_y]
|
1,275 |
\sin(z) = \sin(z + 2 \times \pi)
|
23,344 |
z - x + 1 = z - \left(-1\right) + x
|
-22,264 |
(8 + r) \cdot (r + 6) = r \cdot r + 14 \cdot r + 48
|
27,749 |
31 + (x^2 + 4\cdot x + 9)\cdot (4\cdot (-1) + x) = x^3 - x\cdot 7 + 5\cdot (-1)
|
-30,343 |
0 = \left(r \cdot w_0\right)^2 + 3 \cdot r \cdot w_0 + 18 \cdot (-1) = (r \cdot w_0 + 6) \cdot (r \cdot w_0 + 3 \cdot (-1))
|
17,141 |
-h + f - x = -h + f - x
|
18,392 |
6 \cdot x^2 + \varepsilon \cdot x \cdot 11 - \varepsilon^2 \cdot 35 = (7 \cdot \varepsilon + x \cdot 2) \cdot \left(-5 \cdot \varepsilon + x \cdot 3\right)
|
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