id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-12,332 |
2 \sqrt{6} = \sqrt{24}
|
-15,943 |
-36/10 = -6*\dfrac{8}{10} + 6*2/10
|
4,777 |
y^{\frac{1}{2}}/y = \dfrac{1}{y^{1 / 2}}
|
27,005 |
(y_1 - \gamma)\cdot (-u + y_2) = y_2\cdot y_1 - u\cdot y_1 - \gamma\cdot y_2 + \gamma\cdot u
|
26,428 |
ex = -x*(-e)
|
12,088 |
205200 = \binom{3}{2} \cdot \binom{5}{2} \cdot \binom{20}{1} \cdot \binom{19}{1} \cdot 18
|
-1,116 |
\dfrac{-40}{42} = \dfrac{-40 \div 2}{42 \div 2} = -\dfrac{20}{21}
|
-4,155 |
\tfrac{1}{2k^3} = \frac{1}{k * k * k*2}
|
3,162 |
\sin\left(q\right) = \sin(2π + q)
|
6,183 |
1/(H\cdot G) = 1/(H\cdot G)
|
19,883 |
\mathbb{E}[q_2 q_2] \mathbb{E}[q_1] = \mathbb{E}[q_1 q_2^2]
|
46,168 |
x + 1 = 2^0 + x
|
10,543 |
-(5 - z)*\left(z + 3*(-1)\right) - 4*(-z*2 + 8) + 17 = z^2
|
35,925 |
1/(\frac{1}{\rho}) = \rho
|
-20,845 |
\frac{4}{4} \cdot (-\frac{1}{(-1) + G}) = -\frac{4}{4 \cdot G + 4 \cdot (-1)}
|
19,595 |
\sin^4{x} + \cos^4{x} = (\sin^2{x} + \cos^2{x})^2 - 2*\sin^2{x}*\cos^2{x} = 1 - 2*\sin^2{x}*\cos^2{x}
|
38,789 |
\binom{3}{2} = \frac{1}{2! \cdot 1!}3! = 3
|
-7,297 |
\dfrac{5}{17}*\dfrac{4}{16} = \frac{5}{68}
|
-27,885 |
\frac{\mathrm{d}}{\mathrm{d}z} (2\cdot \tan(z)) = 2\cdot \frac{\mathrm{d}}{\mathrm{d}z} \tan(z) = 2\cdot \sec^2(z)
|
19,759 |
m^{1/2} \cdot z_m = \dfrac{1}{\frac{1}{m^{1/2}}} \cdot z_m
|
-3,067 |
-\sqrt{6} + \sqrt{16}\cdot \sqrt{6} = 4\cdot \sqrt{6} - \sqrt{6}
|
2,195 |
\ln(2) = 1/2 + 1/6 + \dfrac{1}{30} + 1/56 + \ldots \leq 1 + 1/4 + \dfrac{1}{25} + \frac{1}{49} + \ldots
|
-9,471 |
2 \cdot 2 \cdot 3 \cdot 3 + q \cdot 2 \cdot 3 \cdot 7 = 36 + 42 \cdot q
|
11,387 |
4!/\left(2!\cdot 2!\right)\cdot 35/768 = 210/768
|
-4,078 |
\tfrac{k^2}{36\cdot k}\cdot 28 = k \cdot k/k\cdot 28/36
|
21,137 |
\frac14\cdot (f + h + g + x) = \dfrac{1}{2}\cdot (\frac{1}{2}\cdot (g + x) + (f + h)/2)
|
24,624 |
-\dfrac12*(8! - 7!) + \frac{9!}{2!*3!} = 12600
|
-20,186 |
-4/7\cdot \frac{9}{9} = -36/63
|
-20,569 |
\frac{1}{z \cdot 9}(-7z + 5(-1)) \frac{8}{8} = \frac{1}{72 z}(-z \cdot 56 + 40 (-1))
|
36,661 |
3^{10^k} = 9^{\frac{10^k}{2}} = (10 + (-1))^{\frac{10^k}{2}}
|
-1,868 |
-\frac{19}{12} \pi + 19/12 \pi = 0
|
17,849 |
z^{\frac{1}{6} \cdot 2} = z^{1/3}
|
-9,677 |
\frac{4}{25} = \frac{1}{50}8
|
4,144 |
-a\cdot (-f) = --a\cdot f = a\cdot f = a\cdot f
|
9,516 |
\sqrt{z + 4*\left(-1\right)} = i_1 \Rightarrow z = 4 + i_1^2
|
-20,459 |
\frac{1}{2 \cdot k + 5 \cdot \left(-1\right)} \cdot (35 - 14 \cdot k) = \frac{1}{2 \cdot k + 5 \cdot (-1)} \cdot \left(2 \cdot k + 5 \cdot \left(-1\right)\right) \cdot (-\frac71)
|
19,571 |
(n-3)(n-2)=2\binom{n-2}{2}
|
5,229 |
e^{\frac{i}{4} \cdot \pi} \cdot 16 = z\Longrightarrow z^{1/4} = e^{\dfrac{i}{16} \cdot \pi} \cdot 2
|
24,543 |
A \cdot B^2 \cdot A = A^2 \cdot B \cdot B
|
14,353 |
x\cdot y + x - x + y - y + 1 + (-1) + (-1) = 1 + x + (-1) + y + (-1) + x\cdot y - x - y
|
9,052 |
2*\left(3*x + 1\right) = 2 + 6*x
|
41,896 |
\frac{1}{z^2 + z + 3} = \frac{1}{z^2 + z + 3}
|
-7,647 |
\frac{1}{-1}\times (-3\times i + 3) = -\frac{i\times 3}{-1} + \frac{3}{-1}
|
-5,329 |
1.82*10 = \frac{10}{10^5}1.82 = \frac{1.82}{10000}
|
17,511 |
\dfrac{1}{2^n \cdot 2^n} = \dfrac{1}{4^n}
|
-20,042 |
\dfrac{36\cdot \left(-1\right) - z\cdot 12}{4\cdot (-1) + 24\cdot z} = \frac{9\cdot \left(-1\right) - z\cdot 3}{z\cdot 6 + (-1)}\cdot \frac44
|
-3,984 |
\frac{p^4}{p}\cdot \dfrac{1}{81}\cdot 90 = 90\cdot p^4/(81\cdot p)
|
13,434 |
h\cdot d = -d\cdot \left(-h\right)
|
-9,176 |
12 (-1) - 12 n = -n*2*2*3 - 2*2*3
|
13,769 |
\psi r_1 + (x + r_3) r_2 + r_3 r_4 = r_3 r_2 + r_3 r_4 + r_1 \psi + r_2 x
|
-20,556 |
(24 - y \cdot 6)/54 = (-y + 4)/9 \cdot 6/6
|
30,451 |
2 \cdot (-1) + 2^7 = 126
|
-2,590 |
\sqrt{3}*(5 + 1 + 3*(-1)) = \sqrt{3}*3
|
-22,712 |
60/90 = \frac{30 \cdot 2}{3 \cdot 30}
|
13,829 |
d^2/4 - (-d/2 + r)^2 = -r^2 + d\times r
|
539 |
-\frac{1}{8}\cdot (\cos(\pi) - \cos(0)) = -\frac{1}{8}\cdot \left(-1 + \left(-1\right)\right) = 1/4
|
11,573 |
(1 + y) \cdot (1 + k \cdot y) = 1 + (k + 1) \cdot y + k \cdot y \cdot y \geq 1 + (k + 1) \cdot y
|
-2,731 |
80^{1/2} - 20^{1/2} = (16\cdot 5)^{1/2} - (4\cdot 5)^{1/2}
|
31,567 |
14.5 = \frac{1}{20}*(30 + 252 + 8)
|
3,633 |
\cos\left(\operatorname{asin}\left(x\right)\right) = \sqrt{1 - \sin^2(\operatorname{asin}(x))} = \sqrt{1 - x^2}
|
7,801 |
1/A*1/x/C = \frac{1}{A x C}
|
28,644 |
n^2 + 2 \cdot n + 6 = (1 + n) \cdot (1 + n) + 5
|
14,237 |
L = 2 \cdot L \Rightarrow L = 0
|
5,568 |
4 \cdot (-1) + k = k - 2 \cdot (3 + (-1))
|
32,099 |
|u \times u - v^2 + 2 \times i \times u \times v| = \sqrt{(u \times u - v^2)^2 + \left(2 \times u \times v\right)^2} = u^2 + v \times v
|
-20,286 |
-30/21 = -10/7\cdot \frac33
|
-1,599 |
-\frac{\pi}{4} + \pi/2 = \frac{\pi}{4}
|
-2,880 |
-5^{1 / 2} + (4\cdot 5)^{1 / 2} = 20^{1 / 2} - 5^{\frac{1}{2}}
|
26,707 |
128 = (3 + 1) (1 + 1) (1 + 1) (1 + 1) (1 + 3)
|
6,402 |
1 \leq 4\cdot y \lt 2\Longrightarrow y\cdot 4 + 1 = 4\cdot y
|
-5,768 |
\frac{x \cdot 2}{x^2 + x \cdot 14 + 45} = \frac{2 \cdot x}{\left(x + 5\right) \cdot (9 + x)}
|
32,874 |
2 \cdot 2^2\cdot 3^{2\cdot 3} = 5832
|
7,302 |
e^V = e^V
|
22,679 |
\dfrac{1}{6}\cdot 10 + 1/6\cdot 9 + 4/6\cdot 7 = \frac16\cdot 47 \lt 8
|
24,514 |
(-x)^{1/2}*\left(-x\right)^{1/2} = (\left(-x\right)^{1/2})^2 = -x
|
24,454 |
1 + 2\cdot \infty = \infty \Rightarrow \infty = -1
|
29,094 |
3\cdot y + 3\cdot \left(-1\right) + (y^2 + y + 2\cdot (-1))\cdot (y + (-1)) = y^3 + (-1)
|
18,357 |
73 = (-\sqrt{2}\cdot 12 + 19) (19 + \sqrt{2}\cdot 12)
|
18,933 |
\sin(3\cdot z) = \sin(2\cdot z + z) = \sin\left(2\cdot z\right)\cdot \cos(z) + \cos(2\cdot z)\cdot \sin(z)
|
-3,024 |
63^{1/2} + 28^{1/2} = (4*7)^{1/2} + (9*7)^{1/2}
|
4,935 |
e^{1/n} = e^{1/n} = 1 + 1/n + ... > 1 + \frac1n
|
4,389 |
a_1 + d\cdot 2 = 71\Longrightarrow a_1 = 71 - 2\cdot d = 71 - 2\cdot (-4) = 71 + 8 = 79
|
21,947 |
\frac{1}{B \cdot k} \cdot (k \cdot k + B^2) = B/k + k/B
|
3,340 |
\left(C + D\cdot i\right)\cdot W = 0 rightarrow C\cdot W = 0,0 = W\cdot D
|
28,165 |
y \cdot t_1 \cdot t_2 = t_1 \cdot t_2 \cdot y
|
-17,646 |
68 + 24 = 92
|
8,651 |
\mathbb{E}\left[U_1^2\right] + \mathbb{E}\left[U_2\right] = \mathbb{E}\left[U_1 \cdot U_1 + U_2\right]
|
54,564 |
1+\omega=\omega<\omega+1
|
15,663 |
\sin(x)\sin(\frac{\pi}{2}-x)=\sin(x)\cos(x)
|
22,993 |
b^k \cdot g^k \cdot b^k \cdot g^k \cdot b^k \cdot g^k = g^k \cdot b^{2 \cdot k} \cdot b^k \cdot g^{2 \cdot k}
|
-22,156 |
\frac{1}{40}35 = \dfrac{1}{8}7
|
-8,016 |
(12 + 6\cdot i)/3 = \frac13\cdot 6\cdot i + \frac13\cdot 12
|
18,590 |
\sin(\frac{1}{2}*(\left(-3\right)*\pi)) = 1
|
18,088 |
e^{\frac{i*x}{2}} - e^{((-1)*i*x)/2} = \cos(\frac{x}{2}) + i*\sin(\frac{x}{2}) - \cos(((-1)*x)/2) + i*\sin(\frac{(-1)*x}{2}) = 2*i*\sin\left(x/2\right)
|
-2,315 |
-\frac{1}{13} + \frac{1}{13} 4 = \frac{1}{13} 3
|
-20,769 |
\tfrac{-y\cdot 30 + 50}{y\cdot 36 + 60\cdot (-1)} = -5/6\cdot \dfrac{y\cdot 6 + 10\cdot (-1)}{y\cdot 6 + 10\cdot (-1)}
|
15,957 |
x \cdot x + 1 = 3 - 2 - x^2
|
9,582 |
\frac{\partial}{\partial x} (v\cdot u) = \frac{\partial}{\partial x} \left(v\cdot u\right) + u\cdot \frac{dv}{dx}
|
19,883 |
E(X_1) E(X_2 X_2) = E(X_1 X_2^2)
|
21,208 |
0.0001 = 0.01*0.01
|
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