id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
31,451 |
0 = c_1 + c_2\cdot |1| \Rightarrow c_1 = -c_2
|
34,310 |
1 + 2015 + 1007*\left(-1\right) = 1009
|
20,084 |
1 = 5^{x/2} - 2^x = 5^{\frac12 \cdot x} - 4^{x/2}
|
26,917 |
\int \sin(x)/\cos(x)\,\mathrm{d}x = \int \tan(x)\,\mathrm{d}x
|
2,773 |
j \cdot 4 + 1 + k \cdot 4 + 1 = 2 + (j + k) \cdot 4
|
26,887 |
det\left(E*Z\right) = det\left(Z*E\right) = det\left(E\right)*det\left(Z\right)
|
12,007 |
i^2 + i \cdot x \cdot 2 = y^2 \Rightarrow (i \cdot x \cdot 2 + i^2)^{\tfrac{1}{2}} = y
|
-3,832 |
144/72 \frac{\eta^5}{\eta} = \eta^5/\eta \frac{144}{72} 1
|
11,557 |
y^2 - 2\cdot y + 5 = 4 + (y + (-1))^2
|
35,138 |
\frac{P^3}{\left(P^2 + 1\right)^{5/2}} = -\frac{P}{\left(1 + P^2\right)^{5/2}} + \dfrac{P}{(P^2 + 1)^{\frac{1}{2}\cdot 3}}
|
8,197 |
\dfrac{\sin\left(\alpha\right)}{\cos\left(\alpha\right)} = \tan(\alpha)
|
-26,173 |
\frac{8}{2} + 3\cdot 7 + 18\cdot \left(-1\right) = 4 + 21 + 18\cdot (-1) = 7
|
34,243 |
T^\complement^k = T^1 \dots T^k
|
-20,226 |
-\frac{1}{-21} \cdot 9 = -3/(-3) \cdot 3/7
|
30,284 |
( x_1 + (-1), z') = \varnothing \Rightarrow \left[x_1, z'\right] = \varnothing
|
31,349 |
x \cdot x + 3\cdot x + 10\cdot \left(-1\right) = (x + 2\cdot (-1))^2 + 7\cdot x + 14\cdot (-1) = \left(x + 2\cdot (-1)\right)^2 + 7\cdot x + 14\cdot (-1) = (x + 2\cdot (-1))^2 + 7\cdot (x + 2\cdot (-1))
|
21,327 |
\sum_{i=1}^l x_i = \sum_{i=1}^l x_i
|
11,569 |
x\cdot f = \frac{1}{\tfrac1x\cdot \frac1f} = 1/\left(1/f\cdot 1/x\right) = f\cdot x
|
33,443 |
T\Longrightarrow T
|
5,645 |
\sin(\frac12π - x) = \cos{x}
|
17,200 |
x = \lambda = \dfrac{x^2}{\lambda}
|
28,088 |
\binom{10}{3} = \dfrac{10!}{3! \cdot 7!}
|
19,213 |
\frac{1}{1 + \tanh^2\left(y\right)}\frac{\mathrm{d}}{\mathrm{d}y} \tanh(y) = \frac{\mathrm{d}}{\mathrm{d}y} \tan^{-1}(\tanh(y))
|
48,342 |
2 * 2*127 = 508
|
15,348 |
\mathbb{E}[x - 2\cdot (x + (-1))^2] = \mathbb{E}[x - 2\cdot (x^2 - 2\cdot x + 1)] = \mathbb{E}[-2\cdot x^2 + 5\cdot x + 2\cdot (-1)] = -2\cdot \mathbb{E}[x^2] + 5\cdot \mathbb{E}[x] + 2\cdot (-1)
|
22,242 |
2=1\times 2
|
-10,538 |
-6/(s\times 8)\times \frac22 = -\dfrac{12}{16\times s}
|
11,098 |
\tfrac{x*y*\dfrac{1}{y*x}}{x*y} = 1/\left(x*y\right)
|
664 |
\left(-1\right) + r = \frac{r + (-1)}{\left( r + (-1), f \cdot x\right)} \implies ( \left(-1\right) + r, x \cdot f) = 1
|
8,985 |
\frac{1}{V*U} = 1/\left(V*U\right)
|
42,488 |
6\cdot7\cdot49=2058
|
1,769 |
1/2 = \frac12 \cdot (3 + 2 \cdot \left(-1\right))
|
18,398 |
\dfrac{\sqrt{2}}{8}\cdot 3 = \frac{3}{\sqrt{32}}
|
38,823 |
3/35 = \frac{4/7\times 1/2}{2}\times 3/5
|
24,011 |
1 + u^2 = \frac{1}{\cos^2(x)}\Longrightarrow \cos^2(x) = \dfrac{1}{u^2 + 1}
|
-7,263 |
6/14\cdot \frac{4}{13} = \dfrac{12}{91}
|
31,827 |
4(-1) + 35 + 60 (-1) + 20 = -9
|
12,445 |
p = 1/6 + 5/6 \cdot (-p + 1) \Rightarrow \frac{6}{11} = p
|
28,524 |
\dfrac{\frac{1}{6}}{3}\cdot 2\cdot 2/3 = 2/27
|
-26,134 |
-9 \cdot 1^{-3} - 3 - -9/(-1) - 3 \cdot (-1) = -12 + 12 \cdot (-1) = -24
|
-11,739 |
\left(\dfrac{5}{2}\right)^3 = 125/8
|
538 |
\frac{db}{dy} = \frac{db}{dx}*i
|
8,095 |
-\frac{1}{-8}\cdot 4^3 + 15 = -\dfrac{1}{-8}\cdot 64 + 15
|
-141 |
-32 = 6\cdot (-1) - 26
|
25,068 |
1/2 = 0 + \frac14 + \frac{1}{8} + \ldots
|
13,853 |
n^2 \cdot 4 + n \cdot 4 + 1 = 1 + \left(n + n^2\right) \cdot 4
|
30,893 |
(3 - \sqrt{2})(3 + \sqrt{2}) = 3^2 - 2 \times 1^2 = 7
|
7,555 |
((98 \times 100 + 2) \times (2 + 100 \times 102) + (100 \times 2)^2)^{1 / 2} = 10002
|
30,416 |
134 = 11^2 + 3^2 + 2^2 = 10^2 + 5^2 + 3^2 = 9^2 + 7^2 + 2 * 2 = 7^2 + 7^2 + 6^2
|
15,579 |
19^2*4 = 36^2 + 2^2 + 12^2
|
10,568 |
k\cdot s + r = k\cdot s - k + k + r = (s + \left(-1\right))\cdot k + k + r
|
5,819 |
5/12\cdot \frac{25}{25} = \dfrac{125}{300}
|
12,698 |
x^T\times y = (x^T\times y)^T = y^T\times x
|
1,826 |
2*π/8 = \tfrac{2*π}{8} = \frac{π}{4}
|
39,119 |
120 = 15\cdot 8
|
9,196 |
y \cdot 2 \cdot \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{\mathrm{d}}{\mathrm{d}x} y^2
|
-20,451 |
\frac{1}{10 + p}\times (9\times (-1) + 9\times p)\times \frac{6}{6} = \dfrac{1}{60 + 6\times p}\times \left(54\times (-1) + p\times 54\right)
|
-5,196 |
0.43\cdot 10^{(-3)\cdot \left(-1\right) + 0} = 10^3\cdot 0.43
|
15,315 |
i\cdot i\cdot \sqrt{x}\cdot \cdots = i\cdot \sqrt{-x}
|
14,932 |
\left(a + x\right)^2 = a^2 + x^2 + 2*x*a
|
18,583 |
\frac{1}{2} - \frac{1}{3 \cdot 4} = \frac{5}{12}
|
28,192 |
\dfrac{1}{\dfrac1a} = a
|
20,909 |
8\cdot (\cos{-\pi} + i\cdot \sin{-\pi}) = -8
|
1,529 |
\cos(\pi/2) \sin(r) + \cos(r) \sin(\dfrac{\pi}{2}) = \sin\left(\frac12 \pi + r\right)
|
31,457 |
2 + \nu \geq 1 + 2x \Rightarrow x \cdot 2 \leq \nu + 1
|
-3,971 |
\frac{n}{n^4} = \frac{n}{nn n n} = \frac{1}{n^3}
|
-6,352 |
\frac{3}{4 \cdot (t + 2 \cdot (-1))} = \frac{1}{4 \cdot t + 8 \cdot \left(-1\right)} \cdot 3
|
11,112 |
-2*5 + 5*3 = (3 + 2(-1))*5
|
14,766 |
|\varepsilon\cdot x|\cdot |\varepsilon \cap x| = |\varepsilon\cdot x| = |\varepsilon|\cdot |x|
|
24,663 |
\left(m\cdot h\right)!/m! = (m + 1)\cdot (m + 2)\cdot \cdots\cdot m\cdot h
|
10,988 |
3 = 2\cdot (-1) + x\Longrightarrow x = 5
|
25,896 |
\binom{n}{x} = \binom{n}{n - x} = \left(-1\right)^{n - x} \binom{-x + (-1)}{n - x}
|
-20,023 |
\tfrac{1}{14} \left(7 - a*56\right) = \frac{1}{7} 7 (-8 a + 1)/2
|
-20,309 |
\frac{-k\cdot 35 + 14\cdot (-1)}{12\cdot (-1) - 30\cdot k} = 7/6\cdot \frac{1}{2\cdot (-1) - 5\cdot k}\cdot (2\cdot \left(-1\right) - 5\cdot k)
|
24,729 |
204 = 224 + 20\cdot (-1)
|
1,870 |
\left(1 - t\right) \cdot (1 + s) = -t \cdot s + 1 + s - t
|
-6,691 |
1/100 + \frac{50}{100} = \frac{1}{100} + 5/10
|
3,135 |
(1 + y)^{k + l} = \left(y + 1\right)^k\cdot (1 + y)^l
|
-9,153 |
-80 \cdot t = -t \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5
|
15,562 |
\frac{1}{z_2} z_2/\left(z_1 z_2\right) = 1/(z_1 z_2)
|
5,548 |
2\sin\left(A\right) \cos(A) = \sin(2A)
|
22,205 |
\frac{\partial}{\partial t} (gf) = g\frac{df}{dt} + \frac{dg}{dt} f
|
8,814 |
(x + y)^3 = \left(x + y\right) \cdot (x + y) \cdot (x + y) = x \cdot x \cdot x + x \cdot x \cdot y + x \cdot y \cdot x + x \cdot y \cdot y + y \cdot x \cdot x + y \cdot x \cdot y + y \cdot y \cdot x + y \cdot y \cdot y
|
-29,059 |
0.19 \cdot 7 = 1.33
|
20,203 |
3 = 5 + 2 \left(-1\right)
|
-9,198 |
z \cdot z \cdot z \cdot 12 - z^2 \cdot 96 = z \cdot 2 \cdot 2 \cdot 3 \cdot z \cdot z - z \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot z
|
-7,005 |
\frac37 \cdot 2/6 = 1/7
|
-1,463 |
5\cdot 1/4/(\dfrac{1}{7}\cdot (-6)) = -7/6\cdot 5/4
|
10,137 |
(-1) + l^2 = (l + (-1))*(1 + l)
|
43,036 |
\frac{\partial}{\partial x} d^x = d^x
|
14,808 |
\frac{1}{1 + y} \cdot ((-1) + y) = 1 - \frac{2}{1 + y}
|
8,213 |
2^d \cdot 5^d = 10^d
|
16,314 |
\left(b + g\right)^2 = b^2 + g^2 + 2\cdot b\cdot g \Rightarrow g^2 + b^2 = \left(g + b\right)^2 - 2\cdot g\cdot b
|
3,211 |
\left(7 = 8 + (-1) \Rightarrow (-1) + 8M = 7^{1 + 2n}\right) \Rightarrow M*8 = 1 + 7^{n*2 + 1}
|
16,203 |
\sin(\alpha) \cdot \cos(\alpha) \cdot 2 = \sin\left(2 \cdot \alpha\right)
|
2,540 |
F^T \cdot F = F^T \cdot F
|
18,283 |
\arctan\left(-y\right) = -\arctan\left(y\right)
|
16,088 |
2^{1024}\cdot 2^{64}\cdot 2^4\cdot 2^1 = 2^{1093}
|
-1,255 |
\frac{5 / 8}{9\times \dfrac{1}{7}}\times 1 = \dfrac58\times \frac{1}{9}\times 7
|
32,087 |
180 = 3 \cdot 6 \cdot 10
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.