id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
9,544 |
x_{l + \left(-1\right)} + x_{2 (-1) + l} = x_l \Rightarrow -x_{2 \left(-1\right) + l} + x_l = x_{(-1) + l}
|
-20,929 |
81/(-18) = -9/(-9) \left(-\frac{9}{2}\right)
|
15,935 |
\frac{2^0 + (-1)}{2 + 0} = 0
|
14,446 |
3/11 = \frac{1\cdot 3}{4\cdot 2 + 1\cdot 3}
|
-9,380 |
-2 \times k + 16 = -k \times 2 + 2 \times 2 \times 2 \times 2
|
41,797 |
\frac{1}{100}\cdot 95\cdot 60 = 57
|
5,674 |
Q = Q^\complement = Q
|
5,326 |
\frac{\partial}{\partial x} (w_1 \cdot w_2) = \frac{\partial}{\partial x} w_2 \cdot w_1 + \frac{\partial}{\partial x} w_1 \cdot w_2
|
29,900 |
4^2 + 10^2 + 28^2 = 15^2 \cdot 4
|
-19,734 |
\frac58 \cdot 7 = 35/8
|
-4,415 |
(y + 4) \cdot (y + 1) = 4 + y^2 + 5 \cdot y
|
19,058 |
3/2 - x = x \cdot 2 - 6 \Rightarrow \frac52 = x
|
11,626 |
|4^2 - 14\cdot 1^2| = 2
|
16,660 |
-101 = (-13) \cdot 7 + 10 \cdot \left(-1\right) = (-8) \cdot 13 + 3
|
24,197 |
\frac{5x+6}{(2+x)(1-x)} = \frac{\frac52 x + 3}{\left(1+\frac12 x\right)(1-x)}
|
36,761 |
\dfrac{8}{27} = 1/405\cdot 120
|
-16,375 |
\sqrt{4*2}*12 = 12 \sqrt{8}
|
10,088 |
\left(d^2 + d \cdot b + b^2\right) \cdot \left(-b + d\right) = d^2 \cdot d - b^3
|
27,422 |
z = \left(z^{1/2}\right)^2
|
-10,655 |
\frac{t \cdot 6 + 30}{t \cdot 12} = \frac{1}{t \cdot 2} (t + 5) \cdot 6/6
|
-28,770 |
\tfrac{1}{2\cdot x + 6} + \frac12 = \frac{x + 4}{6 + 2\cdot x}
|
26,559 |
(z + 2)\times \left(3\times z + 8\right) = 16 + 3\times z \times z + 14\times z
|
25,848 |
E(E(Q) \cdot Y) = E(Q) \cdot E(Y)
|
38,015 |
1 + 2 + 1 = 1 + 1 + 2
|
35,529 |
\frac{y^a}{y^c} = y^{a - c} = \frac{1}{y^{c - a}}
|
8,324 |
-2 \cdot (k + 1) + 3 \cdot k + 2 = k
|
8,873 |
\binom{k + i}{i} = -\binom{i + k}{i + (-1)} + \binom{i + k + 1}{i}
|
-11,715 |
(\frac{8}{5}) \cdot (\frac{8}{5}) = \frac{64}{25}
|
-28,816 |
\frac12 \cdot \left(2 + 6\right) = \dfrac{1}{2} \cdot 8 = 4
|
1,854 |
|\lambda|\cdot B\cdot |\mu|\cdot C = C\cdot B\cdot |\mu|\cdot |\lambda|
|
-14,616 |
90 = \dfrac{1}{9}810
|
27,242 |
\left(2*a + 2*b + c\right)/3 = \dfrac15*(3*a + 4*c) = \frac{1}{3}*(2*a + b + 2*c)
|
15,824 |
0 \leq y + \sqrt{26} \Rightarrow -\sqrt{26} \leq y
|
-18,592 |
-\frac{16}{11} = - \frac{16}{11}
|
23,530 |
c_2^2 - c_1^2 = (c_1 + c_2)*(c_2 - c_1)
|
21,944 |
(2^{33} + (-1))*(2^{33} + 1) = 2^{66} + \left(-1\right)
|
-7,147 |
3/11*\frac{3}{12} = 3/44
|
-1,281 |
-35/14 = \frac{(-35)\cdot 1/7}{14\cdot \frac17} = -5/2
|
23,789 |
(AA^Z)^Z = (A^Z)^Z A^Z = AA^Z
|
28,904 |
\frac{1}{2}\cdot (i + l + 2\cdot (-1))\cdot (i + l + \left(-1\right)) = \sum_{m=1}^{i + l + 2\cdot \left(-1\right)} m = \sum_{m=2}^{i + l + (-1)} (m + (-1))
|
25,715 |
(-1) + x^6 = ((-1) + x) \cdot (1 + x^2 + x) \cdot (x^3 + 1)
|
-30,096 |
d/dy \left(5 + 2\cdot y^2 - 6\cdot y\right) = 4\cdot y + 6\cdot \left(-1\right)
|
22,760 |
\operatorname{Var}\left(1.08 \cdot R + B\right) = \operatorname{Var}\left(B + 500 + R \cdot 1.08\right)
|
10,798 |
2 \cdot l + 6 \cdot (-1) = 0 \Rightarrow l = 3
|
-27,514 |
6a = 2*3a
|
20,806 |
a + b = ( a, b) ( 1, 1) \leq (a^2 + b^2)^{\frac12}
|
25,220 |
\left(T_1 + T_2\right)^2 - T_2 \times T_1 \times 2 = T_1 \times T_1 + T_2^2
|
30,112 |
\cos{\frac{4*\pi}{9}}*2 = 2*\sin{\pi/18}
|
-23,062 |
\frac{1}{27} \cdot 16 \cdot \left(-\dfrac{2}{3}\right) = -\frac{32}{81}
|
37,408 |
\left( w_1, w_2\right) + ( 0, 0) = ( w_1 + 0, w_2 + 0) = [w_1, w_2] = ( 0, 0) + \left( w_2, w_1\right)
|
13,841 |
\cosh(p) = \left(e^p + e^{-p}\right)/2 = \cos(i\cdot p)
|
633 |
\left(x^n + a^n \Leftrightarrow x + a = 0\right) \implies 0 = a^n + x^n
|
23,303 |
y\cdot x^3 = b + \int x \cdot x \cdot x\cdot x\,\mathrm{d}x \Rightarrow x^5/5 + b = y\cdot x^3
|
21,132 |
r + y * y*s + t*y = \pi*(4*k + 1) \Rightarrow 0 = s*y^2 + y*t + r - \left(k*4 + 1\right)*\pi
|
1,385 |
\frac16\times \frac26 = \frac2{36}
|
-24,447 |
\frac{1}{8 + 9}*170 = \frac{170}{17} = \frac{170}{17} = 10
|
30,531 |
\left( u, v\right) + ( 0, 1) = ( u + 0, v) = [u, v]
|
15,895 |
qF = bF \Rightarrow F/b = F/q
|
14,936 |
(\mathbb{E}[Q]^2 + \mathbb{Var}[Q])/2 = \mathbb{E}[Q^2/2]
|
6,213 |
f = z\cdot Y \Rightarrow z = f/Y
|
4,690 |
426*5!^3/15! = \frac{1}{126126}71 \approx 0.00056292
|
16,664 |
8 = a + h\Longrightarrow -h + a = 2
|
22,650 |
(x + f)^2 = f^2 + x \cdot x + 2\cdot x\cdot f
|
21,546 |
\frac{1}{m \cdot k + 2 \cdot (-1)} \cdot (-((-1) + m) \cdot 2 + m \cdot k + 2 \cdot (-1)) = \dfrac{m}{k \cdot m + 2 \cdot (-1)} \cdot (2 \cdot (-1) + k)
|
26,596 |
z^2 - 3 \cdot z + 2 = ((-1) + z) \cdot (2 \cdot (-1) + z)
|
20,493 |
\sin(3\cdot A) = \sin(3\cdot (4\cdot \pi/3 + A))
|
10,383 |
\int\limits_a^b k\,\text{d}y = \int_a^b k\,\text{d}y
|
-22,619 |
-7/8\cdot \frac{1}{4}3 = \frac{1}{8\cdot 4}((-7)\cdot 3) = -\frac{21}{32} = -\dfrac{21}{32}
|
19,775 |
\frac{1}{n^2} \cdot n \cdot i = i/n
|
20,846 |
\mathbb{E}\left[Q\right] = \mathbb{E}\left[\sum_{j=1}^k Q_j\right] = \sum_{j=1}^k \mathbb{E}\left[Q_j\right]
|
-22,097 |
\frac{1}{12} \cdot 20 = \frac{5}{3}
|
23,147 |
-4*i = 4*(\cos{-\frac{\pi}{2}} + i*\sin{-\frac{\pi}{2}}) = -4*i
|
-22,243 |
q^2 + 10 \cdot q + 21 = (q + 3) \cdot (q + 7)
|
-22,868 |
110/66 = \frac{22 \cdot 5}{22 \cdot 3}
|
-25,584 |
\frac{3}{x^2} = d/dx (-\dfrac3x)
|
-3,143 |
13^{\dfrac{1}{2}}\cdot (4 + 1) = 5\cdot 13^{1 / 2}
|
11,386 |
y^4 - y^3 + y^3 + (-1) = y^4 + \left(-1\right)
|
28,137 |
m_l \times m_i = m_i \times m_l
|
17,238 |
(f + g*i)^{-1} = (g*i + f)^{-1}
|
17,990 |
2*\sqrt{3} + 4 = (1 + \sqrt{3})*(1 + \sqrt{3})
|
12,557 |
\frac{1}{\left(m + 1\right)!}\cdot m! = \dfrac{m!}{(m + 1)\cdot m!} = \frac{1}{m + 1}
|
11,449 |
-\sin(\frac56 \cdot \pi) \cdot (-1) - \sin(\pi/6) = 0
|
15,176 |
z_x = f' x \cdot 2 y \Rightarrow xf' y \cdot y^2 \cdot 2 = y^2 z_x
|
30,875 |
x^4 + 4 \cdot y^4 = (x^2 + 2 \cdot y^2) \cdot (x^2 + 2 \cdot y^2) - (2 \cdot x \cdot y)^2 = (x^2 + 2 \cdot x \cdot y + 2 \cdot y^2) \cdot (x^2 - 2 \cdot x \cdot y + 2 \cdot y^2)
|
-28,922 |
\dfrac{7}{7 \times \frac{1}{20}} = 7 \times \dfrac{20}{7} = 20
|
33,233 |
\frac12 \cdot 3200 + \frac{800}{2} = 2000
|
-12,907 |
8/18 = \frac19 \cdot 4
|
23,124 |
\frac{x}{4}*x * x + \frac{x*x^2}{4} + A = A + \frac{x^3}{2}
|
18,463 |
-y^k + \left(1 + k\right)^2\cdot y^k - k\cdot y^k\cdot 2 = k^2\cdot y^k
|
37,910 |
\frac{i +1}{1 +i} =1
|
14,743 |
-(1 + i) (i + 1 + 2(-1)) + z \cdot (i + 1 + (-1)) = -\left(i + 1\right) (i + (-1)) + zi
|
27,551 |
z_1 \cdot r_1 + \dotsm + z_k \cdot r_n = \overline{r_1} \cdot z_1 + \dotsm + z_k \cdot \overline{r_n}
|
6,595 |
(g + (-1)) \cdot \left(1 + g^2 + g\right) = g^3 + (-1)
|
23,612 |
\cos\left(-y + z\right) = \sin{y}\cdot \sin{z} + \cos{y}\cdot \cos{z}
|
-10,535 |
\tfrac{4}{4}\cdot \dfrac{1}{m + 3\left(-1\right)}10 = \dfrac{40}{12 (-1) + m\cdot 4}
|
2,894 |
4\cdot (18\cdot t - 6\cdot i + 10) + 6\cdot i + 4\cdot (-1) = 72\cdot t - 24\cdot i + 40 + 6\cdot i + 4\cdot (-1) = 18\cdot (4\cdot t - i + 2)
|
532 |
\frac{\mathrm{d}}{\mathrm{d}x} \sin^{-1}(x) = \frac{1}{\cos\left(\cos^{-1}\left(x - \pi/2\right)\right)}
|
28,364 |
-\frac{1}{(1 - x)^2} = -\frac{1}{\left(1 - x\right) \cdot \left(1 - x\right)}
|
21,627 |
x^2 + x + 1 = (1 + x^2 + x) + 0
|
-20,616 |
30/(-18) = -6/\left(-6\right)\cdot (-\frac{5}{3})
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.