id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
11,871 |
t < w + 1,w < 1 + t \implies w = t
|
34,186 |
84 = \binom{\left(-1\right) + 6 + 3}{3 + (-1)}*3
|
32,431 |
\dfrac{1}{z_1*z_2} = \frac{1}{z_1*z_2}
|
9,502 |
(-3/2 + 2)^2 = \left(1 - 3/2\right) \times \left(1 - 3/2\right)
|
-22,360 |
(3 + a) \cdot \left(a + 5\right) = a^2 + a \cdot 8 + 15
|
25,357 |
(x + \sqrt{C}*y - \sqrt{R}*z)*(x + y*\sqrt{C} + \sqrt{R}*z) = x^2 + C*y^2 + y*\sqrt{C}*x*2 - R*z^2
|
-18,469 |
4 \cdot n + 4 \cdot (-1) = 5 \cdot \left(5 \cdot n + 8 \cdot (-1)\right) = 25 \cdot n + 40 \cdot \left(-1\right)
|
-20,137 |
-\dfrac{1}{-9} \cdot 81 = \frac{9}{1} \cdot (-\frac{1}{-9} \cdot 9)
|
5,768 |
(z + 1)^2 = (z + 1)\cdot (z + 1) = z^2 + 2\cdot z + 1^2
|
38,287 |
105 = (1 + 2 + 3 + 4) \cdot 10 + 5
|
22,323 |
n^2 + 2 \cdot n + 3 \cdot (-1) = (n + 3) \cdot \left((-1) + n\right)
|
26,234 |
(1 + n) ((-1) + n) + 1 = n^2
|
23,361 |
1 + \tfrac12 \cdot (4 + \left(-1\right)) = 1 + \frac{3}{2} = \frac{1}{2} \cdot 2
|
19,799 |
z^2 + y y - z y = (-y + z)^2 + y z
|
24,127 |
\dfrac12 (9999 + 1000 (-1) + 1) = 4500
|
1,769 |
\frac12 = (2 \cdot \left(-1\right) + 3)/2
|
-110 |
-10 + 3 \cdot (-1) = -13
|
27,076 |
(-1) + 100^{1/2} = 9
|
22,989 |
s = z + \dfrac{1}{z} \cdot r \implies z = \frac12 \cdot (s ± (s^2 - 4 \cdot r)^{1/2})
|
30,999 |
5^{-n} = 2^n\cdot 10^{-n}
|
19,042 |
28 = 4*6 + 3*0 + 4 + 2*0
|
25,451 |
(2^3)^A = 8^A
|
15,574 |
(b + a) \cdot (b + a) = b^2 + a \cdot a + 2\cdot b\cdot a
|
30,794 |
u = \frac1x \implies x = \frac1u
|
15,984 |
(c - g) \cdot (c - g) = g^2 + c^2 - 2 \cdot c \cdot g
|
12,768 |
n^4 + 4\cdot n^3 + 8\cdot n \cdot n + 8\cdot n + 4 = (n^2 + 2\cdot n + 2)^2 = ((n + 1)^2 + 1)^2
|
1,518 |
1 + f^3 = (1 + f)\cdot (1 - f + f^2) = (1 + f)\cdot \sqrt{3}\cdot f
|
11,816 |
\frac{1}{3 + n*2} = \frac{1}{1 + 2*(n + 1)}
|
3,361 |
(2^{10} + 2 \cdot (-1)) \cdot 6 = {4 \choose 2} \cdot (2^{10} + 2 \cdot (-1))
|
-1,383 |
\dfrac{\tfrac{1}{9} \cdot \left(-2\right)}{1/9 \cdot 8} = \frac{9}{8} \cdot (-2/9)
|
-2,335 |
-1/16 + \dfrac{2}{16} = 1/16
|
15,162 |
\sin(D)\times \cos(G) + \cos(D)\times \sin(G) = \sin\left(D + G\right)
|
28,580 |
0 = d_1^2 - 50\cdot d_1 + 225 \Rightarrow (d_1 + 45\cdot (-1))\cdot (d_1 + 5\cdot (-1)) = 0
|
-18,425 |
\frac{1}{(k + 6(-1)) \left(k + 5(-1)\right)}k\cdot (5(-1) + k) = \frac{1}{k^2 - k\cdot 11 + 30}(k^2 - 5k)
|
-2,097 |
2 \cdot \pi - \pi/3 = \pi \cdot 5/3
|
17,835 |
1 + k*x + x = 1 + (k + 1)*x \leq \left(1 + x\right)^k + x
|
12,804 |
h\cdot x\cdot x\cdot h\cdot h\cdot x = h^3\cdot x^3 rightarrow h^2\cdot x^2 = x\cdot h\cdot x\cdot h = (x\cdot h) \cdot (x\cdot h)
|
20,421 |
(-y + z)\cdot (y^2 + z \cdot z + y\cdot z) = -y^3 + z \cdot z^2
|
1,324 |
9\cdot z\cdot 2\cdot z = 18\cdot z^2
|
-4,981 |
10^2\cdot 2.4 = 10^{4 - 2}\cdot 2.4
|
38,255 |
\frac12\cdot 8\cdot 9 = \dfrac{72}{2} = 36
|
-1,484 |
36/20 = 36\cdot \dfrac{1}{4}/\left(20\cdot 1/4\right) = \frac{9}{5}
|
-30,298 |
\frac53 \times \pi = 2 \times \pi - \pi/3
|
-17,918 |
23\cdot \left(-1\right) + 33 = 10
|
306 |
\left(b + a\right)^2 = a^2 + 2ab + b^2
|
22,516 |
\arcsin\left(\frac{\sqrt{3}-1}{2\sqrt{2}}\right) = \pi/12
|
23,942 |
y_2 + y_1 = 4\cdot y_2 + y_1 + y_1\cdot 4 + y_2
|
-20,927 |
\frac{x + 2(-1)}{x + 2(-1)} \left(-\frac{3}{7}\right) = \tfrac{-3x + 6}{14 (-1) + x*7}
|
23,659 |
2400/l\cdot 2 = 4800/l
|
52,456 |
U = U^+
|
28,706 |
x^6 + (-1) = (x^3 + (-1)) \cdot \left(x^3 + 1\right) = (x^2 + (-1)) \cdot (x^2 + x + 1) \cdot (x \cdot x - x + 1)
|
31,477 |
(2n)^2 + (n*2 + 2)^2 + \left(2n + 4\right) * \left(2n + 4\right) = (3n^2 + 6n + 5)*4
|
42,887 |
4\cdot 3 + 3\cdot 3 = 21
|
13,601 |
0 = h^3 + a_1 \cdot a_1 \cdot a_1 + a_2^3 - 3\cdot h\cdot a_1\cdot a_2 = (h + a_1 + a_2)\cdot (h^2 + a_1^2 + a_2 \cdot a_2 - h\cdot a_1 - a_1\cdot a_2 - a_2\cdot h)
|
8,379 |
\frac{1}{10} = \frac19 \cdot \frac{9}{10}
|
-4,429 |
-\frac{1}{(-1) + x} - \frac{3}{x + 1} = \frac{2 - 4*x}{(-1) + x^2}
|
-22,292 |
d^2 - 3 d + 70 (-1) = (d + 7) (d + 10 (-1))
|
-4,585 |
x^2 - x*8 + 15 = \left(x + 3(-1)\right) (x + 5\left(-1\right))
|
258 |
{r + n + (-1) \choose r} = {n + r + \left(-1\right) \choose r}
|
25,805 |
1 + x^4 = (1 + x^2) \cdot (1 + x^2) - (x\cdot \sqrt{2}) \cdot (x\cdot \sqrt{2})
|
22,763 |
4 = z * z - x^2 = (z - x)*(z + x)
|
27,604 |
64 + 8(-1) + 7(-1) + 7(-1) + 6(-1) = 36
|
14,530 |
c^3 + c^2 \cdot g \cdot 3 + g^2 \cdot c \cdot 3 + g^3 = (c + g) \cdot (c + g)^2
|
15,074 |
k \times n = y - f \Rightarrow y = k \times n + f
|
1,405 |
Gu = \mathbb{E}[uG]
|
-19,042 |
29/30 = \frac{1}{25*\pi}*X_q*25*\pi = X_q
|
-20,176 |
\tfrac{1}{24 \cdot (-1) + y \cdot 3} \cdot (-15 \cdot y + 6 \cdot (-1)) = 3/3 \cdot \frac{-y \cdot 5 + 2 \cdot (-1)}{y + 8 \cdot \left(-1\right)}
|
26,564 |
-3/4*5*\frac16/2 + 1 = \frac{1}{16}*11
|
26,618 |
256*x + 2101*(-1) = \left(x + 8*\left(-1\right)\right)*256 + 53*(-1)
|
-1,568 |
\frac25 = \tfrac{2}{5}
|
2,478 |
1 + \frac{24541}{56660} = 81201/56660
|
-1,632 |
\pi/2 + \pi = 3/2\times \pi
|
26,168 |
x \cdot 2 \gt 3 - x\Longrightarrow 1 < x
|
15,609 |
\frac{1}{10^2}*(10 - 2*3) * (10 - 2*3) = \tfrac{4^2}{10^2} = 0.16
|
-19,240 |
4/9 = \frac{W_t}{9 \cdot \pi} \cdot 9 \cdot \pi = W_t
|
18,857 |
\frac{2}{16} + 1/17 = 50/(16\cdot 17)
|
21,383 |
6 = (17/21)^2 \times \left(\frac{1}{21}\times 17\right) + (37/21)^3
|
9,054 |
\tfrac{\sin\left(z/2\right)}{z} = 1/(z\cdot 1/2)\cdot \sin(\frac12\cdot z)/2
|
12,005 |
x \cdot 10 + (-1) = ((-1) + x) \cdot 10 + 9
|
-7,532 |
\frac13 \cdot (-i \cdot 12 + 6) = 6/3 - i \cdot 12/3
|
21,102 |
e^{A + B} = e^A\times e^B = e^B\times e^A
|
-1,080 |
1/\left(6 (-5/9)\right) = ((-9)*1/5)/6
|
10,744 |
n/2 + \dfrac13\cdot n + \frac{1}{4}\cdot n = \dfrac{13\cdot n}{12}\cdot 1 \gt n
|
-2,289 |
1/18 = 2/18 - \dfrac{1}{18}
|
5,961 |
(x^3 - x^2 + 1)*(1 + x^2 + x) = x^5 + x + 1
|
15,424 |
\left( E * E f, f\right) = ( Ef, Ef) = \|Ef\|^2
|
31,494 |
7^2\cdot 2^2\cdot 3^3\cdot 5 = 26460
|
12,756 |
x = k*x/k = \frac{1}{k}*x + x/k
|
19,401 |
\dfrac{4}{3}*x + x = \dfrac{1}{3}*7*x
|
7,695 |
3^2 + 2^2 + 2*2*3 = (3 + 2)^2
|
19,109 |
\tan\left(4 \cdot x\right) = \tan\left(π - 3 \cdot x\right) = -\tan(3 \cdot x)
|
25,201 |
S \cdot M - I = S - L \implies S \cdot (-I + M) = I - L
|
18,530 |
d^2 * d^2 = d^4
|
9,163 |
1/4 \cdot 0 + \frac14 + \dfrac{1}{2 \cdot 2} = 1/2
|
19,140 |
\frac{1}{1 + k}\cdot \left(k + 2\right) = 1 + \frac{1}{k + 1}
|
-4,025 |
\frac{y^3 \cdot 15}{3 \cdot y^5} \cdot 1 = \frac{15}{3} \cdot \dfrac{y^3}{y^5}
|
29,055 |
\binom{4}{2}*4*7 \binom{6}{2} = 2520
|
20,217 |
15 = (0.5 \cdot ((-1) \cdot 0.5 + 1) \cdot 900)^{1 / 2}
|
8,359 |
{S \choose y} = \frac{1}{(-y + S)!\cdot y!}\cdot S!
|
-1,715 |
13/6 \cdot π = π \cdot \frac{4}{3} + π \cdot 5/6
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.