id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
13,265 |
a^{-k + l} = \frac{1}{a^k} a^l
|
19,612 |
|B/E| = \frac{|B|}{|E|}
|
13,740 |
(2 + k)\cdot \left(k + 2\cdot (-1)\right) = k^2 + 4\cdot (-1)
|
15,163 |
\dfrac{1}{ha} = 1/(ah)
|
-20,829 |
\frac{1}{7}*1 = \frac{\left(-1\right) + k}{7*(-1) + 7*k}
|
20,255 |
1 \gt 1 - 1/8 = 7/8 = 28/32 \gt \dfrac12 + 1/32 = 17/32 > \dots
|
394 |
0*...*\pi*2 = 0
|
23,019 |
\frac1x\cdot (a + c) = (-1) + \dfrac1x\cdot (a + x + c)
|
7,075 |
\frac{3\cdot 17}{4\cdot 17} = \dfrac{51}{68}
|
9,975 |
35 \cdot (-1) + 49 \cdot b^2 = 35 \cdot (-1) + 49 \cdot b^2
|
-15,966 |
19/10 = -10\cdot 3/10 + 7\cdot \dfrac{7}{10}
|
-22,195 |
(x + 2) \cdot (10 + x) = x^2 + x \cdot 12 + 20
|
802 |
1/2 + 1/3 + 1/18 = \frac89
|
21,601 |
W^4 = W^2 \cdot W \cdot W
|
-3,631 |
70 = 2\cdot 5\cdot 7
|
17,208 |
-144 = 9\times (-16)
|
8,539 |
1/27 \cdot 4/180 = \frac{1}{1215}
|
23,521 |
13 = 4 + 3^2
|
6,119 |
\frac{2}{3}\cdot 6\cdot 10 = z\cdot 4/3\Longrightarrow z = 1/3
|
4,086 |
(z\cdot y)^2 \cdot (y\cdot z) = z^3\cdot y^3
|
-2,097 |
\frac{5}{3} \pi = -\frac{\pi}{3} + \pi\cdot 2
|
30,574 |
26^3 = (6\cdot (-1) + 2^5)^3
|
15,218 |
\tan^2(z) = (\sin\left(z\right)/\cos\left(z\right))^2 \approx \frac{1}{(-z + \frac{\pi}{2})^2}
|
30,553 |
\frac18 \times 120 = 15
|
7,663 |
72\cdot 5 - 48\cdot 7 = 24
|
13,589 |
m/2 + \left(-1\right) = \frac{1}{2}\cdot (m + 2\cdot (-1))
|
13,126 |
\frac{\sin{z}}{z} = (z - \frac{1}{3!}*z^2 * z + \dfrac{z^5}{5!} - \dots)/z = 1 - z^2/3! + z^4/5! - \dots
|
-6,179 |
\tfrac{1}{16 + x\cdot 4}\cdot 4 = \frac{4}{(x + 4)\cdot 4}
|
1,994 |
4*\left(5*y\right)^2 = 100*y^2
|
-28,771 |
-1/2 - \frac{4}{-2 \cdot x + 2} = -\frac12 + \frac{1}{x + \left(-1\right)} \cdot 2
|
32,568 |
1/(\sqrt{l}) = \frac{1}{\sqrt{l} + \sqrt{l}}\cdot 2 \gt \tfrac{1}{\sqrt{l} + \sqrt{l + 1}}\cdot 2
|
25,706 |
2\cdot (x - 1/2) = x\cdot 2 + (-1)
|
27,528 |
e^{a \cdot z} \cdot a = \frac{\partial}{\partial z} e^{a \cdot z}
|
-17,368 |
\dfrac{1}{100} 63.3 = 0.633
|
31,134 |
\tan{b} = \frac{\sin{b}}{\cos{b}}
|
31,594 |
|z| < 1 \Rightarrow \dfrac{1}{z + 1} = 1 - z + z^2 - z^3 + \dots
|
-20,355 |
\dfrac{9}{2}\cdot \frac{1}{x + 2\cdot \left(-1\right)}\cdot (2\cdot (-1) + x) = \tfrac{18\cdot (-1) + x\cdot 9}{x\cdot 2 + 4\cdot (-1)}
|
8,912 |
-g + x = -g + x
|
13,728 |
\frac{\text{d}}{\text{d}x} \frac{1}{Z} = \frac1Z \cdot \frac{\text{d}Z}{\text{d}x}/Z
|
-4,910 |
3.3 \cdot 10^3 = 10^{8 + 5\left(-1\right)} \cdot 3.3
|
-9,053 |
43.3\% = \frac{43.3}{100}
|
-9,318 |
-2\cdot 5\cdot 5 - t\cdot 2\cdot 3\cdot 5 = -30\cdot t + 50\cdot (-1)
|
11,673 |
24/14.4 = \dfrac53
|
24,707 |
\operatorname{atan}(16/63) = \operatorname{atan}(\frac{1}{63}16)
|
-10,781 |
\frac22\cdot (-\frac{6}{s\cdot 25 + 20\cdot \left(-1\right)}) = -\frac{12}{40\cdot (-1) + 50\cdot s}
|
25,263 |
\dfrac{1 + \frac{1}{2}}{1 + \frac{1}{4}} = 1.2 \lt 1 + 1/4
|
14,416 |
|y^3 + 3\cdot y \cdot y\cdot g + 3\cdot y\cdot g^2 + g^3 - y \cdot y^2| = |3\cdot y^2\cdot g + 3\cdot y\cdot g \cdot g + g^3| \geq 3\cdot y^2\cdot g
|
11,979 |
\frac{r}{x^2} \cdot d \cdot d = \frac{r \cdot d^2}{x \cdot x}
|
11,873 |
\infty = x < x + 1 = \infty \Rightarrow x = x + 1
|
5,522 |
a\cdot l - l + 1 + 1 = l\cdot (a + (-1))
|
-1,075 |
-63/18 = ((-63)\cdot \frac19)/(18\cdot \frac{1}{9}) = -\dfrac{7}{2}
|
18,726 |
(b^2 + a^2)^{\frac{1}{2}} * (b^2 + a^2)^{\frac{1}{2}} * (b^2 + a^2)^{\frac{1}{2}} = 8 \Rightarrow (a^2 + b^2)^3 = 8 * 8 = (2 * 2 * 2)^2 = 2^6
|
11,559 |
9^2 - 4 \cdot 4\cdot 2 = 49
|
-6,294 |
\frac{1}{x^2 - 14*x + 45}*2 = \dfrac{1}{\left(9*(-1) + x\right)*(5*(-1) + x)}*2
|
25,462 |
\tfrac{10!}{5!*5!} = 252
|
44,115 |
(\sqrt{31 - 8\times \sqrt{15}} + \sqrt{31 + 8\times \sqrt{15}})^2 = 31 - 8\times \sqrt{15} + 31 + 8\times \sqrt{15} + 2\times \sqrt{31^2 - 64.15} = 64
|
26,639 |
\frac{\partial}{\partial t} (y\cdot z) = \frac{\text{d}y}{\text{d}t}\cdot z + y\cdot \frac{\text{d}z}{\text{d}t}
|
-659 |
\left(e^{4 \cdot i \cdot \pi/3}\right)^{10} = e^{10 \cdot \frac{4}{3} \cdot \pi \cdot i}
|
-30,239 |
(2\cdot (-1) + z)\cdot (10\cdot (-1) + z) = z^2 - z\cdot 12 + 20
|
230 |
(C^2 + D^2 - D \cdot C) \cdot \left(D + C\right) = D^3 + C^3
|
5,118 |
\left(x + 1\right)! := x! \cdot (1 + x)
|
3,427 |
|z \cdot E - D \cdot B| = |E \cdot z - D \cdot B|
|
26,733 |
g_2^{i + 1}\cdot g_1^{i + 1} = (g_2\cdot g_1)^{i + 1} = g_2\cdot g_1\cdot (g_2\cdot g_1)^i = g_2\cdot g_1\cdot g_2^i\cdot g_1^i
|
39,490 |
7 \cdot 7^2 = 5 + 13^2 \cdot 2
|
-6,389 |
\frac{2}{n\cdot 5 + 45} = \frac{2}{5\cdot \left(9 + n\right)}
|
-19,343 |
8*1/7/\left(7*\dfrac{1}{5}\right) = \frac57*\frac17*8
|
575 |
(\frac{1}{2})! = \pi^{\frac{1}{2}}/2
|
15,922 |
\frac{h^g}{h^c} = h^{-c + g}
|
16,766 |
(-y)^{1 / 2}\cdot (-y)^{1 / 2} = (-y\cdot (-y))^{1 / 2} = (y^2)^{1 / 2}
|
13,332 |
7^2 + 24^2 = 25 \times 25
|
-22,182 |
21/15 = \frac{1}{5} \cdot 7
|
26,038 |
\frac18 \cdot \pi \cdot 3 + \pi = \pi \cdot 11/8
|
24,427 |
r\cdot m = m\cdot r
|
5,203 |
\dfrac{6!}{3!\cdot 2!\cdot 1!} = 6\cdot 5\cdot 4/2 = 60
|
-20,940 |
\tfrac{54\cdot z + 81\cdot (-1)}{-z\cdot 24 + 36} = \frac{-6\cdot z + 9}{9 - z\cdot 6}\cdot (-\dfrac94)
|
-2,103 |
\pi/2 - \pi/12 = \pi \cdot 5/12
|
8,683 |
z^{t_1} \times z^{t_2} \coloneqq z^{t_1 + t_2}
|
8,614 |
((-1) + y^2)\cdot (y^2 + 1) = (-1) + y^4
|
27,670 |
\cot(A) - \tan(A) = \left(\cos^2(A) - \sin^2(A)\right)/(\sin\left(A\right) \cos\left(A\right)) = 2\cot(2A)
|
27,152 |
1/(2\cdot 2) + \frac{1}{2\cdot 2} = \frac{1}{2}
|
8,839 |
i^2 + 2*i + 1 = (i + 1)^2
|
11,013 |
\left(b + a\right)^3 = a^3 + b a^2 \cdot 3 + a b^2 \cdot 3 + b^3
|
8,389 |
ba = zx, -z^2 + x^2 = a^2 - b^2 \Rightarrow -a * a + x^2 = z^2 - b^2
|
-7,905 |
\tfrac{1}{-3 + i}*(i*4 - 2) = \frac{1}{-3 + i}*(i*4 - 2)*\dfrac{-i - 3}{-3 - i}
|
53,155 |
130801 = 23 \cdot 5687
|
14,620 |
|-(d*(-1))/h + z_0| = |\frac{1}{h} d + z_0|
|
8,673 |
k_1\cdot \dotsm\cdot k_t = k_t\cdot \dotsm\cdot k_1
|
6,201 |
-d*(-1) + (-d) * (-d) * (-d) = -(-d + d^3)
|
10,289 |
\cos{\pi/2} + i \cdot \sin{\frac{\pi}{2}} = i
|
-14,156 |
(5 + 8 - 6\cdot 8)\cdot 2 = (5 + 8 + 48\cdot \left(-1\right))\cdot 2 = \left(5 - 40\right)\cdot 2 = \left(5 + 40\cdot \left(-1\right)\right)\cdot 2 = (-35)\cdot 2 = (-35)\cdot 2 = -70
|
21,474 |
\mathbb{E}\left((Y_2 - Y_1)^2\right) = \mathbb{E}\left(Y_1^2 + Y_2^2 - 2*Y_1*Y_2\right)
|
10,681 |
z + 1/z = z + (-1) + 1 + \tfrac1z \geq (z + (-1))/z + 1/z + 1
|
-5,342 |
11/10000 = \dfrac{11}{10000}
|
-23,255 |
1 - \frac174 = \frac37
|
-20,651 |
\frac{(-18) p}{p*3 + 30 (-1)} = \frac{1}{p + 10 \left(-1\right)} ((-6) p) \frac33
|
14,675 |
-14995\cdot 15190 + 6079\cdot 37469 = 1
|
13,281 |
π = 3 + (6 + \frac{3^2}{6 + \tfrac{5^2}{6 + \dots}})^{-1}
|
-8,036 |
\dfrac{-5*i + 27}{5 - 2*i} = \frac{1}{5 - 2*i}*\left(27 - 5*i\right)*\frac{5 + 2*i}{5 + 2*i}
|
34,753 |
\sin\left(\tau\cdot 2\right) = 2\cos\left(\tau\right) \sin(\tau)
|
32,968 |
\frac{x+1}{x^{2}-x+1}=\frac{x-1/2+3/2}{x^{2}-x+1}=\frac{x-1/2}{x^{2}-x+1} +\frac {3/2}{x^{2}-x+1}
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.