id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
17,601 | x^{\tfrac{1}{q} p} = (x^p)^{1/q} = \left(x^p\right)^{\dfrac1q} |
33,686 | 60 \cdot 60 \cdot 60 = 3^2 \cdot 2 \cdot 5 \cdot 2 \cdot 5^2 \cdot 2^4 \cdot 3 |
-2,611 | 3^{\frac{1}{2}} - \left(9 \times 3\right)^{\frac{1}{2}} + (25 \times 3)^{\frac{1}{2}} = 3^{\frac{1}{2}} - 27^{\frac{1}{2}} + 75^{1 / 2} |
2,805 | -(u_0 + u_2 - u_1 \cdot 2) + u_3 - u_2 \cdot 2 + u_1 = u_3 - u_2 \cdot 3 + 3 \cdot u_1 - u_0 |
31,417 | 3 = (2 + 1)!/(1!*2!) |
-20,987 | \frac{70\cdot m + 28}{-63\cdot m + 49\cdot (-1)} = \frac{10\cdot m + 4}{-9\cdot m + 7\cdot \left(-1\right)}\cdot 7/7 |
27,507 | \sqrt{x} = e^{\tfrac{\ln(x)}{2}} |
3,850 | (z^2 + z + 1) \left(z + (-1)\right) = z^3 + (-1) |
31,386 | 2.999 \cdot \dots = 3 |
15,674 | |y| = |y - y_l + y_l| \leq |y - y_l| + |y_l| |
-20,267 | \frac{2}{7}\cdot \tfrac{1}{y\cdot 10 + 2\cdot (-1)}\cdot (2\cdot \left(-1\right) + 10\cdot y) = \dfrac{20\cdot y + 4\cdot (-1)}{70\cdot y + 14\cdot (-1)} |
7,181 | \frac{1 + k}{2 + k} = \frac{1}{k + 2}\cdot (k + 1) |
32,271 | -1 \geq \cos(x^2\times p + h\times x + s) \Rightarrow \cos\left(x^2\times p + h\times x + s\right) = -1 |
35,157 | \sin{\dfrac{\pi}{4}} \lt \sin{\pi \cdot 5/18} |
24,217 | 1 - \tan(y) + \tan^2\left(y\right) - \tan^3(y) + \dotsm = \frac{\tan\left(2 \cdot y\right)}{1 + \tan(2 \cdot y)} |
-11,545 | 12 i + 0 + 15 \left(-1\right) = -15 + 12 i |
22,689 | H\cdot a\cdot g = g\cdot H\cdot a |
6,952 | \frac{3 + 4 \cdot (-1)}{5 + 2 \cdot (-1)} = -\frac13 |
-24,830 | 5221 = -53 + 5274 |
-22,298 | x^2 - 6\cdot x + 7\cdot (-1) = (x + 7\cdot (-1))\cdot (x + 1) |
-5,571 | \frac{2}{9 + k\cdot 3} = \frac{2}{(3 + k)\cdot 3} |
6,206 | -1/((-1) \frac13) = 3 |
31,898 | (m + 1)^3 = m^3 + 3\cdot m^2 + 3\cdot m + 1 > 3\cdot m^2 |
-20,061 | -\tfrac{3}{1} (\left(-8\right) p)/((-8) p) = p\cdot 24/\left(p\cdot (-8)\right) |
551 | x^l a_l + x^l b_l = (a_l + b_l) x^l |
903 | f^d*f^h = f^{h + d} |
16,957 | 8^x - 1^x = 8^x + (-1) |
-4,961 | \frac{1}{100}\cdot 0.18 = 0.18/100 |
17,726 | -2\cdot t + t^2 = 0 \implies t = 0\wedge 2 = t |
-5,570 | \frac{23}{x^2 - x*2 + 8*(-1)} = \frac{1}{x * x - 2*x + 8*(-1)}*(4*x + 8 - x*4 + 16 + (-1)) |
-10,344 | -\frac{1}{2 \cdot a + 2} \cdot (10 + 3 \cdot a) \cdot 5/5 = -\frac{50 + 15 \cdot a}{10 + 10 \cdot a} |
34,380 | \sqrt{g} = \sqrt{g}\cdot \frac{1}{0\cdot (-1) + 1}\cdot (1 + 0) |
29,310 | -\cot(x + \frac{π}{2}) = \tan(x) |
-19,647 | \frac{2\times 2}{3} = 4/3 |
25,815 | 3\cdot (x^2 + y^2)^2\cdot (2\cdot x\cdot x' + 2\cdot y) = (x^2 - y^2)\cdot (x\cdot x'\cdot 2 - 2\cdot y)\cdot 2 |
9,580 | z^2 + (-1) = (1 + z) \cdot (\left(-1\right) + z) |
31,613 | 1/(c*f) = \frac{1}{c*f} |
-6,179 | \dfrac{4}{16 + x\cdot 4} = \tfrac{1}{4\cdot \left(4 + x\right)}\cdot 4 |
20,484 | (1 - x)/x + x \cdot 0 + (1 - x) \cdot \mathbb{Var}\left(X\right) = \left(1 - x\right) \cdot (1/x + \mathbb{Var}\left(X\right)) |
18,428 | \frac{2\cdot \pi}{2\cdot 5} = \pi - 4\cdot \pi/5 |
-4,204 | 45/60 \frac{1}{p^5} p^4 = \frac{45 p^4}{p^5*60} |
-23,108 | -\frac{1}{2}\cdot 7/2 = -\dfrac{7}{4} |
8,187 | z \cdot z + 2\cdot z + 1 = (z + 1)^2 |
-15,799 | 6\cdot \frac{1}{10}\cdot 4 - 5\cdot 6/10 = -6/10 |
17,976 | \frac{1}{\left(1 + i\right)!}\cdot i! = \frac{1}{1 + i} |
-20,729 | \frac{-z*50 + 45*\left(-1\right)}{70*z + 63} = -5/7*\frac{10*z + 9}{10*z + 9} |
-7,061 | 3/10 \cdot \frac29 = \frac{1}{15} |
5,243 | \cot{((-1)\cdot \pi)/4} = \cot{\frac{\pi\cdot 3}{4}} |
-11 | 5 - 1 = 4 |
-11,567 | -3\cdot i - 1 + 10\cdot \left(-1\right) = -i\cdot 3 - 11 |
21,740 | \mathbb{E}\left[Q\right]^4 = \mathbb{E}\left[Q^4\right] |
13,417 | x \cdot y = (x + (-1)) \cdot \left(y + (-1)\right) + 1 + x + \left(-1\right) + y + (-1) |
506 | \frac{1}{d\cdot g} = \frac{1}{d\cdot g} \Rightarrow g\cdot d = g\cdot d |
36,360 | a^{n + 1} = aa^n |
2,929 | \cos(4\times y) = \cos(2\times \pi - 4\times y) = \cos(9\times y) |
33,911 | 145/3 = \dfrac{1}{3} 152 - 7/3 |
24,403 | 1 - \cos(z) = z^2\times \cos(z) \Rightarrow \cos(z) = \frac{1}{1 + z^2} |
17,141 | x - f_1 - f_2 = -f_2 + x - f_1 |
12,953 | 160 + y = (y + 10) \cdot 11 \implies 110 + 11 \cdot y = y + 160 |
7,313 | \frac{1}{12} \cdot 11 + 1 = 23/12 |
8,801 | 2^2\times 4\times 3 = 48 |
-25,219 | x^{(-1) + k}\times k = \frac{\mathrm{d}}{\mathrm{d}x} x^k |
12,969 | (x + 1)*(x + 2) = x^2 + x*3 + 2 |
1,565 | 2^3\cdot b = b\cdot 2\cdot 2\cdot 2 |
26,694 | 48/\left(-10\right) = -24/5 |
15,768 | n \cdot n = 1 + (n + 1)\cdot \left(n + (-1)\right) |
17,588 | \sin(A \cdot 2) = 2 \cdot \cos(A) \cdot \sin\left(A\right) |
24,167 | \frac{2}{12} \cdot \pi = \dfrac{\pi}{6} \approx 0.5236 |
23,211 | \left(|1 + z| = 3 \Rightarrow z + 1 = 3\right) \Rightarrow 2 = z |
24,021 | 0.5 + \cos{z \cdot 2} \cdot 0.5 = \cos^2{z} |
25,551 | \frac{1}{\frac{1}{b}} = b^{\left(-1\right) (-1)} = b^1 = b |
5,569 | \left(-c + a\right) * \left(-c + a\right) + (c + a)^2 = (c * c + a * a)*2 |
7,491 | z^0 = \frac{z^4}{z^4} 1 |
-2,756 | 4\sqrt{7} = \sqrt{7}\cdot (3 + 1) |
5,451 | d^{y_1 \cdot j} \cdot d^{y_2 \cdot j} = d^{j \cdot (y_2 + y_1)} |
-30,908 | 33 = 12*4 + 15 \left(-1\right) |
4,703 | y_3 - 2*y_4 = 0 rightarrow y_3 = y_4*2 |
18,708 | \varepsilon_s f\varepsilon_z = \varepsilon_z \varepsilon_s f |
9,458 | \sin(z) = \frac{z}{1 + \frac{z^2}{2*3 - z^2 + \dotsm}} |
-10,545 | -40 = -3\cdot p + 15\cdot (-1) + 96\cdot (-1) = -3\cdot p + 111\cdot (-1) |
-20,863 | \dfrac{5 \cdot m + 20}{40 \cdot (-1) + m \cdot 35} = \dfrac{1}{5} \cdot 5 \cdot \frac{1}{7 \cdot m + 8 \cdot (-1)} \cdot (m + 4) |
5,777 | 1 = \left(\sqrt{3} + 2\right) \cdot (-\sqrt{3} + 2) |
25,965 | b*y = y*b |
21,952 | {\left(-1\right) + n + p \choose p} = \tfrac{1}{p!\cdot ((-1) + n)!}\cdot \left(n + p + (-1)\right)! |
9,330 | (a^{1/2})^2\cdot g^{1/2} \cdot g^{1/2} = (a^{1/2}\cdot g^{1/2})^2 |
31,090 | c_2 - c_1 + c_1 \times 2 = c_2 + c_1 |
16,746 | (3\cdot g + 2\cdot (-1))\cdot (g\cdot 2 + 3\cdot (-1)) = 6 + 6\cdot g \cdot g - g\cdot 13 |
20,801 | 6^{\frac13} = 2^{1/3} \cdot 3^{1/3} |
19,477 | (-m + n)^2 = \left(-n + m\right)^2 |
22,078 | 2\cdot \sqrt{5} + \sqrt{11} = \sqrt{5}\cdot 2 + \sqrt{11} |
29,912 | g \cdot g^2 + 54 = g^3 + 27 + 27 \geq 27 \cdot g |
39,134 | t = 3\dfrac{1}{3}t |
-6,555 | \frac{2}{2}\cdot \frac{3}{(z + 8)\cdot \left(2\cdot (-1) + z\right)} = \frac{6}{(z + 2\cdot (-1))\cdot (8 + z)\cdot 2} |
-29,028 | x^2 * x*x^4 = x^{3 + 4} = x^7 |
17,157 | i^{-1} = i^{1 + 2 \cdot (-1)} = \frac{1}{i^2} \cdot i = i/(-1) = -i |
20,402 | \chi^3 + \chi^2 + 2 \times \chi + 4 \times (-1) = (4 + \chi \times \chi + 2 \times \chi) \times (\chi + \left(-1\right)) |
18,947 | 0 = h \cdot a \Rightarrow a = 0\text{ or }h = 0 |
-4,024 | 10/3\cdot r = \frac{10}{3}\cdot r |
33,335 | 0 = a\cdot 0 = 0\cdot a |
14,634 | \frac{d}{c*b} = \dfrac{\dfrac1b*d}{c} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.