id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
48,420 | 5\cdot 1/6/6 + \frac{1/6}{6}\cdot 4 + \dfrac{\frac{1}{6}\cdot 3}{6} + \frac{\frac{1}{6}}{6}\cdot 2 + \dfrac{1}{6\cdot 6} + 0\cdot \frac{1}{6}/6 = \frac{1}{6}\cdot \left(\frac06 + \frac{5}{6} + 4/6 + 3/6 + 2/6 + \frac{1}{6}\right) |
2,267 | \cos{a\cdot 2} = -\sin^2{a} + \cos^2{a} |
417 | |c|\cdot |a| = |a\cdot c| |
-4,322 | \frac{y}{y^3} = \dfrac{1}{yy y}y = \frac{1}{y^2} |
2,024 | 1 + m * m * m + m^2 + 2m = m^3 + (1 + m)^2 |
50,470 | \cot{z} - \cot{y} = \cos{z}/\sin{z} - \cos{y}/\sin{y} = \dfrac{1}{\sin{z} \cdot \sin{y}} \cdot (\cos{z} \cdot \sin{y} - \sin{z} \cdot \cos{y}) = \frac{\sin(y - z)}{\sin{z} \cdot \sin{y}} |
29,813 | ((k + 1)\cdot 5 + \left(k + 1\right)^3)/3 = (k^3 + k^2\cdot 3 + k\cdot 8 + 6)/3 |
7,086 | \left(3 \cdot (-1) + x\right) \cdot (x + 1) = 3 \cdot (-1) + x^2 - 2 \cdot x |
25,859 | (x^2)^a = (\frac{1}{x})^a = x^{a + \left(-1\right)} |
21,063 | \frac{16}{3} = 1/2*6 + \frac{1}{3}*5 + 1/6*4 |
37,562 | i\binom{F}{i} = \binom{(-1) + F}{i + (-1)} F |
21,621 | c_m = \dfrac{c_m m}{m}1 |
-2,771 | \sqrt{5}\cdot (4 + 1) = 5\cdot \sqrt{5} |
5,023 | \left(n + 2 \cdot (-1)\right) \cdot (n + 2) = 4 \cdot (-1) + n^2 |
28,517 | \dfrac{1}{5 + 7 \cdot (-1)} \cdot (-2 + 4 \cdot (-1)) = -\frac{1}{-2} \cdot 6 = 3 |
-20,513 | -\frac{1}{1}*2*j*5/(j*5) = (j*(-10))/(j*5) |
12,049 | -c \neq c \Rightarrow 0*(-1) + c \neq -c + 0 |
26,729 | (1 + s)\cdot (s + (-1)) + 1 = s^2 |
46,929 | 5 * 5 * 5 = 5^2*5 |
48,883 | \frac{\sin b}{\cos b}=\frac{3}{4} \Rightarrow \frac{9}{16}\cos^2 b+\cos^2b=1 \Rightarrow \cos b=\frac{4}{5} \Rightarrow \sin b=\frac{3}{5} |
-10,528 | \dfrac{9}{3\left(-1\right) + k}*4/4 = \frac{1}{4k + 12 \left(-1\right)}36 |
11,506 | \sqrt{2}\times 2/3 = \tfrac{\sqrt{2}\times 2}{3} |
1,712 | 2 \cdot (-1) + m - e + m - w = m \cdot 2 + 2 \cdot (-1) - e - w |
33,707 | \sin(x*2) = \cos(x) \sin(x)*2 |
10,206 | u^2 = x^2 \Rightarrow u = x |
20,806 | c + b = ( c, b)*( 1, 1) \leq (c * c + b^2)^{1/2} |
11,292 | (-1) + 3 + 1 + m + (-1) + m = 2*m + 2 |
15,438 | \frac{1}{n! \left(n + 2\right)} = \frac{1}{(n + 2)!}(n + 2 + \left(-1\right)) = \frac{1}{\left(n + 1\right)!} - \frac{1}{(n + 2)!} |
-5,863 | \dfrac{4}{(k + 7 \cdot (-1)) \cdot (k + 10 \cdot (-1))} \cdot k = \dfrac{4 \cdot k}{k^2 - k \cdot 17 + 70} |
18,353 | -\left(2 + z\right)\cdot ((-1) + z)^2 = 2\cdot (-1) + 3\cdot z - z^3 |
-10,802 | \dfrac{144}{12} = 12 |
6,135 | 8 + x^2 + x \cdot 6 = \left(x + 4\right) \cdot (x + 2) |
-15,100 | \tfrac{1}{\frac{1}{i^{16} \cdot \frac{1}{\xi^4}}} \cdot i^4 = \frac{i^4}{\frac{1}{i^{16}} \cdot \xi^4} |
14,084 | \sin{x} = \sin((2\cdot n + 1)\cdot \pi - x) = \sin(x + 2\cdot n\cdot \pi) |
33,118 | \left. \frac{\partial}{\partial i} (\Im{(Z \cdot Z)} \cdot x) \right|_{\substack{ i=i }} = \left. \frac{\partial}{\partial i} (\Im{(Z)} \cdot x) \right|_{\substack{ i=i }} |
11,882 | 8/11 = 1/2 + 1/4 - \frac{1}{44} |
31,090 | b \cdot 2 + h - b = h + b |
15,780 | \sigma*A = \sigma*A |
49,425 | 148894375444481 = 1 + 2^{15} \times 4543895735 |
13,132 | (x\cdot z + w\cdot y)^2 + \left(w\cdot x - z\cdot y\right) \cdot \left(w\cdot x - z\cdot y\right) = (z^2 + w^2)\cdot \left(y^2 + x \cdot x\right) |
1,516 | (x + 2)^{\frac{1}{2}} = (4 + x + 2\times (-1))^{\frac12} = 2\times (1 + (x + 2\times (-1))/4)^{\frac{1}{2}} |
24,987 | z + 0 \cdot (-1) = z + 0 \cdot \left(-1\right) + 0 |
-5,207 | 1.56 \cdot 10 = \tfrac{10}{1000} \cdot 1.56 = 1.56/100 |
14,674 | y^f*y^a = y^{f + a} |
10,623 | (1/2 - i)^2 + 2i = (1/2 + i)^2 |
14,305 | 1 - \tfrac{1}{1 - B}\cdot \left(1 - A\right) = \frac{1}{1 - B}\cdot (1 - B - 1 - A) = \dfrac{A - B}{1 - B} |
10,960 | (1 - \sqrt{x})\cdot (1 + \sqrt{x}) = -x + 1 |
22,695 | z = \dfrac1z*z^2 |
-2,257 | -3/18 + \frac{5}{18} = 2/18 |
18,787 | 0 \leq 3\left(-1\right) + x \cdot 3 \Rightarrow x \geq 1 |
-15,468 | \dfrac{(\frac{1}{x^3})^2}{\frac{1}{1/x \frac{1}{k^2}}} = \dfrac{1}{k^2 x x^6} |
32,079 | ... ... = ... \cdot ... |
10,714 | F^{24} = F^{16}\cdot F^8 |
4,519 | \sin\left(90\cdot (-1) + \alpha\right) = -\sin(90)\cdot \cos\left(\alpha\right) + \sin(\alpha)\cdot \cos(90) |
8,279 | \sin(b\times F) = \sin(b\times F) |
8,220 | \frac{26}{50} \cdot \dfrac{1}{51} \cdot 39 = \frac{169}{425} |
17,402 | 1601 \cdot 1601 - 79\cdot 1601 + 1601 = 1601\cdot \left(1601 + 79\cdot \left(-1\right) + 1\right) = 1601\cdot 1523 |
10,695 | \tan^2{w} = (-s + 1)/s \Rightarrow s = \cos^2{w} |
34,341 | 1 - \frac{1}{(y^{22})!} + \frac{1}{(y^{44})!} - \dotsm = \cos\left(1/y\right) |
28,076 | 2*|z| = d/dz (z*|z|) |
11,037 | (-1) \cdot h \cdot 0 + h \cdot 0 = h \cdot 0 + h \cdot 0 - h \cdot 0 |
45,635 | \sqrt{6 - \sqrt{20}} = \sqrt{1} - \sqrt{5} \lt 0 |
-29,369 | (5 \cdot z + 1) \cdot (5 \cdot z + (-1)) = (5 \cdot z)^2 - 1^2 = 25 \cdot z^2 + (-1) |
-3,245 | \left(5 + 3*(-1) + (-1)\right)*\sqrt{11} = \sqrt{11} |
38,843 | 7*14 \dotsm*7l = 7*7*2 \dotsm*7l = 7^l*1*2 \dotsm l = 7^l l! |
30,834 | \tan^{-1}(-\infty) = -\frac{\pi}{2} |
-18,942 | \dfrac13 = \frac{C_t}{16\cdot \pi}\cdot 16\cdot \pi = C_t |
13,281 | 3 + (6 + \frac{1}{6 + \frac{5^2}{6 + \dots}} \cdot 3^2)^{-1} = π |
15,721 | x^4 = (x \times x)^2 |
5,498 | 2/3 t = t - t/3 |
20,735 | (a - b) \times (b^2 + a^2 + a \times b) = a^3 - b^3 |
6,123 | 1 + \frac{1}{1 - \delta} \cdot \delta = \frac{1}{-\delta + 1} |
20,050 | \cos\left(3 \cdot \left(x + \pi/3\right)\right) = \cos(2 \cdot \pi + 3 \cdot x) = \cos(3 \cdot x) |
18,522 | \left(x^2\right)^2 = x \cdot x \cdot x^2 = x \cdot x \cdot x \cdot x = x^4 = x^{2 \cdot 2} |
-13,941 | \frac{35}{1 + 6} = \frac{35}{7} = \tfrac{35}{7} = 5 |
21,552 | 1 + 2 + 3 + \dots + r = \left(r + 1\right) \cdot r/2 |
-20,224 | -\dfrac{7}{2} \frac{1}{1 + y} (y + 1) = \frac{-7 y + 7 \left(-1\right)}{2 + y*2} |
-6,133 | \frac{12}{4*(k + 5*(-1))*(k + 9*(-1))} = \frac44*\frac{1}{(k + 9*(-1))*(k + 5*\left(-1\right))}*3 |
17,781 | \dfrac43 = -8/3 + 4 |
8,583 | \dfrac{1}{(-1)^k} = \dfrac{1}{(-1)^{k*2}}*(-1)^k |
33,352 | \binom{6}{2}*4! = \dfrac{6!}{2!*4!}*4! = \frac{6!}{2!} = 360 |
49,769 | 1 - \left(1 - 1/365\right)^{80000} = 1 - (\frac{1}{365} \cdot 364)^{80000} \approx 1 - 4.8/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
38,374 | 0 = 162\cdot (-1) + 48 + 24 + 72\cdot (-1) + 162 |
26,434 | {4!\over2!}=12 |
4,730 | \frac{1}{b \cdot d} \cdot (-b \cdot c + f \cdot d) = -\frac{c}{d} + f/b |
17,900 | \left(a^T \cdot U \cdot b\right)^T = b^T \cdot U^T \cdot a = b^T \cdot U \cdot a |
-5,307 | 60.0 \cdot 10^3 = 10^{2 + 1} \cdot 60 |
18,672 | x'*y + y*x' = x'*y |
-1,140 | \frac{1}{3 \cdot 1/4} \cdot (\dfrac19 \cdot (-1)) = -1/9 \cdot \dfrac43 |
6,909 | 2 \cdot h \cdot y \cdot z + 1 = h \cdot y \cdot z + h \cdot y + y \cdot z + z \cdot h + h + y + z + 1 = (h + 1) \cdot (y + 1) \cdot (z + 1) |
14,483 | \cot{H} = \dfrac{\cos{H}}{\sin{H}} |
24,583 | 1 - \frac14 = (\frac12 + 1)\cdot (1 - \frac{1}{2}) |
28,656 | 1 + z^2 + z = \frac{3}{4} + \left(1/2 + z\right) \cdot \left(1/2 + z\right) |
9,823 | 1 + 4*3^{\frac{1}{8}*9}*\lambda - 4*3^{1/8}*\lambda = 0 \implies 8*3^{\frac18}*\lambda = -1 |
-6,440 | \frac{(8 + q)\cdot 4 + 6\cdot (4 + q) + 16\cdot \left(-1\right)}{(4 + q)\cdot (8 + q)\cdot 8} = \frac{4}{8\cdot (8 + q)\cdot \left(q + 4\right)}\cdot \left(8 + q\right) + \frac{6\cdot (q + 4)}{8\cdot (q + 4)\cdot (q + 8)} - \tfrac{16}{8\cdot (4 + q)\cdot (8 + q)} |
8,005 | (-c + a) \cdot \left(b - c\right) = b \cdot a + c \cdot c - \left(a + b\right) \cdot c |
6,043 | -(1 + m^2 + 3\cdot m) + d^2 + d\cdot 3 + 1 = \left(d + m + 3\right)\cdot \left(d - m\right) |
-1,612 | -\pi\cdot \frac{11}{12} + \pi\cdot 4/3 = \pi\cdot 5/12 |
-11,628 | i - 4 + 3 \cdot \left(-1\right) = -7 + i |
31,549 | y^3 + y^2 - 10 y + 8 = (4 + y) (\left(-1\right) + y) (2 (-1) + y) |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.