id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
36,032 | \cos{3x} = \cos^3{x} \cdot 4 - 3\cos{x} |
455 | 205 + 195 (-1) = \frac{1}{\sqrt{20}}24 = 1.862 |
-4,720 | \frac{24 - 8y}{y^2 - y*6 + 8} = -\frac{1}{2\left(-1\right) + y}4 - \frac{4}{y + 4(-1)} |
1,844 | 6 = (1 + \sqrt{7})\cdot (\sqrt{7} + \left(-1\right)) |
12,903 | a^y\times a^z = a^{y + z} |
-2,130 | \pi/3 - \pi \frac{3}{4} = -\pi \frac{5}{12} |
-29,368 | (s + 2) \times (s + 3) = s \times s + 3 \times s + 2 \times s + 6 = s \times s + 5 \times s + 6 |
1,423 | 6!*{5 \choose 1}*5!*2 = 864000 |
27,126 | 10^{1 + m} = 10^m\cdot 10 |
-28,780 | \tan^2(x) = (-1) + \sec^2\left(x\right) |
7,188 | -\frac{1}{49}*24 = -24/49 |
1,070 | z^2 - (f_1 + f_2)\cdot z + f_1\cdot f_2 = (z - f_1)\cdot (-f_2 + z) |
-17,428 | 72 - 58 = 14 |
4,618 | S_{m, k} + S_{k,x} = S_{m,x} \Rightarrow |S_{m, k}| - |S_{k, x}| \leq |S_{m, x}| |
24,033 | 1/2 + 2/7 + \frac{2}{5} = 83/70 |
15,060 | \sqrt{3}\times 0 + 11 = 11 |
207 | AA^Q = A^Q A |
36,240 | \dfrac{28!}{22! \cdot 6!} = \binom{28}{6} |
24,836 | g \cdot g - A \cdot A = (A + g)\cdot (g - A) |
28,097 | -b + a = (\sqrt{a} + \sqrt{b}) \cdot (\sqrt{a} - \sqrt{b}) |
13,233 | \int (1+\cos(x))^3 = \frac{\frac{\sin(3x)}{3}+6\frac{\sin(2x)}{2}+15 \sin(x) + 10x}{4} + c = \frac{\sin(3x)}{12} + \frac{3\sin(2x)}{4} + \frac{15 \sin(x)}{4} + \frac{5x}{2} + c |
55,227 | {13 \choose 1} = 13 |
36,358 | 99 = 81 \cdot (-1) + 180 |
26,127 | (X + E) Y = YE + YX |
16,625 | x^{l_2} \cdot x^{l_1} = x^{l_1 + l_2} |
13,737 | 9 \cdot x^2 + 36 \cdot (-1) = 3 \cdot x^2 - 6 \cdot 6 = (3 \cdot x + 6) \cdot \left(3 \cdot x + 6 \cdot (-1)\right) = 3 \cdot (x + 2) \cdot (3 \cdot x + 6 \cdot (-1)) = 9 \cdot (x + 2) \cdot (x + 2 \cdot (-1)) |
17,069 | 2 \cdot s^2 + s^2 = s^2 \cdot 3 |
-22,235 | (k + 9) \cdot (k + 6) = 54 + k \cdot k + 15 \cdot k |
29,374 | \left(1 + k\right)^2 = k^2 + 2 \cdot k + 1 |
14,171 | n + n + 1 + \ldots + n + 10 = 11 \cdot n + 55 = 11 \cdot (n + 5) |
10,983 | \dfrac{(\dfrac{k}{2})^2}{\frac{k}{2} + k} = \frac{1}{6}\cdot k |
11,432 | 3(m + m^2) = m^2 \cdot 3 + 3m |
-24,456 | (3*2)^2 = 6 * 6 = 6^2 = 36 |
21,264 | |\frac{1}{z^2 + 1} - \frac{1}{1 + u^2}| = |\frac{-z \cdot z + u^2}{(z^2 + 1) \cdot (u^2 + 1)}| |
2,290 | x + (2 - x)/2 = \frac{2}{2} \cdot x + (2 - x)/2 = \frac{1}{2} \cdot (x + 2) |
-20,967 | \dfrac{1}{6}6 \dfrac{1}{(-2) q}\left(-q\cdot 7 + 4\right) = \frac{1}{(-1)\cdot 12 q}(24 - 42 q) |
31,685 | 3^{119}/4 = \dfrac{1}{4}\cdot 599003433304810403471059943169868346577158542512617035467 |
14,257 | \cot(3\cdot \pi/2 - x) = \cot(\pi - x - \pi/2) = -\cot(x - \pi/2) = \cot(\pi/2 - x) = \tan{x} |
8,830 | \cos(\beta) \sin(\alpha) + \sin(\beta) \cos(\alpha) = \sin(\alpha + \beta) |
5,757 | \sin^4\left(x\right) + \cos^4\left(x\right) = (\sin^2(x) + \cos^2(x))^2 - 2\cdot \sin^2(x)\cdot \cos^2(x) = 1 - 2\cdot \sin^2(x)\cdot \cos^2(x) |
13,021 | \frac{42}{q \cdot q + q\cdot 7} = -\dfrac{6}{q + 7} + 6/q |
-30,259 | (z + 3)*(4*(-1) + z) = z^2 - z + 12*(-1) |
30,403 | \dfrac{1}{x + 3} (x^2 + 5 x + 7) = x + \frac{2 x + 7}{x + 3} = x + 2 + \frac{1}{x + 3} |
6,473 | \dfrac{2 \times x + 1}{2 \times n + 2} = (\tfrac{x}{n + 1} + \frac{x + 1}{n + 1})/2 |
5,709 | 1 - \frac{95}{100} = \dfrac{5}{100} |
12,859 | a^{z + x} = a^z \times a^x |
8,194 | \left(0 = (-1) + q^2 - q\cdot 2 \Rightarrow -2\cdot q = -q^2 + 1\right) \Rightarrow -1 = \frac{2\cdot q}{1 - q^2} |
32,114 | (\left(-1\right) + f) \cdot a - f = -f + a \cdot f - a |
12,444 | \dfrac{52!}{25! (25 (-1) + 52)!} = 477551179875952 |
12,242 | \cot{C} = \tan(\tfrac{1}{2}\pi - C) |
18,902 | 9 \cdot 9 + 65 \cdot \left(-1\right) = 16 |
-6,394 | \frac{3}{18 \cdot (-1) + r \cdot 3} = \frac{3}{3 \cdot (r + 6 \cdot (-1))} |
-7,541 | \frac{-37 - 5i}{i*5 + 3} = \frac{-37 - 5i}{3 + i*5} \dfrac{3 - 5i}{3 - i*5} |
10,492 | \omega = \frac{5^{1/3}*\omega}{5^{\frac{1}{3}}} |
29,331 | \frac13\cdot \left(6 + 1 + 2\right) = 3 |
24,577 | 3 \cdot y^2 + 3 \cdot y + 6 \cdot (-1) = 3 \cdot (y^2 + y + 2 \cdot \left(-1\right)) = 3 \cdot \left(y + (-1)\right) \cdot (y + 2) |
-4,683 | -\frac{4}{z + 2\cdot (-1)} + \dfrac{1}{3 + z}\cdot 3 = \frac{-z + 18\cdot (-1)}{z \cdot z + z + 6\cdot (-1)} |
9,792 | x*m = 1 + \frac{7}{10}*(x*m - x) + 3/10*(x*m + x) = x*m + 1 - 2/5*x |
-5,462 | \tfrac{1}{3\cdot \left(p + 10\right)}\cdot 2 = \frac{2}{p\cdot 3 + 30} |
34,947 | z \approx y \Rightarrow z \approx y |
29,890 | \dfrac{\left(-1\right) + z}{(\left(-1\right) + z)^2} = \frac{1}{(-1) + z} |
15,878 | (n^2 + n/2)^2 = n^4 + n^2 \cdot n + \frac{n^2}{4} < n^4 + n^3 + n^2 + n + 1 |
9,588 | F = F \cap x \Rightarrow \{F, x\} |
6,842 | {j + 2*x \choose j} = {j + x*2 \choose x*2} |
-29,716 | \frac{\mathrm{d}}{\mathrm{d}x} x^k = k*x^{k + \left(-1\right)} |
-20,868 | \frac{14}{7 - 56\cdot b} = 7/7\cdot \tfrac{1}{1 - 8\cdot b}\cdot 2 |
34,302 | 17^{\frac{1}{2}} = \dfrac{1}{17^{1 / 2}} \cdot 17 |
38,014 | 7 = 10 - 3 |
4,552 | -\dfrac{1}{x \cdot x} \cdot 7 + 1 = \frac{1}{x^3} \cdot (-7 \cdot x + x^2 \cdot x) |
21,063 | 16/3 = 1/6\cdot 4 + \frac12\cdot 6 + \frac{1}{3}\cdot 5 |
7,336 | 30/81 = \dfrac{6}{9}*5/9 |
-7,223 | 10^{-1} = \frac{4}{16} \times 6/15 |
-20,677 | -8/3 \cdot \frac{2 \cdot (-1) - 8 \cdot m}{2 \cdot (-1) - m \cdot 8} = \frac{16 + m \cdot 64}{6 \cdot (-1) - 24 \cdot m} |
9,647 | \cos(\frac{105}{3}) = \cos\left(35\right) |
15,720 | \max{e,x,m} = \max{e,\max{x, m}} = \max{\max{e,x},m} |
-3,218 | 112^{\frac{1}{2}} + 175^{1 / 2} - 7^{\frac{1}{2}} = (16\cdot 7)^{1 / 2} + (25\cdot 7)^{\frac{1}{2}} - 7^{\frac{1}{2}} |
-458 | e^{17\cdot π\cdot i/3} = \left(e^{\frac{i}{3}\cdot π}\right)^{17} |
16,656 | \frac{\frac{3}{4}*\frac{1}{4} 3}{2} = 9/32 |
10,059 | 32\cdot 2/(2\cdot 72) = \tfrac{1}{72}\cdot 32 |
-4,761 | \frac{17 \cdot (-1) - x}{3 \cdot (-1) + x \cdot x - x \cdot 2} = -\frac{5}{x + 3 \cdot \left(-1\right)} + \frac{1}{1 + x} \cdot 4 |
-3,415 | 4\sqrt{6} = (5 + 3 + 4(-1)) \sqrt{6} |
14,556 | \int a \cdot (f_1 T + \alpha T f_2)\,dy = \int a T \cdot \left(f_1 + \alpha f_2\right)\,dy |
-19,738 | \dfrac{1}{8} \cdot 35 = \frac{35}{8} |
17,752 | (p + 2\cdot \left(-1\right))! = \frac{(p + (-1))!}{\left(-1\right) + p} |
20,409 | (-1) + t^3 = (t + (-1)) \cdot \left(t^2 + t + 1\right) |
30,830 | 2^b \cdot 2^d = 2^{d + b} |
-4,157 | 63/35*\frac{1}{y^5}*y^3 = \frac{63*y^3}{y^5*35} |
21,632 | x = 2\dfrac12x |
-22,941 | \frac{63}{54} = \frac{9 \cdot 7}{9 \cdot 6} |
5,220 | ( (a + 5) \times 2, 3 \times (a + 5), 17) = ( a \times 2 + 10, 15 + 3 \times a, 17) |
6,133 | m\cdot 3 - x\cdot 3 = \left(m - x\right)\cdot 3 |
-24,888 | \frac{1}{18} = \dfrac{1}{6\pi}s \cdot 6\pi = s |
-6,746 | \frac{7}{100} + \frac{1}{100} \cdot 80 = 8/10 + \frac{1}{100} \cdot 7 |
26,531 | \frac{1}{h^{-c}} = h^c |
-3,819 | a^5/a = \frac{a*a*a*a*a}{a} = a^4 |
9,417 | \frac12 \cdot (1 + 3) = 4/2 = 2 |
-18,391 | \frac{1}{x \cdot 7 + x^2} \cdot (42 + x^2 + x \cdot 13) = \frac{1}{(x + 7) \cdot x} \cdot (x + 6) \cdot \left(7 + x\right) |
-22,248 | 20 + x \cdot x - x\cdot 12 = (2(-1) + x) (x + 10 \left(-1\right)) |
8,074 | \frac{1}{2 \cdot u^3} = \dfrac{1}{2 \cdot u^3} |
17,384 | 1 + y^2 - y = (-1/2 + y)^2 + 3/4 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.