id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
78 | -2/3*\frac79 + 1 = \frac{1}{27}13 |
-2,542 | 2 \cdot 2^{1/2} = 2^{1/2} \cdot (1 + 4 \cdot (-1) + 5) |
31,956 | z^6 + 1 = \left(1 + z^2\right) \cdot \left(1 + z \cdot 3^{1/2} + z^2\right) \cdot (1 - 3^{\frac12} \cdot z + z^2) |
9,313 | 1 + x\cdot (x + 2) = (x + 1)^2 |
40,456 | a * a = (a + \left(-1\right)) * (a + \left(-1\right)) + a + (-1) + a |
20,249 | 10*\frac{654321}{123456} = 6*9 + \left(-1\right) + 6*7/123456 \approx 53 |
31,339 | 442^{260} = 442^{257} \times 8 \times 221^3 |
17,748 | \frac{1}{35} \cdot 12 = \frac{3}{5} \cdot \frac47 |
2,290 | t + (2 - t)/2 = \frac{t}{2}\cdot 2 + (2 - t)/2 = (t + 2)/2 |
-24,448 | \frac{1}{8 + 7} \cdot 135 = 135/15 = \frac{135}{15} = 9 |
5,454 | 0 = x^{s + (-1)} + \left(-1\right) = (x + (-1)) \cdot (1 + x + ... \cdot x^{s + 2 \cdot (-1)}) |
3,865 | -1/2 + \sqrt{5}/2 = \frac{1}{2} \cdot \left(-1 + \sqrt{5}\right) |
18,475 | f\times D^n = f\times D^{0 + n} |
757 | (\sqrt{x})^2 = x = 0 + x = (f + g \cdot x)^2 = f \cdot f + 2 \cdot f \cdot g \cdot x + g^2 \cdot x^2 = f^2 - g^2 + 2 \cdot f \cdot g \cdot x |
-4,883 | 10^6*0.49 = 0.49*10^{11 + 5*(-1)} |
10,513 | -3 = 2(-1) + 1 + 2(-1) |
23,555 | (n + 1)^4 - (n + 1)^2 = (n + 1)^2\cdot ((n + 1)^2 + (-1)) = (n + 1)^2\cdot (n + 1 + (-1))\cdot (n + 1 + 1) |
7,092 | (-x + c)\cdot (c + x) = -x^2 + c \cdot c |
-9,325 | -2\cdot 2\cdot 3\cdot 3\cdot m - 2\cdot 2\cdot 2\cdot 2\cdot 2 = -m\cdot 36 + 32\cdot (-1) |
18,085 | (a + b)^2 \left(a + b\right) = b^3 + a^3 + 3 a^2 b + 3 b^2 a |
49,300 | (A\cap B)\cap (A\cap C) = (A\cap A)\cap (B\cap C) = A\cap (B\cap C) = A\cap B\cap C |
-16,607 | \sqrt{16\cdot 11}\cdot 6 = 6\cdot \sqrt{176} |
-12,447 | 3 = \frac{28.5}{9.5} |
7,573 | e \cdot e \cdot e > (5/2)^3 = 125/8 > 80/8 = 10 \gt 3^2 |
30,428 | (2 \cdot x + 1) \cdot x = 2 \cdot (x + (-1)) \cdot x + 3 \cdot x = 4 \cdot {x \choose 2} + 3 \cdot {x \choose 1} |
23,263 | \frac{1}{12} = \dfrac{1}{4 \cdot 3} |
26,714 | g = |g| \cdot g/|g| |
18,205 | 2205 = 5\left(3*7\right) * \left(3*7\right) |
-18,956 | 11/30 = \frac{1}{4 \times \pi} \times B_s \times 4 \times \pi = B_s |
47,112 | 36 = (-9) (-4) |
13,632 | -i^2 + (2 + i) \cdot (2 + i) = 4 + i\cdot 4 |
24,086 | \sin^2{\alpha} = \dfrac14*\cos^2{\alpha} = \left(1 - \sin^2{\alpha}\right)/4 |
-9,649 | -1^{-1} = -\frac55 |
-6,036 | \dfrac{2}{2(x - 8)} \times \dfrac{5(x + 7)}{5(x + 7)} = \dfrac{10(x + 7)}{10(x + 7)(x - 8)} |
3,814 | \left\{\left( 1, 1\right), ( 3, 2), ( 1, 2), \left( 3, 1\right)\right\} = \left\{( 3, 1), ( 3, 2), ( 1, 2), ( 1, 1)\right\} |
-1,666 | 13/6\cdot \pi = \pi\cdot 11/12 + 5/4\cdot \pi |
-22,242 | (9\cdot \left(-1\right) + r)\cdot (r + 3) = 27\cdot (-1) + r^2 - r\cdot 6 |
7,429 | (a + W\cdot d)^2 = a \cdot a + a\cdot d\cdot W\cdot 2 + W^2\cdot d^2 |
46,122 | \left(\operatorname{P}(C_2) - \operatorname{P}(C_1)\right)^2 = \operatorname{P}(C_2)^2 - 2\cdot \operatorname{P}(C_2)\cdot \operatorname{P}(C_1) + \operatorname{P}\left(C_1\right) \cdot \operatorname{P}\left(C_1\right) = 0.8 \implies (\frac{8}{10})^{\dfrac{1}{2}} = \operatorname{P}(C_2) - \operatorname{P}(C_1) |
17,371 | d^2 = d^1*d^1 |
-22,842 | \dfrac{16}{24} = \frac{2 \cdot 8}{8 \cdot 3} |
-10,565 | \frac55*(-\frac{6}{y*4 + 8}) = -\frac{30}{y*20 + 40} |
5,316 | n^2 = 9 \cdot k \cdot k + 12 \cdot k + 4 = 3 \cdot (3 \cdot k \cdot k + 4 \cdot k + 1) + 1 \implies \left(3 \cdot k^2 + 4 \cdot k + 1\right) \cdot 3 = n^2 + (-1) |
15,613 | C^k Gx = C^k x G |
25,623 | \cos{x} \times \sin{x} \times 2 = \sin{x \times 2} |
7,335 | \sqrt{4 \cdot \sqrt{3} + 7} = 2 + \sqrt{3} |
42,837 | \left\{1, 3\right\} \neq \left\{3, 2, 1\right\} |
-20,843 | (t\cdot (-16))/(t\cdot 28) = \frac{t\cdot 4}{4\cdot t}\cdot \left(-4/7\right) |
4,650 | \left(5^2 + 3*5\right)/2 + 4(-1) = 16 |
32,172 | m\sin{1/m} = \frac{\sin{\dfrac{1}{m}}}{\dfrac1m} |
38,373 | \frac{1 + r\cdot 2}{1 + r} = 2 - \dfrac{1}{r + 1} |
-5,230 | 6.51 \cdot 10 = 6.51 \cdot 10 \cdot 10 \cdot 10^2 = 6.51 \cdot 10^4 |
-7,678 | (12 + 44 i - 24 i + 88)/20 = (100 + 20 i)/20 = 5 + i |
-20,392 | -4/7\cdot \frac{1}{4\cdot \phi + 9\cdot (-1)}\cdot (9\cdot (-1) + \phi\cdot 4) = \frac{-\phi\cdot 16 + 36}{28\cdot \phi + 63\cdot (-1)} |
35,114 | 8100 + 49*(-1) = \left(90 + 7*(-1)\right)*(90 + 7) = 83*97 |
16,159 | (3 + 6 + 9)/2 + \left(3 + 9\right)/2 = 9 + 6 = 15 |
4,843 | E[Z]\times E[A] = E[A\times Z] |
18,812 | \dfrac{1}{36} \cdot 6 \cdot x_0 = \frac{x_0}{6} |
24,832 | 5/2 = \frac{5}{6} \cdot 3 |
-13,356 | \frac{7}{6 + 5(-1)} = 7/1 = \dfrac71 = 7 |
20,771 | 2y + (-1) = 0 \Rightarrow 1/2 = y |
1,737 | (2^{2^{25}} - 2^{2^{24}} + 1)\times (2^{2^{24}} + 1) = 1 + 8^{8^8} |
-22,930 | \frac{1}{45}40 = 8\cdot 5/(5\cdot 9) |
29,461 | F^6 = (F^2 + 2F)^2 = F^4 + 4F^3 + 4F^2 = F^3 + 2F^2 + 4F * F + 8F + 4F^2 = 11 F^2 + 10 F |
54,012 | 19\cdot 37 = 703 |
17,205 | 2^{1/(\frac{1}{2})} = 2^{\tfrac{1}{\frac{1}{2}}} = 2^2 = 4 |
-3,304 | 63^{1 / 2} + 112^{1 / 2} - 175^{1 / 2} = -\left(25 \cdot 7\right)^{\frac{1}{2}} + (9 \cdot 7)^{\frac{1}{2}} + (16 \cdot 7)^{1 / 2} |
-11,508 | -8 - 8\cdot i = -i\cdot 8 - 8 + 0\cdot (-1) |
19,280 | y/v + \left(-1\right) = \frac{y}{v} + \dfrac1v\cdot ((-1)\cdot v) |
-14,824 | 90 + 92 + 81 + 81 = 344 |
18,745 | -l^2 + c_x^2 = l\cdot (c_x - l)\cdot 2 + \left(c_x - l\right)^2 |
14,793 | (-1) + z^3 = (z + \left(-1\right)) \cdot (1 + z^2 + z) |
-25,237 | \frac{d}{dI} \sqrt{I^5} = \frac{1}{2}5 I |
22,285 | m\cdot 2 + 3\cdot (-1) = 2\cdot (-1) + m + \left(-1\right) + m |
3,966 | 0 = (a - b) \cdot \left(a \cdot a + a \cdot b + b^2\right) = a^3 - b^3 |
12,191 | 2^{2 \cdot y + 1} = (\frac{1}{2^5})^y = \frac{1}{2^{5 \cdot y}} |
29,467 | 7*\dfrac{2}{1 - \dfrac{2}{100}}*1/100 = 7*\dfrac{2}{100 + 2*(-1)} = 7*\tfrac{1}{98}*2 |
19,706 | z_1^2 + 4 \cdot z_2^2 + 5 \cdot z_1 \cdot z_2 = (z_2 \cdot 4 + z_1) \cdot \left(z_2 + z_1\right) |
14,246 | (-\frac{1}{8} + \frac{1}{24} + \frac{1}{2} - \tfrac{1}{3}) \times 2 = 1/6 |
-19,511 | \frac97\cdot \dfrac{1}{3}\cdot 8 = \dfrac{9\cdot \tfrac{1}{7}}{1/8\cdot 3} |
36,639 | m + 884 = 891 \Rightarrow m = 7 |
13,618 | 0 = y^8 + 6\cdot y^4 + 1\Longrightarrow y^4 = -3 \pm \sqrt{2}\cdot 2 |
-4,203 | \frac{16}{14*y^4}*y^5 = \frac{1}{y^4}*y^5*16/14 |
-16,940 | 5 = 5 \cdot 2a + 5\left(-4\right) = 10 a - 20 = 10 a + 20 (-1) |
-11,164 | (x - 6)^2 + b = (x - 6)(x - 6) + b = x^2 - 12x + 36 + b |
27,129 | (x - d) \cdot (x^{n + (-1)} + d \cdot x^{n + 2 \cdot (-1)} + \dotsm + d^{n + 2 \cdot \left(-1\right)} \cdot x + d^{\left(-1\right) + n}) = -d^n + x^n |
18,406 | z^2 + 1 = 1 + \frac{\text{d}z}{\text{d}t} \Rightarrow \frac{\text{d}z}{\text{d}t} = z^2 |
8,870 | 1 \leq c \cdot c + d^2 \leq 2^2 \implies 1 \leq c^2 + d \cdot d \leq 4 |
-22,270 | (5 + x) (x + 10) = 50 + x x + 15 x |
2,070 | (95 + 12 \cdot (-1)) \cdot (12 + 95) = 8881 |
31,051 | 3000=2^3\cdot5^3\cdot3 |
26,121 | (\sec{2\cdot z} + (-1))/\tan{2\cdot z} = \dfrac{1}{\sin{2\cdot z}}\cdot (1 - \cos{2\cdot z}) = \tan{z} |
-10,366 | -\dfrac{10}{4(-1) + 2c} \cdot 5/5 = -\frac{50}{20 \left(-1\right) + c \cdot 10} |
-16,546 | \left(4 \cdot 2\right)^{1/2} \cdot 9 = 9 \cdot 8^{1/2} |
6,690 | \cos{y} = t\Longrightarrow \cos^{-1}{t} = y |
25,270 | C_1\cdot C_2^2 = C_1\cdot C_2^2 |
2,358 | ( x', y', t') \cdot ( x, y, t) = ( x, y, t) \cdot ( x', y', t') |
25,605 | \dfrac{12!}{8! \cdot 4!} = {12 \choose 4} |
-20,217 | 7/7*(4 - P*6)/\left(-3\right) = (-P*42 + 28)/(-21) |
7,971 | 1 + z + z^2 + z^3 = (z \cdot z + 1) (1 + z) |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.