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.