id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
-3,821 | 2 \cdot f^4 = 2 \cdot f^4 |
41,208 | 11 \times 73 \times 101 \times 137 = 11111111 |
-11,258 | (y + a)^2 = (y + a) \left(y + a\right) = y^2 + 2 a y + a^2 |
29,611 | 0 = (-3*2 + 2) + 3*\left(2*(-1) + 3\right) - 1*(2*(-1) + 1) |
-15,724 | \frac{t^9\cdot \dfrac{1}{l^{15}}}{1/t\cdot l^3} = \dfrac{1}{\dfrac{1}{t\cdot \frac{1}{l^3}}}\cdot (\frac{1}{l^5}\cdot t \cdot t \cdot t)^3 |
1,682 | \dfrac{y + 2*(-1)}{1 - y + 2 + 2*(-1)} = \frac{y + 2*(-1)}{-1 - y + 2*(-1)} = -\frac{y + 2*(-1)}{1 + y + 2*(-1)} |
5,065 | -(i + 1) + (1 + i)^3 = i^3 + 3\cdot i^2 + 2\cdot i |
42,485 | 108 = 9 \cdot 12 |
-3,613 | \frac{n}{4}\cdot 5 = n\cdot \frac14\cdot 5 |
-15,264 | \dfrac{i\cdot \gamma^2}{\frac{1}{\tfrac{1}{\gamma^8}\cdot i^8}} = \frac{\gamma^2}{\gamma^8\cdot \frac{1}{i^8}}\cdot i |
-26,429 | 5 = 3/2 \cdot 10/3 |
20,633 | h^2 \times x + 3 \times a^2 \times x = x \times \left(h \times 2 + a \times 3\right) \times a + h \times x \times (-2 \times a + h) |
-16,354 | 6 \cdot 25^{1 / 2} \cdot 3^{\frac{1}{2}} = 6 \cdot 5 \cdot 3^{\frac{1}{2}} = 30 \cdot 3^{1 / 2} |
15,357 | p^2 = 4*a*u \Rightarrow 4*a*u = p * p |
-1,380 | -7/9 \times (-9/7) = \frac{1/7 \times (-9)}{\left(-1\right) \times 9 \times \frac17} |
-1,086 | 7/4 \cdot (-4/3) = \frac{\dfrac{1}{4}}{(-3) \cdot 1/4} \cdot 7 |
26,235 | 6^{1/2}/2 = (3/2)^{1/2} |
18,189 | |3\times \pi\times \frac23\times \pi + 5| = 2\times \pi \times \pi + 5 \neq 3 |
8,923 | 0 = \left(-1\right) + v^6 - v^3\cdot 4 rightarrow v^3 = 2 \pm \sqrt{5} |
18,546 | \cos\left(h\right) = \cos\left(-h\right) |
20,056 | det\left(5E^3\right) = 5^4 det\left(E \cdot E \cdot E\right) = 5^4 det\left(E\right)^3 |
25,621 | (2^2 \cdot 2 + 4(-1)) \cdot (2^2 \cdot 2 + 4(-1)) \cdot (2^2 \cdot 2 + 4(-1)) = 4^3 |
-28,658 | 6x * x + 36 x + 78 = 6(x * x + 6x + 13) = 6(x^2 + 6x + 9 + 4) = 6\left((x + 3)^2 + 4\right) = 6\left((x + 3) * (x + 3) + 2^2\right) |
50,583 | 50 \times (0.79 \times 2 + 0.06 \times 3 + 0.05 \times 2 + 0.11 \times 16) = 181 |
535 | H\cdot x_0 = b \Rightarrow \frac{b}{H} = x_0 |
19,785 | {m \choose x} = \frac{m!}{x! \cdot (m - x)!} = \dfrac{1}{\left(m - x\right)!} \cdot 156 |
5,167 | 2^c \cdot 2^x = 2^{c + x} |
15,273 | \tfrac{b}{x}\cdot x = b\cdot \frac{x}{x} |
-20,216 | \frac{1}{-x*45 + 72*(-1)}*(35*x + 56) = -\dfrac19*7*\frac{1}{-x*5 + 8*\left(-1\right)}*(-x*5 + 8*\left(-1\right)) |
42,219 | 0 = -g + 1 \implies g = 1 |
17,798 | \frac{30}{1.15} + \tfrac{30}{1.3} + 40/1.5 = 26.1 + 23.1 + 26.7 = 75.9 |
31,306 | \dfrac{1}{\frac{1}{81}} = \frac{1}{\frac{1}{3^4}} = 3^4 |
-23,422 | 4*1/7/2 = \frac{2}{7} |
25,141 | (F^2)^T = (F\times F)^T = F^T\times F^T = (F^T)^2 |
19,736 | \left\{1, 2, 3, 4\right\} = \left\{3, 2, 1, 4\right\} |
1,058 | 341444579376 = 342527319476 + 1082740100 \left(-1\right) |
17,098 | x\cdot 90 \lt 92\cdot c rightarrow 2\cdot c > 90\cdot (x - c) \geq 90\cdot 2 = 180 |
-2,728 | 4 \cdot \sqrt{11} = \left(5 + 1 + 2 \cdot (-1)\right) \cdot \sqrt{11} |
37,122 | \lceil\sqrt[4]{4000}\rceil=8 |
18,150 | 1=3(xyz)^{\frac{2}{3}} -2\leq xy+yz+zx-2 |
-27,721 | -\csc(\tau) \cdot \cot(\tau) = \frac{d}{d\tau} \csc(\tau) |
15,126 | (g/f f)^k = fg^k/f |
1,901 | \sqrt{2}\cdot \dfrac{2}{2 + \sqrt{2}}\cdot \sqrt{2} = \frac{1}{2 + \sqrt{2}}\cdot 4 |
3,478 | z^2 + z + 6(-1) = (z + 3) (z + 2(-1)) |
12,469 | -\sin{x} = \cos(x + \dfrac{\pi}{2}) |
31,080 | |9*(-1) + 8| = 1 |
-6,095 | \tfrac{3}{5*\left(8 + t\right)} = \frac{3}{40 + 5*t} |
-2,177 | \frac{7}{12} - \dfrac{4}{12} = \frac{3}{12} |
8,542 | 1/(2*2) + 1/2 = 3/4 |
5,001 | 2/9 = \frac{4}{2}\cdot 1/9 |
19,365 | 0 = |f| \Rightarrow 0 = f |
10,523 | 6666*(120/2)=6666*60 |
-4,354 | \dfrac{1}{6z^3} = \frac{1}{6z^3} |
-9,429 | -q \cdot q \cdot 2 \cdot 5 \cdot q = -q^3 \cdot 10 |
19,213 | d/dy \tan^{-1}(\tanh(y)) = \dfrac{d/dy \tanh(y)}{1 + \tanh^2(y)} |
3,399 | 63\%\cdot z + z\cdot 24\% = z\cdot 87\% |
9,727 | x^3 + d^3 + h^3 - d\cdot x\cdot h\cdot 3 = (h + x + d)\cdot (x^2 + d^2 + h^2 - x\cdot d - h\cdot x - d\cdot h) |
10,254 | (z + \chi)^2 = \chi^2 + 2\cdot z\cdot \chi + z \cdot z |
31,225 | 3^2\cdot 2^2 \cdot 2\cdot 5\cdot 7 = 2520 |
16,575 | 299.5 \times 36 = 10782 |
33,589 | b\cdot (x + 1) + (x + 1)\cdot e = (1 + x)\cdot (e + b) |
26,412 | 1 = y^p + x^p \Rightarrow y = (1 - x^p)^{\tfrac1p} |
21,841 | i^3 = i \cdot i \cdot i = w \cdot w^2 \cdot i \cdot i \cdot i = (i \cdot w)^3 |
20,941 | q^2 - 2 \cdot q + 2 = 1 + ((-1) + q)^2 |
19,469 | \left(z + 3\right)*(z + 2*\left(-1\right)) = 6*(-1) + z * z + z |
-22,715 | \frac{30}{18} = \frac{6 \cdot 5}{6 \cdot 3} |
15,284 | -30 = 15 (-1) - 15 |
-8,826 | \pi\times 4 + 4\times \pi + 20\times \pi = 28\times \pi |
17,171 | 27 (-1) + 259^3 \cdot 4 \cdot 4225513 = 17136391^2 |
28,844 | \dfrac{6}{d^2} \cdot b \cdot 2 \cdot \frac{k^4}{b^4} \cdot R^4 = \frac{12 \cdot k^4 \cdot R^4}{b^3 \cdot d^2} \cdot 1 |
20,349 | \dfrac{1}{z \cdot e^{-t}} = e^t + K\Longrightarrow \frac{1}{e^t} \cdot (e^t + K) = 1/z |
-2,028 | 2/3 \cdot π - 5/12 \cdot π = π/4 |
25,029 | \sum_{i=0}^n f^i = \sum_{i=0}^{(-1) + n + 1} f^i |
-19,357 | \dfrac17\cdot 2/(1/5\cdot 2) = 5/2\cdot 2/7 |
17,972 | \tfrac1w(wz + x) = x/w + z + w*0 |
42,882 | 1 - \frac1b = \dfrac{1}{\frac{1}{(-1) + b} + 1} |
20,104 | 7 \cdot 2^4 - 7 \cdot 2 \cdot 2^2 = 7 \cdot 2^3 \cdot (2 + (-1)) = 56 |
-20,442 | (-7 \cdot x + 6 \cdot (-1))/\left(-2\right) \cdot 4/4 = (24 \cdot (-1) - 28 \cdot x)/(-8) |
28,836 | 8^2 - 4^2 = -1^2 + 7^2 |
-22,957 | \dfrac{36}{54} = \dfrac{2 \cdot 18}{ 3\cdot 18} |
11,144 | \|x\|^2 = x \times x^\xi = x \times x^\xi |
29,228 | P(k) := \frac{1}{x^k} := (1/x)^k |
3,547 | x * x * x - z^3 = (x^2 + x*z + z^2)*(x - z) |
12,911 | (1 + y) \cdot \left(y + (-1)\right) \cdot (1 + y^2) = y^4 + (-1) |
6,228 | \frac{a \cdot a}{a + a - b} = \frac{a \cdot a}{2\cdot a - b} |
-29,343 | \left(a + b\right)*(a - b) = -b^2 + a^2 |
37,136 | B^4 + 1 = B^4 - 2B^2 + 1 - B \cdot B = (B^2 + (-1))^2 - B^2 = \left(B^2 - B + \left(-1\right)\right) (B^2 + B + 1) |
28,869 | \sum_{l=1}^\infty \sin{l} = \sin{1} + \sin{2} + \sin{3} + ... + \sin{l} |
19,541 | -9 = 2 \cdot 2 + 9\left(-1\right) \cdot \left(-1\right) - 4 \cdot 2 + 18 \left(-1\right) + 4 |
26,611 | T*a*(x + \varphi)*2 = g*f*a rightarrow \frac{g}{T*a}*f = 2*\left(x + \varphi\right)/a |
16,608 | 19*\left(-5\right) + 12*8 = 1 |
-4,029 | s/6 = s/6 |
378 | \phi^2 - f^2 = \left(-f + \phi\right)\cdot (f + \phi) |
-4,481 | \frac{1}{x^2 + 6\cdot x + 8}\cdot (14\cdot (-1) - x\cdot 5) = -\frac{2}{x + 2} - \dfrac{3}{x + 4} |
-2,784 | \sqrt{3} \cdot 7 = \left(4 + 2 + 1\right) \cdot \sqrt{3} |
3,935 | \left(a + b\right)^2 = a^2 + 2 \cdot b \cdot a + b^2 |
29,812 | a^4 = \frac{m^2}{9} \Rightarrow a^2 = |m|/9 |
28,170 | a^2 + b^2 = (b + a) \cdot (b + a) - 2\cdot a\cdot b |
1,493 | 0 = \left(m \cdot I - D\right)^2 \cdot x_2 = (m \cdot I - D) \cdot (m \cdot I - D) \cdot x_2 |
30,938 | m^2 + (-1) = ((-1) + m)\cdot (1 + m) |
Subsets and Splits