id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
6,127 |
A^{b c} = A^{c b}
|
667 |
p + 1 = \frac{1}{(-1) + p}\cdot (p^2 + (-1))
|
-29,572 |
(3 \cdot \gamma^2 + 10 \cdot (-1))/\gamma = \tfrac{3}{\gamma} \cdot \gamma^2 - \frac{1}{\gamma} \cdot 10
|
1,936 |
1 + x = 3 \pi/2 + \cos\left(\frac{\pi}{2} 3\right)\Longrightarrow 2 (-1) + 3 \pi/2 = x
|
-22,138 |
\frac{1}{2} = \frac{1}{24} 12
|
625 |
|z + w| = |z - w| \implies |-w + z|^2 = |w + z|^2
|
-18,952 |
\frac45 = \dfrac{A_s}{9 \cdot \pi} \cdot 9 \cdot \pi = A_s
|
-4,614 |
\frac{4}{(-1) + x} + \dfrac{5}{2 \cdot (-1) + x} = \frac{9 \cdot x + 13 \cdot \left(-1\right)}{x^2 - 3 \cdot x + 2}
|
-3,798 |
\frac{r^4}{r \cdot r} = \dfrac{r^4}{r\cdot r}\cdot 1 = r^2
|
39,869 |
z/\left(\dfrac{1}{y}\right) = y \cdot z
|
1,667 |
27 + y^6 = (y^2 + y\cdot 3 + 3)\cdot (y \cdot y - 3\cdot y + 3)\cdot (3 + y^2)
|
9,949 |
k/x + l/x = (l + k)/x
|
-873 |
\frac{3}{10000} + 0 + 0/10 + \frac{1}{100} + \frac{7}{1000} = 173/10000
|
16,263 |
1 = \frac{1}{d_2} + \frac{1}{d_2 + b} + \frac{1}{d_2 + b + d_1} \geq \frac{1}{d_2 + b + d_1}3
|
-16,493 |
10 \times \sqrt{9 \times 7} = 10 \times \sqrt{63}
|
-1,874 |
\pi/6 = 7/4 \cdot \pi - 19/12 \cdot \pi
|
-30,543 |
\frac{dy}{dx} = \frac{\left(xy\right)^2}{8} + y^2 = y \cdot y/8 (x \cdot x + 8)
|
33,657 |
x^3 - x^2 + x^2 - x = -x + x^2 \cdot x
|
31,170 |
\frac{16}{3} = \sqrt{64}/3\cdot 2
|
24,993 |
x^R\cdot D^R\cdot D\cdot x = \|D\cdot x\|^2 \leq \|D\|^2\cdot x^R\cdot x
|
-2,989 |
\sqrt{11} = (4 + 3*\left(-1\right))*\sqrt{11}
|
-22,297 |
3\cdot (-1) + k^2 + k\cdot 2 = \left((-1) + k\right)\cdot \left(3 + k\right)
|
-26,490 |
x^2*49 + 100 - 140*x = \left(10 - 7*x\right)^2
|
40,867 |
1 - 1 + 1 - 1 + 5 = (-1) \left(-1\right) \cdot 5 = 5
|
-2 |
-15 = -11 + 4 \cdot (-1)
|
-23,065 |
--4/3 \times 5 = 20/3
|
-18,506 |
5*x + 10 = 6*\left(2*x + 2\right) = 12*x + 12
|
6,101 |
\tfrac{1}{3}\cdot 2/3 = \frac19\cdot 2
|
22,416 |
q^p\cdot s\cdot q^i = q^i\cdot s\cdot q^p
|
38,825 |
3 \cdot 5^2 = 75
|
21,064 |
\dfrac{1}{1 - x * x} = \frac{1}{\left(-1\right)*\left(x + (-1)\right)*(x + 1)} = -\dfrac{1}{(x + (-1))*(x + 1)}
|
-20,600 |
\frac{1}{-18}\cdot \left(-9\cdot y + 12\right) = 3/3\cdot \tfrac{1}{-6}\cdot (-3\cdot y + 4)
|
-15,146 |
\tfrac{y^5}{\dfrac{1}{\frac{1}{s^{25}} \frac{1}{y^{10}}}} = \frac{y^5}{y^{10} s^{25}}
|
35,002 |
-n^2 + m^2 = 0 rightarrow m^2 = n * n
|
-1,700 |
\frac{3}{4}\cdot \pi = \pi/2 + \pi/4
|
-2,546 |
275^{\dfrac{1}{2}} + 11^{1 / 2} = 11^{\frac{1}{2}} + (25\times 11)^{\dfrac{1}{2}}
|
20,217 |
\sqrt{0.5 \cdot ((-1) \cdot 0.5 + 1) \cdot 900} = 15
|
-20,496 |
\frac{1}{16} \times 2 = \frac18 \times 1
|
19,415 |
3 \cdot \left(-1\right) + z \cdot 2 = z\Longrightarrow 3 = z
|
32,548 |
\left(-1 - \frac13\right)^2\cdot \frac59 + 4/9\cdot (2 - 1/3)^2 = 20/9
|
46,119 |
3^{9 + (-1)} = 3^8 = 6561
|
-16,341 |
\sqrt{80} \cdot 10 = 10 \cdot \sqrt{16 \cdot 5}
|
25,446 |
(1 + x)^2 = 1 + x^2 = 1 - x \cdot x
|
-14,605 |
83 = \dfrac{1}{4}*332
|
16,966 |
d^2 - c \times c = (-c + d) \times (d + c)
|
-27,693 |
\frac{\mathrm{d}}{\mathrm{d}z} (-\sin\left(z\right) \cdot 9) = -\cos\left(z\right) \cdot 9
|
-17,009 |
3 = 3*(-u) + 3*(-5) = -3*u - 15 = -3*u + 15*(-1)
|
-2,725 |
(25 \cdot 6)^{1/2} - (4 \cdot 6)^{1/2} = -24^{1/2} + 150^{1/2}
|
47,520 |
|z_1 \cdot y_1 - z_2 \cdot y_2| = |z_1 \cdot y_1 - z_1 \cdot y_2 + z_1 \cdot y_2 - z_2 \cdot y_2| \leq |z_1 \cdot y_1 - z_1 \cdot y_2| + |z_1 \cdot y_2 - z_2 \cdot y_2|
|
18,257 |
1 + (-1) + 1 + (-1) + 1 - \cdots = \frac12
|
26,709 |
(y + x)^2 - (-x + y)^2 = 4yx
|
24,190 |
\frac{4\times 13^3}{26\times 17\times 50} = \dfrac{4\times 13^2}{2\times 17\times 50} = 169/425
|
4,559 |
\sin(y_2 + y_1) = \sin{y_2} \cdot \cos{y_1} + \cos{y_2} \cdot \sin{y_1}
|
7,454 |
W_g x = W_g x
|
8,704 |
\cos(x - y) = \cos(x)*\cos(y) + \sin(x)*\sin\left(y\right)
|
20,499 |
\sin(x) < 0 \Rightarrow x = -2\pi/3
|
4,797 |
((-1) + e^x)\cdot \dfrac{x}{e^x + (-1)} = x
|
-12,290 |
\frac{1}{12} = s/(12 \pi)\cdot 12 \pi = s
|
45,141 |
\frac{x + (-1)}{x^2 - 5\cdot x + 6} = \dfrac{\frac{1}{2}\cdot (2\cdot x + 2\cdot (-1))}{x \cdot x - 5\cdot x + 6} = \dfrac{1}{x^2 - 5\cdot x + 6}\cdot (\frac{3}{2} + \frac12\cdot \left(2\cdot x + 5\cdot (-1)\right)) = \frac{2\cdot x + 5\cdot (-1)}{2\cdot (x^2 - 5\cdot x + 6)} + \frac{3}{2\cdot (x^2 - 5\cdot x + 6)}
|
25,682 |
p = (z - u)/2 \Rightarrow p^2 + 1 = (z \cdot z - u\cdot z\cdot 2 + u^2)/4 + 1
|
34,938 |
det\left(t\cdot I - A\cdot D\right) = det\left(I\cdot t - D\cdot A\right)
|
5,622 |
\left(f - t\right) \cdot \left(t + f\right) = f^2 - t^2
|
18,567 |
2^2 \times x^2 = x^2 \times 4
|
31,500 |
\left(-\sqrt{4^2 + 12 \times (-1)} + 2 = 0 \implies 2 - \sqrt{16 + 12 \times (-1)} = 0\right) \implies 0 = 0
|
35,241 |
\overline{w}\cdot \overline{z} = \overline{z\cdot w}
|
1,027 |
a + \tfrac{1}{(-1) b} = a + (-1) + \frac{1}{1 + \frac{1}{b + (-1)}}
|
-9,629 |
0.01 \cdot (-20) = -\frac{20}{100} = -0.2
|
-16,418 |
5 \cdot \left(16 \cdot 13\right)^{1/2} = 5 \cdot 208^{1/2}
|
34,560 |
\frac{2}{2} \cdot x = \frac12 \cdot 2 \cdot x = x
|
6,782 |
10^{-(m + s)} = 10^{-m - s}
|
-6,103 |
\dfrac{5}{5(m + 10)} = \frac{5}{5m + 50}
|
14,272 |
\log_e\left(d\right)\cdot d^x = \frac{\partial}{\partial x} d^x
|
-9,615 |
-\frac{1}{5}4 = -0.8
|
-26,577 |
(y + 8) \cdot (y + 8 \cdot (-1)) = y^2 - 8^2
|
139 |
4/27 = 2/3/3*2/3
|
-5,924 |
\frac{1}{k \cdot k + 36 \cdot (-1)} \cdot \left(k + 6 + k \cdot 3 + 18 \cdot \left(-1\right) + 3 \cdot k\right) = \dfrac{12 \cdot (-1) + 7 \cdot k}{k \cdot k + 36 \cdot \left(-1\right)}
|
33,321 |
e \cdot 0 = e \cdot (0 + 0) = e \cdot 0 + e \cdot 0
|
21,327 |
\sum_{m=1}^l h_m = \sum_{m=1}^l h_m
|
-1,890 |
\pi\cdot 2 - \dfrac13\cdot 4\cdot \pi = 2/3\cdot \pi
|
1,062 |
(2^p f)^3 = 2^{3 p} f^3
|
19,011 |
20 - 5 \times \sqrt{-2} = -5 \times \sqrt{2} \times i + 20
|
31,627 |
\dfrac{x^2}{z}\cdot t = (t\cdot x)^2/(z\cdot t)
|
-20,471 |
2/2 \frac{-2x + 8}{-x + 1} = \frac{-4x + 16}{-2x + 2}
|
31,424 |
\frac{1}{1 - x^2} = \sum_{k=0}^∞ (x^2)^k = \sum_{k=0}^∞ x^{2k}
|
4,040 |
(-1) + \left(q + (-1)\right) \cdot ((-1) + p) = p \cdot q - p - q
|
-22,228 |
\left(y + 8\right) \cdot (y + 6) = y^2 + y \cdot 14 + 48
|
21,725 |
d^2 - b \times b = \left(-b + d\right)\times (b + d)
|
28,122 |
x_l\cdot x_{l + 1} = x_{l + 1}\cdot x_l
|
19,107 |
\sin(\frac12 \cdot π + x) = \cos(x)
|
14,196 |
\cos(\pi + i) = -\cos{i} = -\frac12\cdot (e^{i^2} + e^{-i \cdot i}) = -\left(e + 1/e\right)/2
|
25,263 |
\dfrac{1}{1 + 1/4} \cdot (1 + \dfrac{1}{2}) = 1.2 < 1 + 1/4
|
20,333 |
24/72 = \tfrac13
|
6,835 |
1 - 80*x * x - 120*x + 45*(-1) = -5*(x^2*16 + 24*x + 9) + 1
|
1,409 |
-n^{\tfrac{1}{2}} + (n + 1)^{1 / 2} = \frac{1}{(n + 1)^{\frac{1}{2}} + n^{\frac{1}{2}}}
|
-18,492 |
-\dfrac{1}{11}\cdot 13 = -\tfrac{13}{11}
|
-12,940 |
5\left(-1\right) + 21 = 16
|
1,045 |
\dfrac19(2^{3^m}*2^{3^m}*2^{3^m} + 1) = (2^{3^{m + 1}} + 1)/9
|
5,489 |
-\pi/20 + \pi/2 = \pi\cdot 9/20
|
1,637 |
\alpha + \beta + \alpha + \alpha = 3 \alpha + \beta
|
7,204 |
(-1) + R^2 = (R + 1) \cdot (R + (-1))
|
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