id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
1,392 |
-4/3\times π\times r^3 = π\times (1/3 - 1 + 1/3 + (-1))\times r^3
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2,467 |
\dfrac16 = \dfrac{1}{4 (-1) + 10}
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-27,808 |
\sec^2\left(x\right) = d/dx \tan\left(x\right)
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-25,313 |
\frac{\mathrm{d}}{\mathrm{d}z} (z * z*\sin(z)) = \sin(z)*z*2 + z^2*\cos(z)
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-27,806 |
\frac{d}{dx} (2\sec{x}) = 2d/dx \sec{x} = 2\sec{x} \tan{x}
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-1,753 |
-\pi*5/6 + \frac{1}{2}*3*\pi = \pi*\dfrac23
|
-434 |
\pi \frac1215 - 6\pi = \pi*3/2
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15,167 |
y \cdot S = y - y^2 + y^3 + y^4 + y^5 + y^6 = y - 1 - S - y + y^6 = 2 \cdot y - y^6 + (-1) + S
|
13,983 |
(1 + 3 \times 3) \times (17 + 3^2) = 260 = 4 \times 65
|
-2,431 |
\sqrt{5}\cdot \sqrt{4} + \sqrt{5}\cdot \sqrt{9} = 2\cdot \sqrt{5} + 3\cdot \sqrt{5}
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24,309 |
T X \cdot 4 = -(X - T) (X - T) + (X + T)^2
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12,248 |
\frac{1}{q + \left(-1\right)} = \frac{2 - q}{(-1) + q} + 1
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17,086 |
\frac{1}{(\left(\frac1n*k\right) * \left(\frac1n*k\right) + 1)*n} = \dfrac{1}{k * k + n^2}*n
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28,341 |
x^{zx + x} = x^{x*(z + 1)}
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-15,358 |
\dfrac{1}{\frac{1}{c^4}*\frac1q}*q^2 = \frac{1}{\frac{1}{c^4}*1/q}*q * q
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28,914 |
7/9 = \frac{1}{9!}\binom{8}{2}\cdot 2!\cdot 7!
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1,281 |
X^2*T = T*X^2\Longrightarrow X*T = T*X
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-25,972 |
\tfrac{9}{0.01} = 900
|
28,226 |
\left(y^4 - y^2 \cdot 2 + 2\right) \cdot (2 + y^4 + y^2 \cdot 2) = y^8 + 4
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-23,802 |
\frac{1}{6 + 10}\cdot 16 = \dfrac{16}{16} = \frac{16}{16} = 1
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13,124 |
5/168 - \tfrac{1}{40} = \frac{1}{840}\cdot (25 + 21\cdot (-1)) = \frac{1}{210}
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-7,408 |
1/6 = 3/8 \times \frac19 \times 4
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16,330 |
1 - z^{l + 1} = 1 - z^l + z^l - z^{1 + l}
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-19,156 |
\dfrac{2}{5} = E_r/(100\cdot \pi)\cdot 100\cdot \pi = E_r
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11,923 |
9!/1! = 9*8*7*6*5*4*3*2
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-11,756 |
(\frac53) \cdot (5/3)^2 = 125/27
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33,630 |
t^9 = (t^3)^3 = (t + 1)^3 = t * t^2 + 1 = t + 2 = t + (-1)
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15,751 |
\cos(2\cdot \theta) = (-1) + 2\cdot \cos^2\left(\theta\right)
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4,977 |
\left(x + y + 2\cdot z = 0\Longrightarrow x = -y - z\cdot 2\right)\Longrightarrow \left( x, y, z\right) = ( -y - z\cdot 2, y, z)
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28,356 |
-2*\left(y + 2\right) = -y*2 + 4*(-1)
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8,895 |
s = k\cdot (-v + d) + (x - m)\cdot v + h + j \Rightarrow -h + s - v\cdot (x - m) - k\cdot \left(d - v\right) = j
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25,583 |
\cos{3*y} = \cos\left(y + 2*y\right)
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4,228 |
\epsilon = a \implies a - \epsilon \geq 0
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13,892 |
m^4 + (-1) = ((-1) + m) \cdot (1 + m) \cdot (1 + m^2)
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-2,827 |
25^{1 / 2} \times 5^{1 / 2} + 16^{1 / 2} \times 5^{1 / 2} = 5 \times 5^{\frac{1}{2}} + 4 \times 5^{1 / 2}
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21,117 |
\mathbb{E}(W_D\cdot W_B) = \mathbb{E}(W_D)\cdot \mathbb{E}(W_B)
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17,849 |
y^{2/6} = y^{\dfrac{1}{3}}
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-5,043 |
0.47 \cdot 10^{2 \cdot \left(-1\right) + 3} = 0.47 \cdot 10^1
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15,083 |
\left(a^2 + z^2\right)*\left(-a^2 + z^2\right) = z^4 - a^4
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-6,688 |
\frac{9}{100} + 6/10 = \frac{9}{100} + \frac{60}{100}
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-4,032 |
\frac{z^4}{z^2} = z*z*z*z/\left(z*z\right) = z^2
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-29,561 |
\frac{1}{z}*\left(z^2 * z*4 - z^2 + 3\right) = 4*z^3/z - z^2/z + \frac{1}{z}*3
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30,401 |
x_n - \sum_{j=1}^n E(X_j) = x_n - \sum_{j=1}^n E(X_j) + x_n
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-11,489 |
16 + 6 \cdot (-1) - i \cdot 20 = 10 - i \cdot 20
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27,752 |
0^2 + 3 = (1 + 2) + 4\cdot 0
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27,614 |
305 + 305 \cdot (1+0.5) \cdot 0.5=305 \cdot (1+0.5+0.5^2)
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-2,226 |
\dfrac{6}{20} - \dfrac{1}{20} = \dfrac{5}{20}
|
4,795 |
\frac{1}{2}\cdot (k + 10\cdot (-1)) = -1.3 \implies 7.4 = k
|
-6,003 |
\frac{3}{(z + 7)\cdot 5} = \dfrac{3}{5\cdot z + 35}
|
6,035 |
\frac{1}{Y_2 Y_1} = 1/(Y_1 Y_2)
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27,583 |
160 = \frac{2}{21}\cdot 1680
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33,270 |
\mathbb{R} = (-\infty,\infty)
|
19,983 |
\dfrac{2}{n/2} = \dfrac{4}{n}
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32,244 |
y*3 + 3b = 3(b + y)
|
-3,961 |
4/7 \cdot n = 4 \cdot n/7
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-12,454 |
126 + 90 (-1) = 36
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33,132 |
\frac{1}{2} \cdot ( 2, 4, 6) = \frac{2}{3} \cdot ( 3, 6, 9)/2 = \tfrac13 \cdot ( 3, 6, 9) = \left( 1, 2, 3\right)
|
23,392 |
\alpha - \beta = \frac{\alpha^2 - \beta^2}{\beta + \alpha}
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-5,497 |
\frac{s}{s^2 - 10 \cdot s + 21} = \frac{1}{(s + 3 \cdot (-1)) \cdot (s + 7 \cdot (-1))} \cdot s
|
-27,774 |
d/dy (-\csc{y}) = -d/dy \csc{y} = \csc{y} \cot{y}
|
7,642 |
K\times K\times 3 = K
|
18,106 |
\frac12 \cdot 3^{1 / 2} = \sin{\pi \cdot 2/3}
|
-18,423 |
\frac{1}{10 \times x + x^2} \times (x^2 + x \times 6 + 40 \times (-1)) = \frac{1}{x \times (x + 10)} \times \left(10 + x\right) \times (x + 4 \times (-1))
|
-2,742 |
\sqrt{5}\times (4 + 5\times (-1) + 2) = \sqrt{5}
|
19,579 |
f^2 + x^2 + \tau^2 + f \cdot x \cdot \tau = 4 \cdot (f + x + \tau) - 2 \cdot \left(f \cdot x + x \cdot \tau + f \cdot \tau\right) + f \cdot x \cdot \tau = 8 - (2 - f) \cdot (2 - x) \cdot \left(2 - \tau\right)
|
25,798 |
|1 - y_1 \bar{y_2}|^2 - |y_1 - y_2|^2 = \dots = \left(1 - |y_1|^2\right) \left(1 - |y_2|^2\right)
|
-15,806 |
-\frac{1}{10}71 = -9*\frac{1}{10}9 + 10/10
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27,749 |
z^3 - 7z + 5\left(-1\right) = 31 + \left(z + 4(-1)\right) (9 + z^2 + z*4)
|
3,454 |
-\frac{1}{2^n} + 1 = \dfrac{1}{2} + \frac14 + ... + \frac{1}{2^n}
|
-3,282 |
\sqrt{10}*\left(5 + 2 + 4 (-1)\right) = 3 \sqrt{10}
|
9,713 |
E\left(X_G \cdot X_x\right) = E\left(X_x\right) \cdot E\left(X_G\right)
|
35,668 |
\epsilon + \epsilon = 2*\epsilon
|
13,165 |
1729 = 10^3 + 9 \cdot 9 \cdot 9 = 12^3 + 1 \cdot 1 \cdot 1
|
23,477 |
\sin(h + x) = \cos{x} \cdot \sin{h} + \sin{x} \cdot \cos{h}
|
28,443 |
\left|{x \cdot \lambda - Y}\right| \cdot \left|{S}\right| \cdot \left|{1/S}\right| = \left|{S}\right| \cdot \left|{-Y + x \cdot \lambda}\right| \cdot \left|{1/S}\right|
|
8,491 |
0 = a*2 + 2 b + c*2 \Rightarrow 0 = a + b + c
|
11,880 |
a^r\cdot a^s=a^{r+s}
|
8,578 |
\sin{3 \times x} = \sin(2 \times x + x) = \sin{2 \times x} \times \cos{x} + \cos{2 \times x} \times \sin{x}
|
29,362 |
\frac{x^2 + 9*(-1)}{x + 3*(-1)} = 3 + x
|
-19,420 |
\frac{\frac12}{1/6}*3 = \frac61*\frac32
|
12,013 |
(a + b) (a + b) = a + ab + ba + b = a + b
|
17,167 |
(x + if) \left(-fi + x\right) (-J + e) (J + e) = (x + fi) \left(J + e\right) (x - fi) \left(e - J\right)
|
9,890 |
\sin{x} \cdot \tan{x} = \frac{\sin^2{x}}{\cos{x}} = \dfrac{1}{\cos{x}} \cdot (1 - \cos^2{x})
|
11,860 |
\dfrac{1}{(r + 1)\cdot \left((-1) + r\right)} = \dfrac{B}{r + 1} + \dfrac{A}{(-1) + r} \implies r\cdot (A + B) + A - B = 1
|
-16,484 |
7*4^{\dfrac{1}{2}}*5^{1 / 2} = 7*2*5^{1 / 2} = 14*5^{1 / 2}
|
17,750 |
-6 \cdot y + y^2 = 9 \cdot (-1) + \left(3 \cdot (-1) + y\right) \cdot \left(3 \cdot (-1) + y\right)
|
-17,592 |
99 + 39 \times (-1) = 60
|
27,570 |
\frac{1}{9}\cdot 2 = \frac{2}{27}\cdot 3
|
5,200 |
\frac{2^{\frac{1}{3}}}{2^{\frac{1}{3}}} \cdot \omega = \omega
|
28,708 |
\dfrac{1}{n! + (1 + n)! + (2 + n)!} = \dfrac{1}{n!*(2 + n)^2}
|
16,771 |
(5*x + (-1))*x/2 = 2 + 7 + 12 + 17 + \ldots + 5*x + 3*(-1)
|
13,884 |
\frac{1}{((-1) + x \cdot x) \cdot ((-1) + x)} \cdot (3 \cdot x \cdot x^2 - 5 \cdot x^2 - 5 \cdot x + 5 \cdot (-1)) \cdot (\left(-1\right) + x) = \frac{1}{\left(-1\right) + x^2} \cdot (5 \cdot (-1) + 3 \cdot x^3 - x^2 \cdot 5 - x \cdot 5)
|
27,780 |
\dfrac{1}{16384}*1001 = \frac{\binom{14}{9}}{2^{15}}
|
32,602 |
2^{2k} = 2^k*2^k
|
14,970 |
x \cdot 22 + 120 \cdot x = x \cdot 142
|
22,605 |
6 k k + 9 k + 2 = 6 (k + 1) (k + 1) - 3 k + 4 (-1) = 6 (k + 1)^2 - 3 (k + 1) + (-1)
|
11,613 |
z^2 + 1 + z = \frac{z^3 + (-1)}{z + \left(-1\right)}
|
-28,902 |
1/4 \cdot 1^2 \cdot π - 1 \cdot \frac12 = π/4 - 1/2
|
-2,820 |
10^{1/2} + 40^{1/2} = (4\cdot 10)^{1/2} + 10^{1/2}
|
-22,721 |
24*5/(4*24) = \dfrac{120}{96}
|
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