id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-22,322 |
(z + 6)\cdot (3\cdot (-1) + z) = 18\cdot (-1) + z^2 + 3\cdot z
|
6,803 |
\frac{1}{x}*(x + 1) = \frac{1}{-\frac{1}{1 + x} + 1}
|
43,103 |
t*\cos{t} = \frac{\frac{\text{d}z}{\text{d}t}}{t} - z*\frac{1}{t^2}*2 \implies \cos{t}*t^2 = \frac{\text{d}z}{\text{d}t} - z*2/t
|
25,613 |
\sqrt{5}/2 + 1 = 1 + \sqrt{5}/2
|
14,844 |
27 + 26\cdot F + L = (1 + F)\cdot 26 + L + 1
|
7,819 |
\frac47 + \frac173*\dfrac{3}{4} = \frac{1}{28}25
|
19,619 |
2^0 \cdot a = a
|
8,829 |
2*\left(4*x^2 - 3*x + (-1)\right) = 2*(x + (-1))*(x + 1/4) = \frac{1}{2*(x + (-1))*(4*x + 1)}
|
46,275 |
(0.3)(0.4)=0.12
|
16,428 |
(z + 4) \cdot (3 + z^2 - z \cdot 4) + (\left(-1\right) + z) \cdot 13 = \left(-1\right) + z \cdot z^2
|
24,095 |
1 - \frac{1}{1 + x} = \frac{x}{1 + x}
|
34,489 |
|-7^2 \cdot 7 + 2 \cdot 2 \cdot 2| = 335
|
2,188 |
0*\cdots = i
|
1,242 |
\gamma \cdot (k + n') = k \cdot \gamma + n' \cdot \gamma
|
29,437 |
(y^2 - 1 - y) \cdot (1 - y + 2 \cdot y^2) = 2 \cdot y^4 - 1 - y \cdot y^2 \cdot 3
|
-22,963 |
72/63 = \frac{72}{7*9}*1
|
27,157 |
a^2 - 2\times x\times a + 2\times x \times x = (-x + a)^2 + x^2
|
-28,859 |
11 + 4\cdot \left(-1\right) + 1 = 8
|
22,655 |
\mathbb{E}(X_x^2) \cdot \mathbb{E}(X_k^2) = \mathbb{E}(X_x^2 \cdot X_k \cdot X_k)
|
31,923 |
0.2112 = 2 \cdot 0.88 \cdot (1 - 0.88)
|
-5,042 |
36.4\cdot 10^{1 + 3} = 36.4\cdot 10^4
|
-19,283 |
\frac{2}{\frac18 \cdot 9} \cdot \frac{1}{9} = 8/9 \cdot \frac{1}{9} \cdot 2
|
-16,573 |
4*\sqrt{75} = 4*\sqrt{25*3}
|
22,791 |
Z^k\times Z^n = Z^{n + k}
|
-1,466 |
-18/28 = \frac{\left(-18\right) \cdot \frac{1}{2}}{28 \cdot 1/2} = -9/14
|
9,319 |
-\phi_1 + 2\phi_2 = \phi_1 + 2\pi n\Longrightarrow \phi_2 = n\pi + \phi_1
|
12,977 |
x = \frac12\cdot (3\cdot (-1) + x) + \frac{1}{2}\cdot (3\cdot (-1) + x) + 3
|
-9,901 |
22/25 (-2/25) = 22 (-2)/(25\cdot 25) = -\frac{1}{625}44
|
-2,830 |
6^{\dfrac{1}{2}} \cdot 25^{1 / 2} + 6^{\frac{1}{2}} = 6^{1 / 2} + 6^{1 / 2} \cdot 5
|
9,631 |
x^0 \times x^n = x^{n + 0} = x^n
|
-20,365 |
5/5\cdot \frac{t + (-1)}{1 + 6\cdot t} = \frac{1}{t\cdot 30 + 5}\cdot (5\cdot t + 5\cdot (-1))
|
-27,339 |
\cos{z}*\sin{z}*2 = \sin{z*2}
|
1,098 |
E_2 * E_2 + E_2*E_1 + E_1*E_2 + E_1^2 = E_2^2 + 2*E_2*E_1 + E_1^2
|
-20,697 |
\tfrac{1}{20*(-1) + 45*r}*(5*r + 20) = 5/5*\dfrac{1}{4*\left(-1\right) + 9*r}*\left(4 + r\right)
|
18,893 |
\sin(z + s) = 2\cdot \sin((s + z)/2)\cdot \cos(\dfrac12\cdot \left(s + z\right))
|
36,915 |
\alpha_k = \alpha_k
|
953 |
\left(\sqrt{(-1) + d^2} = -i\cdot d \Rightarrow d^2 + \left(-1\right) = -d \cdot d\right) \Rightarrow d = -\frac{1}{\sqrt{2}}
|
2,752 |
\frac{1}{n!} \cdot (n! - (n + \left(-1\right))!) = \dfrac{1}{n} \cdot (n + (-1))
|
2,627 |
\binom{6}{5} \cdot \frac{5^1}{6^6} = 30/46656
|
9,301 |
G_{11}\cdot Z = Z\cdot G_{11}
|
13,395 |
15 \cdot 0.9 \cdot 0.1 = 1.35
|
-29,240 |
0(-1) + 5 \cdot 0 = 0
|
-10,552 |
4/4\cdot \dfrac{z + 3}{z\cdot 5 + 10} = \dfrac{z\cdot 4 + 12}{z\cdot 20 + 40}
|
17,724 |
\dfrac{3}{8} + 9/16 = \dfrac{15}{16} \leq 1
|
34,440 |
\dfrac{\binom{7}{5}}{7!} = 1/240
|
-8,061 |
\frac{1}{-i*5 - 2}*\left(26 + 7*i\right) = \frac{1}{-2 + i*5}*(-2 + 5*i)*\frac{1}{-2 - i*5}*(26 + i*7)
|
26,924 |
39 = (-1) + 10 \cdot 4
|
-7,338 |
1/6 = \frac{1}{10}\cdot 3\cdot \frac59
|
21,167 |
0 = 60 + g^2 - 16 \cdot g \Rightarrow g = \frac{1}{2} \cdot (16 \pm \left(256 + 240 \cdot (-1)\right)^{\dfrac{1}{2}}) = 6,10
|
-18,954 |
\tfrac{3}{4} = \frac{1}{4 \cdot π} \cdot A_s \cdot 4 \cdot π = A_s
|
22,179 |
0 = 1 - \cos(c)*\cosh\left(c\right)\Longrightarrow \cos(c) - 1/\cosh(c) = 0
|
36,107 |
3^{1997} = \left(3^{20}\right)^{99} \cdot 3^{17}
|
23,857 |
4 + 9\times 7 = 67
|
-4,877 |
\tfrac{1}{100} \cdot 27.2 = 27.2/100
|
40,810 |
630 - 3\cdot 180 + 3\cdot 60 + 24\cdot \left(-1\right) = 246
|
8,301 |
0 = z^3 - 2\cdot z^2 - 5\cdot z + 6 = (z + \left(-1\right))\cdot \left(z + 2\right)\cdot (z + 3\cdot (-1))
|
24,702 |
2 \left(a_x + 2 (-1)\right) = 2 a_x + 4 (-1) > a_x
|
3,267 |
z^2 + z\cdot 5 + 6 = (2 + z) (3 + z)
|
9,870 |
\frac{1}{2!\cdot 2!\cdot 4!}8! + \frac{8!}{2!\cdot 4!} = 1260
|
-3,357 |
-\sqrt{13} + \sqrt{117} + \sqrt{325} = \sqrt{9\cdot 13} + \sqrt{25\cdot 13} - \sqrt{13}
|
14,676 |
36 \cdot (-1) + 16 = 45 \cdot (-1) + 25
|
8,440 |
z_2 \cdot z_1 = \frac{1}{z_2 \cdot z_1} = z_1 \cdot z_2
|
2,272 |
r_l - r \lt x \implies r_l \lt x + r
|
31,219 |
\dfrac16 \cdot (\sin(\pi) - \sin(0)) = 0
|
31,313 |
\cos\left(2\cdot \pi + x\right) = \cos(x)
|
9,520 |
\sin^2{x} = \cos^2{x}/4 = \dfrac{1}{4}*(1 - \sin^2{x})
|
-12,044 |
\frac{3}{4} = \tfrac{p}{16 \pi}*16 \pi = p
|
16,425 |
(a - b)^2 = \left(-a + b\right) \cdot \left(-a + b\right)
|
-15,794 |
67/10 = -\dfrac{5}{10} + 9/10\cdot 8
|
1,070 |
\left(x - a\right) (x - b) = x \cdot x - x\cdot (b + a) + ba
|
-4,751 |
\frac{1}{5 \cdot (-1) + x} \cdot 4 - \frac{3}{x + 4} = \frac{1}{x^2 - x + 20 \cdot \left(-1\right)} \cdot (31 + x)
|
28,226 |
y^8 + 4 = (2 + y^4 + 2 \cdot y^2) \cdot (2 + y^4 - 2 \cdot y^2)
|
-20,221 |
\dfrac19*8*9/9 = \frac{72}{81}
|
2,117 |
x + 1 - j + (-1) = 2 + x - j
|
-20,826 |
54\cdot s/(s\cdot \left(-45\right)) = ((-9)\cdot s)/(\left(-9\right)\cdot s)\cdot (-\frac65)
|
9,537 |
-\sin(b)*\cos(f) + \sin(f)*\cos(b) = \sin\left(f - b\right)
|
24,165 |
\sin\left(x\right) = 0\Longrightarrow 0 \neq \cos\left(x\right)
|
40,710 |
200\cdot 0.5 = 100
|
40,877 |
0 = 4\cdot x^2 - y^2 = (2\cdot x + y)\cdot (2\cdot x - y)
|
15,037 |
47^4 + 3\cdot 28^4 = 2593 \cdot 2593
|
8,159 |
3 = (12^{1 / 2}/2) \times (12^{1 / 2}/2)
|
9,878 |
\left(x^X\cdot A\cdot x\right)^X = x^X\cdot A^X\cdot x = -x^X\cdot A\cdot x
|
37,567 |
-\frac{33}{16} = -2 - 1/16
|
-10,269 |
\dfrac{9\cdot p + 6\cdot (-1)}{12\cdot (-1) + 24\cdot p} = \frac{3\cdot p + 2\cdot \left(-1\right)}{4\cdot (-1) + 8\cdot p}\cdot \frac{1}{3}\cdot 3
|
34,547 |
-5\cdot (5 + a\cdot 4) = -a\cdot 20 + 25\cdot (-1)
|
-25,213 |
\frac{\mathrm{d}}{\mathrm{d}\vartheta} \cos(e^\vartheta) = -e^\vartheta \cdot \sin\left(e^\vartheta\right)
|
9,530 |
p\cdot 2 = \beta + \alpha \Rightarrow 2\cdot p - \beta = \alpha
|
17,550 |
b + a' x a + a b' = a x a' + b a' + b'
|
-19,187 |
9/10 = X_p/(4\cdot \pi)\cdot 4\cdot \pi = X_p
|
12,118 |
(n + 5*(-1))*2 + (6*(-1) + n)*\left(n + 5*(-1)\right) = (5*(-1) + n)*(n + 4*(-1))
|
29,649 |
(n \cdot n + n \cdot 3 + 2 + 4 \cdot n + 4 + 6)/2 = \dfrac12 \cdot (n^2 + n \cdot 7 + 12)
|
54,714 |
\frac{49}{1.001} + \frac{1}{0.951} = 48.951048951 + 1.051524711 = 50.002573662
|
-17,812 |
65\times (-1) + 71 = 6
|
-3,371 |
275^{1 / 2} + 99^{1 / 2} = (9 \cdot 11)^{1 / 2} + \left(25 \cdot 11\right)^{1 / 2}
|
25,106 |
-y^n + z^n = \left(-y + z\right)*(z^{n + (-1)} + z^{2*(-1) + n}*y + y^2*z^{n + 3*(-1)} + \cdots + z*y^{n + 2*(-1)} + y^{n + (-1)})
|
26,944 |
3^{2*\frac14*3} = 9*((3^3)^{\frac{1}{2}})^{\dfrac{1}{2}} \approx 20.5
|
22,814 |
x_1 - x_4*1/2 = 0 \Rightarrow x_4*1/2 = x_1
|
6,901 |
\sin^2(z) = \frac{1}{-4}(e^{iz} - e^{-iz})^2 = -\dfrac{1}{4}\left(e^{2iz} + 2\left(-1\right) + e^{-2iz}\right)
|
1,389 |
g^{\frac{1}{2}}*g^{1 / 2} = g
|
24,878 |
\left(x^2 + x\right)^2 = x \cdot x + x + x^3 + x^3 = x^2 + x
|
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