id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
1,108 |
\|E\| \cdot \|E\| = \|E\| \cdot \|E\|
|
-4,658 |
\frac{1}{2 + x^2 - x*3}*(11*(-1) + x*8) = \dfrac{1}{\left(-1\right) + x}*3 + \dfrac{5}{x + 2*(-1)}
|
4,425 |
\cos{a\cdot b} = \cos\left(0.5\cdot a\cdot b + 0.5\cdot a\cdot b\right) = \cos^2{0.5\cdot a\cdot b} - \sin^2{0.5\cdot a\cdot b}
|
38,255 |
\frac{1}{2}\times 8\times 9 = \dfrac{72}{2} = 36
|
-6,701 |
\frac{8}{100} + \frac{2}{10} = 20/100 + 8/100
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33,341 |
65^2 - 8 \cdot 8 = 4161
|
-3,050 |
\sqrt{16 \cdot 10} - \sqrt{4 \cdot 10} = -\sqrt{40} + \sqrt{160}
|
14,690 |
-10x=1\pm \sqrt{4x^4-4x^2+1}=1\pm \sqrt{(2x^2-1)^2}
|
33,919 |
h^n \coloneqq \frac{1}{h^{-n}}
|
22,264 |
1 \cdot 1^2 = 1^2\Longrightarrow 3 = 2
|
14,495 |
-r^3 + 1 = 1 + r + r^2 - r^3 + r + r \cdot r
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5,754 |
x^j \cdot x^i = x^i \cdot x^j
|
22,347 |
(1 + y^{25} + y^{50} + y^{75}) (1 - y^{25}) = 1 - y^{100}
|
2,776 |
\cos(\rho - x) = \cos{\rho} \cos{x} + \sin{x} \sin{\rho}
|
-5,737 |
\frac{4}{3*x + 9*(-1)} = \dfrac{1}{\left(3*(-1) + x\right)*3}*4
|
-2,597 |
5 \cdot \sqrt{6} = (2 + 4 + (-1)) \cdot \sqrt{6}
|
-22,198 |
3 + c^2 - 4 \times c = (c + 3 \times (-1)) \times (c + (-1))
|
-18,317 |
\frac{(p + 7)\cdot \left(2 + p\right)}{(p + 7)\cdot p} = \dfrac{1}{p^2 + 7\cdot p}\cdot (p^2 + 9\cdot p + 14)
|
11,449 |
0 = -\sin(\pi/6) - -\sin(\frac56 \cdot \pi)
|
15,120 |
2 \cdot \sqrt{\pi} = \sqrt{2 \cdot \pi} \cdot \sqrt{2}
|
29,299 |
\frac{1}{4}3 = \dfrac143
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-23,908 |
\dfrac{16}{10 + 6} = 16/16 = 16/16 = 1
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33,293 |
4 = \frac{2*20}{10}
|
-20,923 |
(16 - 4k)/(-18) = \frac{1}{-9}\left(-2k + 8\right) \frac{1}{2}2
|
14,125 |
-z_4 + z_1 - z_3 = 0 rightarrow z_1 = z_3 + z_4
|
2,219 |
N_x \cdot D_x = D_x \cdot N_x
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-29,871 |
\frac{\mathrm{d}}{\mathrm{d}x} \left(5x^4\right) = 5\frac{\mathrm{d}}{\mathrm{d}x} x^4 = 5\cdot 4x^3 = 20 x^3
|
17,951 |
t \cdot t = (t + 3 \cdot (-1) + 3) \cdot (t + 3 \cdot (-1) + 3) = (t + 3 \cdot (-1))^2 + 2 \cdot \left(t + 3 \cdot (-1)\right) \cdot 3 + 3^2 = (t + 3 \cdot (-1))^2 + 6 \cdot (t + 3 \cdot (-1)) + 9
|
-10,485 |
\frac{4}{4} \cdot (t \cdot 3 + 10 \cdot (-1))/t = \frac{1}{t \cdot 4} \cdot (12 \cdot t + 40 \cdot (-1))
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25,853 |
639 = 720 + 24 (-1) + 24 (-1) + 24 \left(-1\right) + 24 \left(-1\right) + 6 + 6 + 6 + 2 (-1) + 2 (-1) + 1
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14,362 |
\dfrac{\sqrt{0 + 1}}{1 + \sqrt{1 + 0}} = 1/2
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40,338 |
-22 = 0 + 7 (-1) + 15 (-1)
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22,160 |
2\cos{x/2} \sin{\tfrac{x}{2}} = \sin{x}
|
5,265 |
1 + a + a * a + a^3 + \ldots + a^n = \frac{1}{1 - a}*(1 - a^{1 + n})
|
6,559 |
\tan^{-1}{0} + \tan^{-1}(0^2 + (-1)) = 0 + \tan^{-1}{-1} = \frac{1}{4} \cdot (\left(-1\right) \cdot \pi)
|
7,130 |
\frac{10}{23 - -7} = \frac{10}{30} = \frac{1}{3}
|
32,657 |
n^2 - ((-1) + n)^2 = 2\cdot n + (-1)
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14,303 |
\frac{1}{79}3 = 15/79*\frac{16}{80}
|
17,040 |
Xe^A/X = e^{AX/X}
|
-1,366 |
7/1\cdot (-9/2) = \frac{1}{\dfrac17}\cdot (1/2\cdot \left(-9\right))
|
13,554 |
12 = -84*2 + \left(-84 + 144\right)*3
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15,932 |
-\int \sin{x}\,\mathrm{d}x + \sin{x}\cdot ((-1) + x) = \cos{x} + \sin{x}\cdot ((-1) + x)
|
17,092 |
1 + (l + 1)^2 - l + 1 = 1 + l^2 + l
|
11,612 |
(1/2 + x) \cdot (1/2 + x) - \dfrac{1}{4} = x^2 + x
|
2,228 |
|z - x|^2 = \left(z - x\right) \overline{z - x} = |z|^2 - z\overline{x} - \overline{z} x + |x|^2
|
1,050 |
\frac45 \cdot y + \dfrac{y}{4} = y \cdot 21/20
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21,543 |
h*w_{i_0} = h*x*w_{i_0} = x*h*w_{i_0}
|
-549 |
e^{6\cdot \frac{19}{12}\cdot i\cdot \pi} = (e^{19\cdot i\cdot \pi/12})^6
|
41,092 |
22\cdot 360 = 7920
|
3,842 |
E[Y^b \cdot X^a] = E[Y^b] \cdot E[X^a]
|
412 |
\sin(2 \cdot z - z) = \sin{z}
|
33,702 |
f_3 \cdot f_2 = f_3 \cdot f_2
|
6,269 |
s + (-1) = \frac{1}{2} \cdot ((-1) + s) \cdot 2
|
-4,493 |
\frac{5}{4 \cdot (-1) + x} + \frac{4}{(-1) + x} = \frac{x \cdot 9 + 21 \cdot (-1)}{x \cdot x - x \cdot 5 + 4}
|
19,186 |
\frac{1}{x^2 - y^2}*\left(x^2 + 2*x*y + y^2\right) = \frac{(x + y)^2}{(x + y)*\left(x - y\right)} = \dfrac{x + y}{x - y}
|
-19,278 |
\frac{\frac17\times 4}{7\times \frac12} = \frac27\times \frac{4}{7}
|
48,475 |
B_2 = B_2
|
19,673 |
1 + 3 + 5 + \cdots + n\cdot 2 + (-1) = n^2
|
27,551 |
r_1 x_1 + \cdots + r_n x_n = \overline{r_1} x_1 + \cdots + \overline{r_n} x_n
|
8,915 |
w_1^T \times z_1 = z_1 \times w_1^T
|
9,477 |
e^p = e^{q\cdot y} \Rightarrow e^y = e^\frac{p}{q} = (e^p)^\tfrac{1}{q}
|
31,574 |
p + 1 + 2 = 13 \implies 10 = p
|
3,261 |
\frac{\sin\left(x\right)}{\cos(x) + 1} = (-\cos(x) + 1)/\sin(x)
|
7,789 |
\chi! = \chi \cdot ((-1) + \chi)!
|
15,572 |
(z + 2 \times (-1)) \times (z + 3 \times (-1)) = z \times z - z \times 5 + 6
|
-6,133 |
\frac{12}{4 \cdot \left(9 \cdot (-1) + m\right) \cdot (m + 5 \cdot (-1))} = \frac44 \cdot \frac{3}{(5 \cdot (-1) + m) \cdot (9 \cdot (-1) + m)}
|
9,498 |
det\left(F*F^Q\right) = det\left(F*F^Q\right)
|
27,423 |
M \cdot x_v = x_w \Rightarrow \dfrac{1}{M} \cdot x_w = x_v
|
3,913 |
x \cdot 3/2 = 2/3 + n \Rightarrow x = (2/3)^2 + n \cdot 2/3
|
25,635 |
\frac{\partial}{\partial y} y^l = l \cdot y^{\left(-1\right) + l}
|
-25,053 |
5/10*\frac19*4 = 20/90 = \frac29
|
-18,416 |
\frac{-v + v^2}{2(-1) + v^2 + v} = \frac{v}{(v + 2) (v + (-1))}((-1) + v)
|
-20,317 |
3/5 \cdot \frac{1}{x + 3} \cdot (x + 3) = \frac{x \cdot 3 + 9}{5 \cdot x + 15}
|
12,824 |
x^2 \cdot C \cdot x^2 \cdot C \cdot C \cdot x^2 \cdot x^2 \cdot C \cdot C \cdot x \cdot x = (x^2 \cdot C)^5
|
-12,960 |
14 = 7 (-1) + 21
|
-3,563 |
\frac{k}{k^2} = \tfrac{k}{kk} = 1/k
|
43,460 |
|z+z_{0}|=|z-z_{0}+2z_{0}|\leq|z-z_{0}|+|2z_{0}|=|z-z_{0}|+2|z_{0}|<1+2|z_{0}|
|
-9,385 |
49 - 7r = -7r + 7\cdot 7
|
35,139 |
0 = x^2 + 2*i*x \Rightarrow x
|
30,721 |
1 + p^2 + p^4 = (1 + p^2)^2 - p \cdot p = (1 + p + p \cdot p)\cdot \left(1 - p + p^2\right)
|
-29,871 |
\frac{d}{dx} \left(5\cdot x^4\right) = 5\cdot d/dx x^4 = 5\cdot 4\cdot x^3 = 20\cdot x^3
|
47,579 |
90\cdot 8 = 720
|
33,041 |
x^3 = x^2 \cdot x = x \cdot x = x^2
|
-6,128 |
\dfrac{3}{\left(k + 9*(-1)\right)*(5*(-1) + k)} = \tfrac{3}{45 + k^2 - k*14}
|
28,967 |
\left(-1\right)^{k + (-1)} \left(-z\right)^k = \left(-1\right)^{k + \left(-1\right)} (-1)^k z^k = (-1)^{2 k + (-1)} z^k = -z^k
|
-23,992 |
\tfrac{1}{8 + 2} \times 30 = 30/10 = \frac{30}{10} = 3
|
936 |
\dfrac{1}{6^3}\cdot (91 + 1050 + 1134) = \dfrac{1}{216}\cdot 2275 \approx 10.53
|
16,918 |
B_1*F + F*B_2 - F*B_1 - B_2*F = F*B_2 - F*B_2 + F*B_1 - F*B_1
|
15,578 |
-\cos{\phi} = \sin(-\frac12\cdot \pi + \phi)
|
-3,052 |
(5 + 1 + 4)\cdot 10^{1/2} = 10\cdot 10^{1/2}
|
25,902 |
z^2 + z \times 2 + 1 = (z + 1)^2
|
32,222 |
4 + 6 + 2\left(-1\right) = 8
|
15,868 |
\frac{m \cdot f + h}{d + x \cdot m} = \frac{f \cdot m}{d + x \cdot m} + \tfrac{1}{d + x \cdot m} \cdot h
|
24,357 |
\cos{2*P} = \cos^2{P} - 1 - \cos^2{P} = 2*\cos^2{P} + (-1)
|
19,880 |
\frac{1}{4}(1 + 1 + 1 + 0) = \tfrac34
|
11,842 |
\frac{3*\cos{6*0}}{\cos{2*0}} = \frac{3*\cos{0}}{\cos{0}} = \frac{3}{1} = 3
|
13,295 |
(1 + y)^{2\cdot n} = \left(1 + y\right)^n\cdot \left(1 + y\right)^n
|
1,163 |
\dfrac{2^n\cdot n!}{n^n} = \frac{2\cdot n}{n^n}\cdot 2\cdot 4\cdot 6\cdot \dots
|
17,284 |
L = \frac{1}{4 - L}\Longrightarrow 1 \pm \frac{\sqrt{3}}{2} = L
|
2,390 |
r = \frac{1}{\cos(x) - 4\cdot \sin(x)}\cdot 4 \Rightarrow 4 = r\cdot \cos\left(x\right) - 4\cdot r\cdot \sin(x)
|
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