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ddrg
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math_formulas

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int64
-30,985
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16,249
-\frac{1}{2} = 1 + 1 + 1 + 1 + 1 + \dotsm
12,398
4*11!*41!/52! = \frac{{4 \choose 3}}{{52 \choose 11}}
-26,135
e^7 \cdot 7 - \frac{1}{e^{14}} \cdot 7 = 7 \cdot \left(e^7 - \dfrac{1}{e^{14}}\right)
-469
\left(e^{i*\pi*19/12}\right)^{20} = e^{19*\pi*i/12*20}
-2,589
27^{1 / 2} + 75^{1 / 2} = (25\cdot 3)^{1 / 2} + (9\cdot 3)^{\frac{1}{2}}
8,815
\lambda < y rightarrow y/2 \gt \tfrac{\lambda}{2}
11,789
v - P(v) + P(v) = v
23,383
\frac{4}{51}*48/52 + 3/51*4/52 = 4/52
24,957
z^{a - b} = \frac{1}{z^b}z^a
40,070
Q*I = I = I*Q
18,548
\dfrac{2\cdot \pi}{1/6\cdot \pi} = 12
-10,459
\frac{8}{20\times (-1) + p\times 16}\times \frac15\times 5 = \frac{40}{80\times p + 100\times (-1)}
-7,047
\dfrac{1}{4} \cdot 1 / 5 = \frac{1}{20}
-22,332
\left((-1) + s\right)\cdot (s + 5) = 5\cdot (-1) + s^2 + s\cdot 4
13,592
(a + c)^2 = a^2 + c^2 = a + c
18,197
(x \cdot x + (-1))^3 = x^6 - 3 \cdot x^4 + 3 \cdot x^2 + (-1)
-11,505
-i \times 20 - 8 = -8 + 0 \times (-1) - i \times 20
21,365
b^p \frac{1}{0! p!}p! = b^p
31,749
(1 + 1) \cdot \left(a + c\right) = a + c + a + c = a + c + a + c
622
\dfrac{1}{(1 + \frac1y) y} = \frac{1}{1 + y}
-2,277
\frac{1}{14} \times 3 = -3/14 + \frac{6}{14}
-11,535
-i\cdot 2 + 15 + 8 = -i\cdot 2 + 23
-30,629
4 \cdot (-1) + z \cdot 12 = 4 \cdot (3 \cdot z + (-1))
110
d \cdot a \cdot 2 + a \cdot a + d^2 = \left(d + a\right)^2
-20,940
\frac{54*z + 81*\left(-1\right)}{-24*z + 36} = -9/4*\frac{-z*6 + 9}{-z*6 + 9}
-26,613
(-9\cdot x + k\cdot 7)^2 = 49\cdot k^2 - k\cdot x\cdot 126 + 81\cdot x^2
7,531
(z + a)\cdot (h + z) = z^2 + (a + h)\cdot z + a\cdot h
8,779
(n * n*2 + z^2 - 2nz) (z^2 + 2nz + n^2*2) = n^4*4 + z^4
-19,996
12/2 = 2/2 \cdot 6/1
40,961
a/x := a/x
12,845
1/9 = \frac{2}{6}*\frac{1}{6}2
-11,938
4.838\cdot 0.001 = \frac{1}{1000}4.838
11,901
\frac{2 + \zeta + (-1)}{((-1) + \zeta) (\zeta + 1)} = \frac{1}{(-1) + \zeta}
-10,515
-6/(k\cdot 15)\cdot \frac44 = -24/(60\cdot k)
-7,788
8/2 + i \cdot 4/2 = \left(8 + 4 \cdot i\right)/2
14,989
g^4 \cdot 4 + c^4 = (c^2 - 2gc + 2g^2) (g^2 \cdot 2 + c^2 + 2gc)
-6,721
8/100 + \dfrac{4}{10} = 40/100 + 8/100
14,978
(1 - x - z)^2 = x^2 + z^2 \Rightarrow (-1) + 2\cdot x + z\cdot 2 = 2\cdot z\cdot x
24,838
\mathbb{E}[U*V] = \mathbb{E}[V]*\mathbb{E}[U]
-11,493
i\times 36 + 16 + 20\times (-1) = 36\times i - 4
-22,152
24/9 = \dfrac{8}{3}
1,856
4^2 \cdot 5 + 1 = 9^2
25,431
2^k \cdot 3 = 2^k + 2^k + 2^k
23,657
z = x\Longrightarrow x \approx z
-3,102
3\cdot 5^{1/2} + 5^{1/2}\cdot 5 = 25^{1/2}\cdot 5^{1/2} + 5^{1/2}\cdot 9^{1/2}
27,024
3^2 + 6(-1) = 9 + 6(-1) = 3
18,622
(x^4 - z^4) (x^4 - z^4) + (2 x^2 z^2)^2 = \left(z^4 + x^4\right)^2
39,359
5^{2\cdot A} = (5^2)^A = 25^A
27,496
\sin{y \cdot \pi} = \sin{\pi \cdot y/2} \cdot \cos{y \cdot \pi/2} \cdot 2
37,704
\frac{1}{8!} = 1/40320 \approx 2.5\cdot 10^{-5}
-9,399
s \cdot 2 \cdot 2 \cdot 2 \cdot 3 + 2 \cdot 3 \cdot 3 = 18 + 24 s
7,684
\left(A\cdot Z\right) \cdot \left(A\cdot Z\right) = Z \cdot Z\cdot A^2
-8,035
\frac12 \cdot (5 + 3 \cdot i + 5 \cdot i + 3 \cdot (-1)) = (2 + 8 \cdot i)/2 = 1 + 4 \cdot i
-17,843
6 = 15 + 9*(-1)
9,224
|\lambda \mu| = |\mu| |\lambda|
-25,807
1*2/(6*7) = 2/42
6,385
6*4*2*3*5 = 720
-729
\frac{\pi}{4} = -\pi \cdot 26 + \dfrac{105}{4} \cdot \pi
3,529
\dfrac{1}{2} \cdot (3 \pm \sqrt{-4 \cdot (3 - i) + 9}) = \left(3 \pm \sqrt{-3 + i \cdot 4}\right)/2
13,650
f_1^2 + f_2 \cdot f_2 = \dotsm = f_1^2\cdot f_2^2
27,266
r\cdot x\cdot r = x\cdot r^2
13,298
5^2 + 5^2 = \left(4 \cdot 4 + 3^2\right)\cdot 2
25,782
\sin(z\cdot 2) = 2\cos(z) \sin\left(z\right)
2,121
(\left(x^3 + 2 + x + x^2\right)^{1 / 2} + 1)^{\frac{1}{2}} = v \Rightarrow 2 + x + x^2 + x \cdot x^2 = (v^2 + (-1))^2
21,416
\pi \cdot 2/(\frac1b) = \pi \cdot b \cdot 2
-17,538
27 \cdot \left(-1\right) + 36 = 9
2,120
25 = x^2 + y^2 \implies y = \sqrt{25 - x^2}
-2,467
\sqrt{7} \cdot (1 + 5) = 6 \cdot \sqrt{7}
-17,200
\dfrac{1}{\cos^2{x}} \cdot (1 - \sin^2{x}) = \tfrac{\cos^2{x}}{\cos^2{x}}
6,730
g^{b_2}*g^{b_1} = g^{b_2 + b_1}
22,611
7 \cdot ((-1) + 2 \cdot 4)^2 = 2 \cdot (2 \cdot 7 + \left(-1\right))^2 + 5 \cdot ((-1) + 2)^2
-2,489
-3\cdot \sqrt{2} + \sqrt{2}\cdot 2 + \sqrt{2}\cdot 5 = -\sqrt{9}\cdot \sqrt{2} + \sqrt{2}\cdot \sqrt{4} + \sqrt{25}\cdot \sqrt{2}
11,272
i - 1 = C\cdot i \implies C = 1 + i
-5,204
\frac{1}{1000}\cdot 0.33 = \frac{0.33}{1000}
8,103
4 x^2 - x^2 = 4 x^2 - x^2 = \left(4 + (-1)\right) x^2 = 3 x^2
22,246
\frac{1}{(k + 2)!}\times (2\times k + 2)! = (k + 3)\times \left(k + 4\right)\times \dots\times (2\times k + 2) \gt (k + 2)\times \dots\times (k + 2)
15,671
\frac{1}{y + 3}*\left(y + 2\right) = \frac{1}{y + 3}*(y + 3 + (-1)) = 1 - \frac{1}{y + 3}
6,876
(y - d)^2 + g \cdot g = y^2 - 2 \cdot y \cdot d + d^2 + g^2
-11,790
(\dfrac{1}{125})^{1/3} = 125^{-1/3}
36,007
15/16 + \dfrac{3}{64} = 63/64 = 1 - \tfrac{1}{64}
7,777
\frac13((-1) r) + r - r/3 = r/3
28,103
\sin{l} = \frac{1}{2 \cdot i} \cdot \left(e^{i \cdot l} - e^{-i \cdot l}\right) \cdot \cos{l} = (e^{i \cdot l} + e^{-i \cdot l})/2
-30,274
\frac{1}{2} \cdot (8 - 4) = \frac{1}{2} \cdot 4 = 2
26,447
i^{12} = i^4 \times i^4 \times i^4
15,412
g\times U = U = U\times g
1,012
n + (-1) + n + 2 \cdot (-1) + n + 3 \cdot (-1) = 6 \cdot (-1) + n \cdot 3
35,712
-\frac{1}{10} + \dfrac{1}{30} + \dfrac{1}{15} = 0
7,021
2x + 2 = (1 + x)^2 - x^2 + 1
50,342
\frac{1}{2!}\cdot 4! = 4\cdot 3 = 12
21,091
2 \sin{b} \cos{b} = \sin{b \cdot 2}
15,977
\dfrac{1}{x + (-1)}*(x * x * x + (-1)) = x^2 + x + 1
-2,220
10/17 - 9/17 = \frac{1}{17}
-2,333
\dfrac{6}{11} = 10/11 - 4/11
13,740
\left(i + 2\right) \cdot (i + 2 \cdot (-1)) = i^2 + 4 \cdot (-1)
10,857
-\frac{1}{36} + 1 = \dfrac{1}{6^2}*(6^2 - 1^2)
29,695
(x^T G x)^T = x^T G^T x = -x^T G x
-18,388
\frac{s^2 + s\cdot 3}{9(-1) + s^2} = \tfrac{(3 + s) s}{(3(-1) + s) \left(3 + s\right)}
-16,747
-5 = -5\cdot 4\cdot y - -30 = -20\cdot y + 30 = -20\cdot y + 30
20,554
C = y*H_1 + y*H_2 \Rightarrow y*(H_2 + H_1) = C
6,468
\frac{d}{dt} e^E = E \times e^E = e^E \times E