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ddrg
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math_formulas

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int64
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23,877
\sin(x) = \sin(\frac{1}{2} \cdot x + \frac{1}{2} \cdot x) = 2 \cdot \sin(x/2) \cdot \cos(\frac{x}{2})
-21,001
\frac{1}{-63}*\left(90*(-1) + 9*m\right) = \frac{1}{-7}*(10*\left(-1\right) + m)*\frac19*9
-2,013
\dfrac{25}{12} \pi = 7/6 \pi + \pi \frac{11}{12}
39,310
0 = h + a + x + g + d + v \Rightarrow h = -(a + x + g + d + v)
29,495
a^2 + h^2 = 0 \Rightarrow a = h = 0
19,336
n' f = f m \Rightarrow n' = f \frac1f m
11,579
\dfrac{1}{14}(21 + 30 + 10 + 12 + 3) = \frac{1}{14}76
10,498
\frac{x^2 + 4(-1)}{2(-1) + x} = 2 + x
19,964
y^2 + y^2 + 1 = y*y + y + y + y*y = y^2 + y + y + y * y + 1
-20,992
-14/2 = -7/1\cdot 2/2
-7,111
\frac{5}{8} \cdot 4/7 = \frac{5}{14}
17,030
x - d \lt \delta \implies x \lt \delta + d
-3,362
2\cdot 13^{\dfrac{1}{2}} + 13^{\tfrac{1}{2}} = 4^{1 / 2}\cdot 13^{\frac{1}{2}} + 13^{\frac{1}{2}}
17,448
x^4\cdot 2 + x^6 = ((-1) + x^4 + x^2)\cdot (x^2 + 1) + 1
-4,019
\dfrac{1}{q^2} \cdot q^3 \cdot 10/60 = \tfrac{q^3 \cdot 10}{60 \cdot q \cdot q}
23,258
(n \cdot 2)! = 2 \cdot n \cdot \left(n \cdot 2 + \left(-1\right)\right)!
-27,619
-25 + 21 + 4 \cdot \left(-1\right) + 25 = -25 + 25 + 21 + 4 \cdot (-1) = 0 + 21 + 4 \cdot (-1)
-14,450
4 + (7 \times 10) = 4 + (70) = 4 + 70 = 74
23,279
x = y + x*y rightarrow x = \dfrac{1}{-y + 1}*y
-18,364
\frac{(8\left(-1\right) + q) q}{(q + 8\left(-1\right)) (q + 5)} = \dfrac{1}{q^2 - q*3 + 40 (-1)}(-q*8 + q^2)
20,879
1/\tan(K) = \cot(K)
11,807
h^2 + b^2 + h^2 \cdot b^2 = (h - b)^2 + 2 \cdot h \cdot b + h^2 \cdot b^2 = 1 + 2 \cdot h \cdot b + h^2 \cdot b^2 = \left(1 + h \cdot b\right)^2
-3,512
2\cdot 4/(2\cdot 50) = \frac{1}{100}\cdot 8
24,450
\sqrt{(2 \cdot 3^3 \cdot 5)^2} \cdot \sqrt{2 \cdot 587} = \sqrt{2 \cdot 587 \cdot (2 \cdot 3^3 \cdot 5)^2}
13,089
\frac{5}{216} + \frac{2}{27} + 4/27 + 1/9 = 77/216
23,291
8 \cdot 8 = \left(1 + 3 + 3 + 1\right)\cdot 8
3,593
2\cdot \sin(F)\cdot \cos(F) = \sin(F\cdot 2)
19,731
\sum_{H=1}^e g = \sum_{H=1}^g e
49,753
124 = 2*62 = 2*2*31
5,911
a \cdot a - 4\cdot a + 5\cdot (-1) = (a + 5\cdot (-1))\cdot (a + 1) = 0\Longrightarrow a = -1, 5
26,998
\tfrac{4}{100000000} = 4.0*10^{-8}
-6,425
\frac{t}{(t + 10 \cdot (-1)) \cdot (t + 9)} = \frac{t}{90 \cdot (-1) + t^2 - t}
39,926
\beta*2 = 1.59549 = \beta*3
6,367
1/12 = \dfrac{1}{52} + 1/26 + 1/39
33,311
2^m = 2^{m + (-1)} + 2^{m + (-1)}
16,278
\left(1 + x\right)^{k + 1} = (1 + x)*(1 + x)^k \geq (1 + x)*(1 + k*x)
-19,667
\frac25 \cdot 7 = 14/5
30,581
|e^{i \cdot x} - e^{-i \cdot x}| = |2 \cdot i \cdot \sin\left(x\right)| = |2 \cdot \sin(x)| = 2 \cdot \sin\left(x\right)
7,669
(s - l)\cdot 4 = -\left(l - s\right)\cdot 4
19,168
-\dfrac{n}{n - k + 1} + \frac{n^2}{(n - k + 1) \cdot (n - k + 1)} = \frac{n\cdot (k + (-1))}{\left(1 + n - k\right)^2}
-19,674
\dfrac{24}{7} = 6 \cdot 4/(7)
18,218
0 = \left(1 - a\right) + (-a + 2)\Longrightarrow 1.5 = a
6,989
152 = 6^3 - 4^3 = 5 \cdot 5 \cdot 5 + 3^3
16,243
x + x^2 + \dotsm x^n = \frac{1 - x^n}{-x + 1} x
22,964
\tfrac{1}{x^2} \cdot x = \dfrac{1}{x}
1,347
2^{n + \left(-1\right)} = \dfrac{2^n}{2}
-6,400
\dfrac{1}{n^2 + n\cdot 16 + 63}\cdot 4 = \frac{4}{(n + 7)\cdot (9 + n)}
6,385
6*5*3*2*4 = 720
1,120
-BD \cdot D + DDB = D \cdot (-DB + BD)
19,491
-3\cdot (x - c) = (c + a + x)\cdot (x - c) \implies -3 = a + x + c
14,452
xd N = dxN
-7,569
\tfrac{-9 + i\cdot 21}{3 - 3 i} \frac{3 i + 3}{3 + 3 i} = \frac{-9 + i\cdot 21}{3 - 3 i}
41,303
79 = 80 + \left(-1\right)
36,266
2 \cdot 2^{n + (-1)} = 2^1 \cdot 2^{n + \left(-1\right)} = 2^{1 + n + \left(-1\right)} = 2^n
26,094
(h + b)^2 = h^2 + b b + 2 h b = h^2 + b b + h b = h + b + h b = h b
-24,984
3*\pi*2 = 6*\pi
-28,901
\dfrac{1}{2} \cdot (\sqrt{2}/2)^2 \cdot π = π/4
29,328
f\cdot z^2 + b\cdot z = -c \Rightarrow (z^2\cdot f + b\cdot z)^3 = (-c)^3
8,420
x^{\left(-1\right) + m}\cdot x^1 = x^m
20,998
h^2 - c^2 = (h + c)*(-c + h)
6,180
(\sin{\gamma} + \cos{\gamma})^2 = 1 + 2\cdot \sin{\gamma}\cdot \cos{\gamma} = 1 + \sin{2\cdot \gamma} = 1^2 = 1 \Rightarrow \sin{\gamma\cdot 2} = 0
25,453
\frac{1}{-xy + 1} = 1 + yx + \left(xy\right)^2 + \dots
17,163
\tan(x/2) = \frac{1}{1 + \cos(x)} \cdot \sin\left(x\right) = (1 - \cos(x))/\sin(x)
-20,058
\frac{-n\times 6 + 6\times \left(-1\right)}{n + 9}\times \frac{1}{9}\times 9 = \frac{-n\times 54 + 54\times (-1)}{9\times n + 81}
10,804
c^{-k + x} = \dfrac{1}{c^k}*c^x
54,554
807 = 3\times 269
-10,965
\dfrac12 \cdot 146 = 73
21,956
\frac{2\cos(0)}{\cos(0)}1 = 2
26,402
\frac{1}{2} \cdot \frac{3}{4} = \dfrac{1}{8} \cdot 3
11,892
5*\left(10^{800} + (-1)\right)/9 = \frac59 \left(10^{400} + (-1)\right) \left(1 + 10^{400}\right)
230
C^3 + D^3 = (D * D + C^2 - C*D)*(C + D)
27,409
s_1 b_1 + \dotsm + b_q s_q = b_1 s_1 + \dotsm + b_q s_q
12,387
10 * 10 = 7^2 + 5^2 + 4 * 4 + 3 * 3 + 1^2
-26,542
(10 + 3*x)*(10 - 3*x) = 100 - 9*x^2
24,990
2^{\frac{1}{2} \cdot p_1} \cdot (-\dfrac{1}{2} + p_2)^{\tfrac{p_1}{2}} = (\left(-1\right) + p_2 \cdot 2)^{\dfrac{p_1}{2}}
33,361
(f - b)*(f + b) = f * f - b * b
14,964
zx/100 = \frac{z}{100} x
8,949
2\times \sqrt{-2} + 1 = \left(-1 + \sqrt{-2}\right)\times (1 - \sqrt{-2})
28,778
2 \cdot 3 \cdot i + 5 = 2 \cdot 3 \cdot i + 4 + 1 = 2 \cdot \left(3 \cdot i + 2\right) + 1
-563
e^{\pi \cdot i/2 \cdot 10} = \left(e^{\frac{\pi}{2} \cdot i}\right)^{10}
-12,171
19/72 = s/\left(18\cdot \pi\right)\cdot 18\cdot \pi = s
14,847
\frac{\partial}{\partial x} (x \cdot x\cdot z) = \frac{\mathrm{d}}{\mathrm{d}x} x^2\cdot z + x^2\cdot \frac{\mathrm{d}z}{\mathrm{d}x} = 2\cdot x\cdot z + x \cdot x\cdot \frac{\mathrm{d}z}{\mathrm{d}x}
-28,841
7 \cdot z + 14 \cdot (-1) + 1.25 \cdot z = z \cdot 7 + 14 \cdot (-1) + z \cdot 1.25
28,459
\left(1 + \sqrt{2} + \sqrt{3}\right) \cdot \sqrt{i} = \sqrt{i} + \sqrt{i \cdot 2} + \sqrt{i \cdot 3}
28,891
|B_1 \cup B_1| = 1 + |B_1|
38,946
3^{10^{20}} = ...\cdot 8084427865522000000000000000000001
17,677
z^3 - 3 \cdot z^2 + 4 = z^3 + 1 - 3 \cdot z^2 + 3 = (z + 1) \cdot \dotsm - 3 \cdot (z^2 + (-1))
2,902
\left(y + z\right)\cdot (z^2 - z\cdot y + y^2) = z \cdot z \cdot z + y^3
24,364
(1 + y)^{n_2}*(1 + y)^{n_1} = (1 + y)^{n_2 + n_1}
-24,369
\dfrac{152}{9 + 10} = \dfrac{152}{19} = \dfrac{152}{19} = 8
26,468
10800 = 5 * 5*3^3*2^4
-27,629
-8 + 3\cdot (-1) + 8 + 3\cdot (-1) = -8 + 8 + 3\cdot (-1) + 3\cdot \left(-1\right) = 0 + 6\cdot \left(-1\right) = -6
14,465
\binom{5}{5}\cdot 4!\cdot 5!/4! = 120
2,595
1 + (3 (-1) + n) = 2 \left(-1\right) + n
-17,535
33 = 21\cdot \left(-1\right) + 54
-5,323
2.4 \cdot 10^5 = 2.4 \cdot 10^{3 - -2}
-7,364
\frac{1/5}{2} \cdot 4 = 2/5
4,970
\left(2 z + y\right) (y*2 + z) = 2 y y + 2 z^2 + y z*5
-15,510
\frac{g^4}{\frac{1}{l^3}*g^2} = \dfrac{g^4}{g^2*\dfrac{1}{l^3}}
6,213
a = x*A rightarrow a/A = x