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ddrg
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math_formulas

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1
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int64
-30,985
55.9k
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437k
13,506
-2x + T = -(-T + 2x)
-26,474
(g - d)^2 = d^2 + g^2 - 2*d*g
-2,480
5*\sqrt{6} - \sqrt{6} + 3*\sqrt{6} = \sqrt{25}*\sqrt{6} - \sqrt{6} + \sqrt{9}*\sqrt{6}
-10,653
\frac{135}{45 + 15 s} = 15/15*\dfrac{9}{3 + s}
28,004
33*3 + 84 = 183
-626
\pi*65/12 - \pi*4 = \frac{17}{12} \pi
49,517
4*9^3 = 2916 < 10000
-24,369
\frac{152}{9 + 10} = \dfrac{152}{19} = \tfrac{1}{19}152 = 8
-11,942
9.801*0.1 = \tfrac{9.801}{10}
11,545
2 \cdot \cos{2 \cdot q} \cdot \sin{2 \cdot q} = \sin{4 \cdot q}
-20,888
(x \cdot 81 + 18 \cdot (-1))/(-36) = (x \cdot 9 + 2 \cdot (-1))/(-4) \cdot 9/9
18,169
(4*y^2 + y - 21/2)*2 = y * y*8 + y*2 + 21*\left(-1\right)
-18,422
\dfrac{-z + z^2}{3\cdot (-1) + z^2 + 2\cdot z} = \frac{\left(z + (-1)\right)\cdot z}{(z + 3)\cdot (z + (-1))}
35,449
(-1) + k^2 = (1 + k)\cdot ((-1) + k)
16,623
\frac{1}{35} = \dfrac16\times 2\times 3/7/5
10,267
(g + a) \cdot \left(a - g\right) = a \cdot a - g^2
24,537
k_1^2 + k_2^2 = k_1 * k_1 + k_2^2 + a^2 + g^2 - (k_1 - a)^2 + (k_2 - g)^2 = 2*a*k_1 + 2*g*k_2
21,265
7 = \sqrt{13}\cdot \sqrt{(36 + 13)/13}
14,755
det\left(A\cdot X + I\right) = det\left(X\cdot A + I\right)
4,362
p_1*\ldots*p_k = p_1^2 + \ldots*p_k^2
11,036
\sqrt[2]{(x+1)^1} = (x+1)^\frac{1}{2}
-30,582
-z\cdot 14 + 21\cdot (-1) = -7\cdot (3 + 2\cdot z)
32,459
FBC = BCF = CBF
15,703
26\times \left(26\times (-1) + 62\right)^7 = 26\times 36^7
3,387
\frac{8 + 5*(-1)}{-4 - -3} = 3/(-1) = -3
30,701
4^{\binom{n}{2}} = 2^{n^2-n}
13,629
(z^2 - z \cdot 2 + 3 \cdot (-1)) \cdot 2 = 6 \cdot \left(-1\right) + z^2 \cdot 2 - z \cdot 4
33,989
E \cdot Z = Z \cdot E
-1,688
-\dfrac56\cdot \pi = -\pi\cdot \dfrac54 + \frac{1}{12}\cdot 5\cdot \pi
19,520
(8^2 + 3)^{1/2} = 67^{1/2}
20,843
5 \cdot (-1) + 38 = 33
-7,446
\frac{3}{12} \cdot 6/11 = \frac{3}{22}
5,467
-\dfrac{1}{x + 2}\cdot (x + 2\cdot (-1)) = \dfrac{2 - x}{x + 2}
10,941
\cos{\alpha \cdot 2} = \left(-1\right) + 2 \cos^2{\alpha}
-3,470
\dfrac{9 \times 5}{20 \times 5} = \dfrac{45}{100}
20,918
z_2^2 = t \cdot t - m^2 \Rightarrow -(-m^2 + t^2)^{1 / 2} = z_2
3,867
1/2 = -\frac{1}{2^1} \cdot (2 + 1) + 2
-4,881
0.98*10^{9 + 4*(-1)} = 0.98*10^5
26,892
-34 = (-1)\cdot 2\cdot 17 = \left(-1\right) (-2) (-17)
-4,760
z^2 - z\cdot 3 + 2 = (z + 2\cdot (-1))\cdot (z + (-1))
2,460
\frac{d}{dx} \arctan(\cos\left(x\right)) = \frac{1}{\cos^2(x) + 1}(\sin(x) (-2))
-18,261
\frac{n\cdot 3 + n^2}{30\cdot (-1) + n \cdot n - n\cdot 7} = \dfrac{n\cdot (3 + n)}{(n + 3)\cdot (n + 10\cdot (-1))}
12,432
i\cdot w + x = d \implies x\cdot i - w = i\cdot d
17,526
\frac{1}{x \cdot b} = \frac{1}{b \cdot x} = b \cdot x
3,325
ab = \dfrac{1}{ab} = 1/(ba) = ba
32,317
c_2^2 = \tfrac{1}{c_2^8} \cdot c_1^8 \cdot c_1\Longrightarrow c_1^9 = c_2^{10}
-17,015
-6 = -6 (-x) - 24 = 6 x - 24 = 6 x + 24 (-1)
21,904
E[F_2] \cdot E[F_1] = E[F_1 \cdot F_2]
-6,634
\frac{4}{\left(t + 4\right)\cdot (t + 9\cdot (-1))} = \frac{4}{36\cdot (-1) + t^2 - 5\cdot t}
-1,457
63/45 = \frac{63*1/9}{45*1/9} = 7/5
35,834
4 + 2\cdot 3^{\tfrac{1}{2}} = 4 + 3^{1 / 2}\cdot 2
18,433
\frac{2 \cdot y + 1}{\sqrt{1 + 2 \cdot y}} = \sqrt{2 \cdot y + 1}
17,256
a + f + x + d = d + a + f + x
48,004
4 + 12 + 12 = 28
2,420
\sin(z) = \frac{2 \times \tan(z/2)}{1 + \tan^2(\frac{z}{2})} \times 1
-23,271
1/4 = -3/4 + 1
-12,908
15/24 = \frac18*5
-532
\tfrac{4}{3}*\pi = 22/3*\pi - 6*\pi
11,721
\frac{\partial}{\partial x} \left(e\cdot E\right) = e\cdot \frac{\text{d}E}{\text{d}x}
18,207
\frac{1}{C \cdot i} = \frac{1}{C \cdot i}
-26,321
4 = F \times e^{(-5) \times 0} = F
28,808
(-y + z \times 2) \times 3 = z \times 6 - 3 \times y
9,038
\frac{1}{x + 2*(-1)}*\left(x^3*2 - 10*x + 4\right) = x^2*2 + x*4 + 2*(-1)
23,050
5^0\times 2^1\times 3^2 = 18
-28,981
p\cdot 90 + p^2\cdot 10 = p\cdot (p\cdot 10 + 90)
-2,874
13^{1/2}*(3 + 1 + 4) = 13^{1/2}*8
16,105
4 \cdot (c + 3) = 4 \cdot c + 12
81
\left(\left(b > a \Rightarrow b + a \gt a + a\right) \Rightarrow 2a < b + a\right) \Rightarrow a \lt \frac{1}{2}\left(a + b\right)
6,997
c*a + b*a = \left(c + b\right)*a
-20,652
5/5\cdot \frac{1}{9 - 8\cdot k}\cdot ((-1)\cdot 10\cdot k) = \frac{(-1)\cdot 50\cdot k}{-40\cdot k + 45}
23,243
0\cdots \cdot 1.5 = 0
7,902
z_2 \cdot z_2 \cdot z_2 - z_1 \cdot z_1 \cdot z_1 = (-z_1 + z_2) \cdot \left(z_2^2 + z_1 \cdot z_2 + z_1^2\right)
20,176
-g\cdot g = -g^2
14,523
17^2 - 16^2 = 289 + 256\cdot (-1) = 33 = 49 + 16\cdot (-1) = 7^2 - 4 \cdot 4
5,214
f = B*z*X \Rightarrow B*z = \frac{1}{X}*f
8,840
(b + g)^2 = 2\cdot g\cdot b + g^2 + b^2
13,325
\frac{x^n}{g}\cdot g = \left(\frac{1}{g}\cdot x\cdot g\right)^n
45,476
k\cdot x = x\cdot k
-3,509
\frac{15}{100} = \dfrac{3 \cdot 5}{20 \cdot 5}
1,154
I \cdot J = 0 \Rightarrow I \cap J = 0
12,155
\left(x + (-1)\right)^2 = x^2 - 2\cdot x + 1
23,017
-11/12 - \dfrac{1}{12} = -\dfrac{12}{12} = -1
-5,014
9.1 \cdot 10^{5 + 3} = 10^8 \cdot 9.1
5,345
\frac{1}{2}*5 = \frac12*5
-2,862
-\sqrt{13}\cdot \sqrt{16} + \sqrt{13}\cdot \sqrt{25} = 5\cdot \sqrt{13} - 4\cdot \sqrt{13}
9,088
5.021*3.3942037 = \frac{1}{10000000}33942037*5021/1000
24,086
\sin^2(\alpha) = \cos^2(\alpha)/4 = \left(1 - \sin^2(\alpha)\right)/4
43,024
2000 = 6 \cdot 334 + 4 \cdot (-1)
27,209
\cos(\sin^{-1}(-x)) = \cos(-\sin^{-1}(x)) = \cos(\sin^{-1}(x))
4,357
q \cdot q \cdot q + 1 = (q + 1) \cdot \left(1 + q^2 - q\right)
-9,737
\tfrac{1}{10}(\left(-1\right) \cdot 1/4) (-\frac{1}{8}7) = \dfrac{(-1) (-7)}{10 \cdot 4 \cdot 8} = 7/320
9,167
2\cdot \cos{\frac14\cdot \pi}\cdot \sin{0} = 0
21,630
d - L + C = -(L + C) + d + C
3,622
\frac12*(\arccos{0} - \arccos{1}) = \dfrac{1}{4}*\pi
5,287
\dfrac{1}{12}(m^4 + m^2*8 + 3m^2) = \frac{m^4}{12} + m^2*11/12
36,131
20*48 = 960 > 874
20,288
\tfrac{7^{369}}{350} = \frac{1}{50}*7^{368}
-21,068
2/4 = 4/8
-5,462
\frac{1}{r \cdot 3 + 30} \cdot 2 = \dfrac{1}{3 \cdot (10 + r)} \cdot 2
-29,947
d/dz z^n = z^{n + \left(-1\right)} \cdot n