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ddrg
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math_formulas

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int64
-30,985
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22,156
\frac{3 - 1 + 2 + 4}{1\cdot 2 - 3\cdot 4} = \tfrac{4}{-10} \neq 0
1,934
140 + 85 (-1) = 55
1,158
\tfrac{1}{0} 0 = 0
9,514
(z - N)\cdot (N + z) = z^2 - N^2
-22,350
18 + x^2 - x\cdot 11 = \left(x + 9\cdot (-1)\right)\cdot \left(x + 2\cdot (-1)\right)
-19,465
5*1/4/(\frac14*3) = 4/3*\dfrac145
20,711
\sin(\theta) \times \cos(\theta) \times 2 = \sin(\theta \times 2)
-22,001
7/4 - 7/5 = \frac{7 \times 5}{4 \times 5} - \frac{7 \times 4}{5 \times 4} = 35/20 - 28/20 = \frac{1}{20} \times (35 + 28 \times (-1)) = \frac{7}{20}
18,958
p + d = 2\left(d - ldl\right) \Rightarrow p = -2ld l + d
1,638
(y^9\cdot y^3)^2 = y^{24}
35,434
51\times 52/2 = 1326
23,257
c^5 + b^5 = (b + c) (b^4 + c^4 - c^3 b + b b c^2 - b b b c)
23,526
1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 2^0 \cdot 0 = 10
-29,594
\frac{\mathrm{d}}{\mathrm{d}x} (3x^4) = 3\frac{\mathrm{d}}{\mathrm{d}x} x^4 = 3\cdot 4x^3 = 12 x^3
22,909
\frac{1}{2} = 3/4\cdot 2/3
17,237
k/j = \frac{j}{i} = \frac{k - j}{j - i}
22,828
\frac34 = \dfrac{2 + 1}{2 + 2}
-11,518
-20 + 3\times \left(-1\right) + i\times 11 = 11\times i - 23
-21,066
\frac13 = \dfrac16*2
-10,460
\frac{1}{50 \cdot k + 50} \cdot (25 \cdot k + 35 \cdot (-1)) = \dfrac{1}{10 \cdot k + 10} \cdot (5 \cdot k + 7 \cdot (-1)) \cdot \dfrac{5}{5}
47,023
\frac{1 + i + 1}{2 + 2\cdot i} = (1 - \frac{1}{(i + 1) \cdot (i + 1)})\cdot \left(i + 1\right)/(2\cdot i)
-5,082
10 \cdot 10^2 \cdot 18.0 = 18 \cdot 10^{2 + 1}
8,227
6/49 + 1/7 = \frac{1}{49} \cdot 13
2,217
5!*4/2! = 4^5 - \binom{4}{1}*3^5 + \binom{4}{2}*2^5 - \binom{4}{3}*1^5
-1,424
\left(1/3\cdot (-4)\right)/(\tfrac{1}{8}\cdot (-7)) = -4/3\cdot (-\frac17\cdot 8)
4,044
\frac{\partial}{\partial z} \tan^l{z} = \tan^{l + (-1)}{z} l
35,579
25^{l + 2} - 5^{2\times l + 2} = 5^{2\times l + 2}\times ((-1) + 25)
13,609
16 \cdot 14 \cdot 13 \cdot 12 \cdot 15 = \binom{16}{5} \cdot 3 \cdot 2 \cdot 4 \cdot 5
661
\mathbb{Var}[R] = \mathbb{E}[(R - \mathbb{E}[R])^2] = \mathbb{E}[R^2] - \mathbb{E}[R] \cdot \mathbb{E}[R]
8,173
\sqrt{6} \sqrt{30} = \sqrt{5} \cdot 6
54,137
219 = 3*73
30,452
5\cdot e = 5\cdot e + 0\cdot (-1) = 5\cdot e - 5\cdot 0
-2,457
\left(5 + 3(-1)\right) \sqrt{5} = 2\sqrt{5}
418
0.9999998 = \dfrac{1}{10^7}\cdot 9.999998 = \frac{1}{5\cdot 10^6}\cdot 4999999
41,240
263^{16} = \left(263^8\right)^2 = 22890010290541014721 * 22890010290541014721
11,438
0 = \dfrac{2\cdot 0^2}{0 + 3}
12,114
y'^2 - zy' + x = 0\Longrightarrow \dfrac{1}{2}(z \pm (z \cdot z - x \cdot 4)^{\frac{1}{2}}) = y'
-19,318
3/4\cdot \dfrac{3}{7} = 3\cdot 3/\left(4\cdot 7\right) = 9/28
3,439
(x - y) \cdot z = z \cdot x - y \cdot z
-19,413
\dfrac25\cdot \dfrac58 = 2\cdot 5/(5\cdot 8) = 10/40
20,497
u*(-x) = -ux
-20,678
\frac{16}{32 - 16 t} = 8/8*\frac{1}{4 - 2t}2
12,369
-x^2\times a = -a\times x^2
8,251
\left(2/5 = \frac{3 z - y}{-y + 7 z} \Rightarrow -2 y + z \cdot 14 = z \cdot 15 - y \cdot 5\right) \Rightarrow z/3 = y
29,140
D\cdot t = D\cdot t
12,911
z^4 + (-1) = \left(1 + z^2\right) \cdot (z + (-1)) \cdot (z + 1)
31,778
17! = 17*16*15*\dotsm*2
1,167
(x - q)/x*\frac{q}{(-1) + x} = \dfrac{1}{-x + x^2}*(-q^2 + q*x)
-15,916
-\frac{58}{10} = 5/10 - \frac{9}{10} \cdot 7
-30,638
14 (-1) - z*6 = -2*\left(7 + 3z\right)
5,796
\left|{A}\right| = \left|{G}\right| \left|{A}\right| = \left|{GA}\right|
19,366
|z| \gt 1\Longrightarrow 1/|z| < 1
-4,352
\dfrac{44\cdot m^5}{22\cdot m^2} = 44/22\cdot \frac{m^5}{m^2}
35,917
\sqrt{d} \cdot \sqrt{d} = d
4,255
x^9 + \left(-1\right) = (x^3 + \left(-1\right))\cdot \left(x^6 + x \cdot x \cdot x + 1\right) = (x + (-1))\cdot (x^2 + x + 1)\cdot (x^6 + x^3 + 1)
23,656
7^2 \times 3^5 \times 43 = 1 + 80^2 \times 80
13,862
(1 + x)^{k + 1} = (1 + x)\cdot (1 + x)^k \geq (1 + x)\cdot (1 + k\cdot x) = 1 + (k + 1)\cdot x + k\cdot x^2 \geq 1 + (k + 1)\cdot x
22,966
(1 + x \cdot x - x)\cdot (x^2 + x + 1) = 1 + x^4 + x^2
-3,867
t^4*90/(10*t) = 90/10*t^4/t
38,946
\dotsm*8084427865522000000000000000000001 = 3^{10^{20}}
-5,488
\frac{p}{(p + (-1)) (p + 4(-1))}2 = \frac{2p}{4 + p^2 - p \cdot 5}
15,472
\|G\|_2^2 = \|G^H*G\|_2 \leq \|G^H\|_2*\|G\|_2
35,337
|F_2 \cdot F_1| = |F_2| \cdot |F_1|
20,936
\cos{ny} = \cos{-yn}
-1,325
(\left(-5\right)*\tfrac{1}{7})/\left((-9)*1/2\right) = -5/7*(-\dfrac29)
14,184
2^n\times n! = 2\times 4\times 6\times \dotsm\times n\times 2
5,770
m*k = --m*k = --m*k = --m*k = (-1)*\left(-m\right)*k = m*k
9,346
\mathbb{Var}(X - Y) = \mathbb{Var}(X + Y)
-2,500
\sqrt{2}\cdot (2\cdot (-1) + 4 + 5) = \sqrt{2}\cdot 7
15,442
(B + D) \cdot X = D \cdot X + B \cdot X
-30,561
\dfrac{1}{48}\cdot 96 = 48/24 = \frac{1}{12}\cdot 24 = 2
20,249
10 \cdot \dfrac{1}{123456} \cdot 654321 = 6 \cdot 9 + (-1) + \frac{42}{123456} \cdot 1 \approx 53
2,317
\left(x \lt 3 \Rightarrow 9 - 2 \cdot x \leq x\right) \Rightarrow x \geq 3
10,565
(1 + x \cdot x)\cdot (1 + x)\cdot \left(x + (-1)\right) = x^4 + \left(-1\right)
10,819
\sin{H*3} = \sin{3*H}
3,160
2 + 7 + 25/2 + 4 + 8 = \frac{1}{2}\cdot 67
12,066
-k*\left(-1\right) + m = m + k
16,667
{13 \choose 1} \cdot {12 \choose 1} = {13 \choose 2} \cdot 2
5,031
{i + (-1) \choose 2} = (i + (-1))\cdot (2\cdot (-1) + i)/2
16,238
6132 = {4 \choose 2} \cdot (2 \cdot \left(-1\right) + 2^{10})
12,449
3165 = (3\cdot 2^{10} + 93)
-1,570
\dfrac47 = 4/7
20,008
\frac{1}{(-q + 1)^2}(nq^{n + 1} + 1 - (1 + n) q^n) = 1 + 2q + 3q^2 + \dotsm + q^{n + (-1)} n
36,898
(c \cdot c + x \cdot x + xc) (x - c) = x^3 - c^3
41,848
672 = -2\cdot 4! + 6!
-20,995
\dfrac{1}{8} \times \dfrac{6t + 4}{6t + 4} = \dfrac{6t + 4}{48t + 32}
5,529
C^3 B^3 = B^3 C^3
7,177
5x = 2x + 3x
-27,500
2 \cdot 7 \cdot h \cdot h \cdot h = 14 \cdot h^3
-9,780
24\% = 24/100 = 0.24
28,085
F_l + F_n = F_l + F_n
2,167
(1 + r)^2 - r^2 = 2\cdot r + 1
-16,309
729^{\frac{1}{3}} = 729^{\frac13} = 9
32,259
a^m = a\cdot a^{m + (-1)} = a^{m + (-1)}\cdot a
3,382
4 + 3^{1/2}*2 = (1 + 3^{1/2})^2
-11,634
-8 \times i + 4 = 4 + 0 \times (-1) - i \times 8
606
\tfrac{1}{1 + 2\cdot g^2\cdot a} = 1 - \frac{2\cdot g^2\cdot a}{1 + 2\cdot g^2\cdot a} \geq 1 - \dfrac{a\cdot g}{\sqrt{2\cdot a}}\cdot 1
3,558
\frac{y^2}{y^2} = \frac{y^2}{y^2}
21,426
95/100 = 19/20
7,273
\dfrac{\pi}{4 \cdot 5^{1/2}} = \frac{5^{1/2} \cdot \pi \cdot 2}{4 \cdot 10} \cdot 1