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ddrg
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math_formulas

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int64
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21,555
\frac38 = 3/(2\cdot 4)
1,791
2 + f = f + (-1) + 3
-2,777
\sqrt{10}\cdot (2 + 4 + \left(-1\right)) = 5\cdot \sqrt{10}
50,346
\lim_{l \to 0} \sin{l} = 0 = \lim_{l \to 0} l
8,279
\sin{x\cdot a} = \sin{a\cdot x}
8,820
h \cdot x \cdot a = h \cdot x \cdot a
1,080
f\cdot a\cdot 2 = \left(a + f\right)^2 - a^2 - f^2
-4,375
\tfrac{1}{48}\cdot 56\cdot \frac{1}{a^3}\cdot a^4 = 7\cdot 8/\left(6\cdot 8\right)\cdot \dfrac{a^4}{a^3}
-20,174
\frac{1}{(-8)\cdot r}\cdot (9 + r)\cdot 7/7 = \left(7\cdot r + 63\right)/(r\cdot (-56))
-10,554
5/5 \cdot \frac{6 + 3 \cdot z}{3 \cdot z + 12 \cdot (-1)} = \frac{30 + z \cdot 15}{15 \cdot z + 60 \cdot (-1)}
-19,069
\frac{1}{40}\times 17 = G_r/\left(64\times \pi\right)\times 64\times \pi = G_r
30,516
\frac{24}{45} = \dfrac{1}{10!} (9!*2 + 2*8*8! + 8!*2*7)
20,162
-\pi/6 + \pi/2 = \frac{1}{3} \cdot \pi
-9,243
-60 y + 90 = 2 \cdot 3 \cdot 3 \cdot 5 - y \cdot 2 \cdot 2 \cdot 3 \cdot 5
13,076
(-B + A)*\left(B + A\right) = A^2 - B^2
8,389
z x = b a\wedge -b b + a a = x^2 - z^2 \Rightarrow z z - b^2 = x^2 - a^2
2,770
\frac{1}{10} = 2!\times 3!/5!
-9,248
-x \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot x \cdot x = -16 \cdot x^3
-4,731
-\frac{4}{3 + y} + \frac{2}{5 \left(-1\right) + y} = \frac{26 - 2 y}{15 (-1) + y^2 - y\cdot 2}
11,308
e^{(-1) - Q} = \frac1e\cdot e^{-Q}
-20,020
2/2\cdot 2/7 = \frac{1}{14}4
18,644
p^2 - q^2 = (-q + p) \cdot (p + q)
11,492
(10 + 6*(-1))/1 = (18 + 2)/5 = \frac17*\left(26 + 2\right)
-11,513
i\cdot 2 - 10 = -6 + 4\cdot \left(-1\right) + 2\cdot i
7,917
\frac{1}{12} - 1/60 = \frac{1}{15} = 1/(3*5)
26,801
21^2 \times 5 \times 3 + 5^2 \times 21 \times 3 + 5^3 = 8315
31,028
(y^a)^{\frac1g} = y^{a/g} = (y^{\frac{1}{g}})^a
12,768
k^4 + 4\cdot k \cdot k \cdot k + 8\cdot k^2 + 8\cdot k + 4 = (k^2 + 2\cdot k + 2)^2 = (\left(k + 1\right)^2 + 1)^2
27,365
|x| \lt 4 \Rightarrow |x|^2 < 16
32,648
((-1) \cdot (-1))^{\frac{1}{4}} = 1
7,775
-(l^2 + (-1))^2 + \left(1 + l^2\right)^2 = 4\cdot l^2
19,674
\left(a - b\right) \left(a - b\right) = b^2 + a^2 - a b*2
-11,797
\frac{1}{8}\cdot 27 = (3/2)^3
2,451
\operatorname{E}\left(B\right)\cdot \operatorname{E}\left(F\right) = \operatorname{E}\left(B\cdot F\right)
785
1/30 = 2/3*\dfrac15/4
20,604
158311 = 8^6 + 10^5\cdot 9 - 8\cdot 9^5 + 9^6
12,305
\frac{1}{2} + \frac{1}{4} + \frac18 + ... = 1
18,710
\alpha^4 + x^4 = (x^2 + \alpha^2)^2 - 2 \cdot (x \cdot \alpha)^2
2,543
-81*12 + (1 + 12)*75 = -81*12 + 75*13
-17,897
31 = 24 + 7
26,930
\frac{1}{2}\cdot (\sqrt{5} + 1) = 1/2 + \sqrt{5}/2
24,966
x = 2 + e^z\Longrightarrow \frac{\mathrm{d}x}{\mathrm{d}z} = e^z = x + 2*(-1)
8,229
-\dfrac{1}{2^x} + 1 = \tfrac{1}{2} + \frac{1}{2 \cdot 2} + \ldots + \frac{1}{2^x}
32,636
\frac{\partial}{\partial z} \operatorname{asin}\left((z + b)/a\right) = \frac{1}{a \times (1 - \dfrac{1}{a^2} \times \left(z + b\right)^2)^{1/2}} = \frac{1}{(a^2 - \left(z + b\right)^2)^{1/2}}
-17,336
\dfrac{50.3}{100} = 0.503
-2,811
\sqrt{6} + \sqrt{25*6} = \sqrt{150} + \sqrt{6}
12,937
G^2\times I = H^2\times I \implies H\times I = I\times G
29,776
a + \left(-1\right) + \dfrac{99}{9} = a + 10
10,236
x \cdot b \cdot z = x \cdot z = x \cdot b \cdot z
20,178
\frac{\pi}{12} = \frac{\tfrac16}{2}\pi
17,383
-n + 2 \cdot d = d - n - d
31,046
det\left(A_1 \cdot \cdots \cdot A_n\right) = det\left(A_1\right) \cdot \cdots \cdot det\left(A_n\right)
15,804
\ln(2) \ln(n) = \ln(2) \ln(n)
-22,367
48\cdot \left(-1\right) + y^2 - y\cdot 2 = (6 + y)\cdot (8\cdot (-1) + y)
16,112
-\tanh^2{V} + 1 = \frac{d}{dV} \tanh{V}
-20,786
\frac{-l \cdot 10 + 7}{-l \cdot 10 + 7} \cdot 9/1 = \frac{-90 \cdot l + 63}{-10 \cdot l + 7}
16,423
(z + 2(-1)) (\bar{z} + 2) = z\bar{z} + 2\left(z - \bar{z}\right) + 4(-1) = |z|^2 + 4\left(-1\right) + 4i\Im{(z)}
-3,662
\frac{1}{r^4}\cdot r\cdot \frac{63}{70} = \frac{r}{r^4}\cdot \frac{63}{7\cdot 10}\cdot 1
-2,610
250^{1/2} - 40^{1/2} = \left(25\cdot 10\right)^{1/2} - \left(4\cdot 10\right)^{1/2}
31,076
55/42 = \frac{49}{42}\cdot 44/42\cdot \frac{1}{42}\cdot 45
16,580
\frac{y}{15}\cdot 2 = \frac{2}{15}\cdot y
8,363
-\cos(\pi) - -\cos(0) = 2
5,739
7\cdot h = 2\cdot h\cdot 4 - h
3,554
\sqrt{\overline{y}} = \sqrt{|y| \cdot e^{-i \cdot \phi}} = \sqrt{|y|} \cdot e^{((-1) \cdot i \cdot \phi)/2}
-29,319
-7 - 17 i = 3 + 10 (-1) - i*17
23,225
9\cdot x + 5\cdot z + 4\cdot (x\cdot 2 + 3\cdot z) = x\cdot 17 + 17\cdot z
-13,501
2 \times 9 + 10 \times \dfrac{ 30 }{ 5 } = 2 \times 9 + 10 \times 6 = 18 + 10 \times 6 = 18 + 60 = 78
-9,667
\frac25 = \frac{10}{25}
3,600
(x + y)^3 \geq x^3 + y^3 = 2\Longrightarrow 2^{\frac13} \leq x + y
-5,390
39.6\cdot 10^{5 - 4} = 10^1\cdot 39.6
-11,310
(x + 6 \cdot (-1))^2 + b = (x + 6 \cdot (-1)) \cdot (x + 6 \cdot (-1)) + b = x \cdot x - 12 \cdot x + 36 + b
-20,233
\dfrac11 \cdot 1 = \tfrac{1}{-7 \cdot z + 10} \cdot \left(-7 \cdot z + 10\right)
-4,640
\dfrac{-6\cdot x + 21}{20\cdot (-1) + x^2 - x} = -\dfrac{1}{5\cdot (-1) + x} - \dfrac{5}{x + 4}
19,063
\frac{1}{w - z} = \frac{1}{\left(w - z\right) \cdot \left(w - z\right)}
-10,263
-\frac{8}{20\cdot x^3}\cdot \frac{5}{5} = -\frac{1}{100\cdot x^3}\cdot 40
5,471
-\sqrt{5}/2 + \frac12 = \dfrac{1}{2} \cdot (1 - \sqrt{5})
1,770
x^2 + \left(z + 1\right) (z + (-1)) = x^2 + z^2 + \left(-1\right)
-23,043
-3/2 \cdot (-\frac{21}{2}) = \frac{1}{4} \cdot 63
10,047
1 - \frac{1}{2^{32}} = \frac{1}{2^{32}} \times (2^{32} + (-1))
-14,275
10 + (5 \times 2) = 10 + (10) = 10 + 10 = 20
24,915
b*(a + b) = (b + a) b
3,228
r \cdot \delta_{i \cdot j} = \delta_{j \cdot i} \cdot r
-26,423
4^{11}/(\tfrac{1}{65536}) = 4^{11 - -8} = 4^{19}
2,571
\frac{1}{2}(4 \cdot 4 - 3^2 + 2^2 - 1^2) = 5
-24,851
\int \frac{1}{x^3}\,\mathrm{d}x = \dfrac{1}{x^2*(-3 + 1)} + C = -\frac{1}{2 x^2} + C
-17,213
-\frac{1}{9}4 = -\frac49
23,557
-c^3 + a^3 = (a - c)*\left(a^2 + a*c + c^2\right)
8,676
y^5 = 1^2\cdot y^1\cdot y^2 \cdot y^2 = 1^1\cdot y^2 \cdot y\cdot (y \cdot y)^1 = 1^0\cdot y^5\cdot (y^2)^0
691
210 = 495 - 5*{7 \choose 3} + {5 \choose 3}*7 + {7 \choose 4} + {5 \choose 4}
18,615
F^{30} = (F^{15})^2 = (\frac{F^{16}}{F})^2
12,131
4/3 \cdot 9/8 \cdot \frac{6}{\pi^2} = \frac{1}{\pi^2} \cdot 9 \approx 0.91189
-20,355
\frac{1}{4(-1) + 2z}\left(9z + 18 (-1)\right) = \frac92 \frac{1}{z + 2(-1)}(2\left(-1\right) + z)
669
y \in \left[0, 1\right] \Rightarrow \left\{y\right\} = y
40,310
y^x = y^{x + (-1)} \cdot y = 2^{(x + (-1))/2} \cdot y
18,988
5/11 = 1 - \tfrac{1}{11}\cdot 6
47,189
6\times 2=12
30,340
x + 20 \cdot (-1) + 20 = x
14,808
1 - \dfrac{1}{1 + x}*2 = \frac{x + (-1)}{1 + x}
8,270
0.54 \cdot N = 0.6 \cdot z + 0.4 \cdot \left(-z + N\right) \Rightarrow z = 0.7 \cdot N
36,074
\tfrac{{6 \choose 2}}{{7 \choose 3}} = \frac{15}{35} = \tfrac{1}{7}*3