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ddrg
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math_formulas

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int64
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4,487
\left(\int \tfrac{x}{x + 2/\pi}\,\mathrm{d}x\right)/\pi = \int \frac{1}{x \pi + 2} x\,\mathrm{d}x
20,270
\frac{1}{2} \cdot (\left(-1\right) + 11) = 5
17,843
\frac{9}{9^2 + 11\cdot (-1)}\cdot \frac89 = 4/35 \approx 0.114285714285714
19,084
-x x + h^2 = (h - x) \left(h + x\right)
5,714
z_2 = i \cdot z_1 rightarrow \frac{z_2}{i} = z_1
9,502
\left(1 - \frac32\right)^2 = (2 - 3/2)^2
8,598
a^3 = a \cdot a \cdot a
7,257
-\dfrac{1}{100} \cdot 30 + \frac{10}{100} + 60/100 \cdot 0 = -0.2
54,289
197 = 49 + 148
2,086
35^{1/2} = (5 \cdot 5 + 3^2 + (-1)^2)^{1/2}
14,409
c \cdot h^n = c \cdot h^n
-3,043
\sqrt{25} \sqrt{11} + \sqrt{11} = \sqrt{11}*5 + \sqrt{11}
1,066
x\cdot a^n/x = \left(x\cdot a/x\right)^n
23,441
\dfrac{-x^{1 + n} + 1}{-x + 1} = 1 + x + x^2 + \cdots + x^n
17,559
2^{4 + n} = 2^{n + 3} + 2^{n + 2} + 2^{1 + n} + 2^n + 2^n
4,243
y^b*y^a = y^{a + b}
-20,591
(25 + n \cdot 5)/45 = \frac19(n + 5) \cdot 5/5
-30,548
-1000/\left(-200\right) = -200/(-40) = -\frac{40}{-8} = 5
-4,381
\frac{22}{1\cdot 22}\cdot 2\cdot \tfrac{1}{k^2}\cdot k^5 = \frac{1}{k \cdot k}\cdot k^5\cdot 44/22
12,141
( a + b, a + b) = \left( a, a\right) + ( b, b) + ( a, b) + ( b, a) = ( a, a) + ( b, b) + 2\left( a, b\right)
-4,601
(y + 2) \left(y + 5(-1)\right) = y^2 - 3y + 10 \left(-1\right)
-621
-\pi*8 + \pi \frac{25}{3} = \dfrac{\pi}{3}
17,741
\dfrac{1}{\sqrt{9 + 4 + 36}}|7 - 3 + 18 (-1)| = 2
15,479
6 = 3 \times \left((-1) + 3\right)
2,535
r^2 = r' \implies r = r'^{1/2}
883
2^{(-1) + n} \cdot 3 - 2^{(-1) + n} + 3 + 2(-1) = 1 + 2 \cdot 2^{n + (-1)}
34,977
\dfrac{1}{4}\times 4 = \frac55
-1,470
\dfrac{2}{7} \div - \dfrac{4}{9} = \dfrac{2}{7} \times - \dfrac{9}{4}
-9,476
-5 \cdot x = -x \cdot 5
28,483
\cos{z} \cdot 2 = 4 \cdot \cos^2{z/2} + 2 \cdot \left(-1\right)
29,607
e^{y \cdot i} = e^{i \cdot y}
36,418
\dfrac{2y}{y + 7(-1)} = \tfrac{1}{y + 7(-1)}\left(2y + 14 (-1) + 14\right) = 2 + \frac{14}{y + 7(-1)}
42,140
3*3 + 3\left(-1\right) = 6
11,791
\cos(x) = \cos\left(-x + 2\cdot \pi\right)
-2,541
(5 + 3 \times (-1) + 4) \times \sqrt{6} = \sqrt{6} \times 6
-9,867
-\frac{1}{25}17 = -\dfrac{1}{50}34
7,059
1/(E*B) = 1/\left(E*B\right)
38,409
-\frac{\pi}{4} = ((-1) \pi)/4
32,032
5\cdot (-1) + y^2 - y\cdot 4 = (y + 2\cdot \left(-1\right))^2 + 9\cdot (-1)
4,552
\frac{x^3 - 7 x}{x^2 x} = -\frac{1}{x^2} 7 + 1
21,105
|y| < 2 \Rightarrow |\frac{y}{2}| \lt 1
24,565
z \cdot (z + 1) = z \cdot \left(z + 1\right) = z \cdot z + z
-13,984
\left(2 + 4 - 6*3\right)*8 = (2 + 4 + 18*(-1))*8 = (2 - 14)*8 = (2 + 14*(-1))*8 = (-12)*8 = \left(-12\right)*8 = -96
3,927
xH = Hx * x\Longrightarrow x \in H
19,522
\cos{5*x} = \sin\left(5/2*\pi - 5*x\right) = \sin{5*(\pi/2 - x)}
18,467
(1 - 6 \cdot a^2) \cdot \tfrac{2}{3} = 0\Longrightarrow a = \dfrac{1}{\sqrt{6}}
-10,470
\frac{9}{q \cdot 15} = \tfrac{3}{5 \cdot q} \cdot \frac33
15,040
(-p + 1)/p\cdot \frac{p \cdot p}{1 - p^2} = \frac{1}{p + 1}\cdot p
-6,424
\frac{4}{3\cdot (9\cdot \left(-1\right) + a)} = \dfrac{4}{27\cdot (-1) + 3\cdot a}
23,888
\dfrac01 + 8 = 8/1
17,188
k + 2\cdot (-1) = k + 4\cdot \left(-1\right) + 2
-20,182
-\frac{36}{18 \cdot (-1) + 81 \cdot p} = 9/9 \cdot (-\frac{4}{9 \cdot p + 2 \cdot (-1)})
18,426
14 = 2\cdot 7 = (1 + (-13)^{1/2}) (1 - \left(-13\right)^{1/2})
12,501
\frac11x = \tfrac{1}{1/x}
5,226
n \times n - \dots \times 2 = n!
-11,499
4 + 2i = 2i + 1 + 3
4,013
h c + c + h + 1 = (h + 1) (c + 1)
-22,028
\dfrac{32}{24}=\dfrac{4}{3}
26,587
l^2 = l!\cdot \frac{1}{(l + (-1))!}\cdot l
46,603
39 = 29 + 2 + 8
13,555
8/216 = \frac{1}{36} \cdot 2 \cdot \frac{1}{6} \cdot 4
30,618
149/32 = \frac{23400 + 8500 (-1)}{11700 + 8500 (-1)}
16,242
\frac{1}{7!} \cdot (7! - 2 \cdot 6!) = \frac{1}{7} \cdot \left(7 + 2 \cdot \left(-1\right)\right) = 5/7
29,691
\frac{1}{2^5} \cdot \binom{5}{3} = \frac{10}{32} = \frac{1}{16} \cdot 5
8,069
\left((-1) + 2*a\right)*x_1*x_2 = (a + (-1))*x_1*x_2 + a*x_2*x_1
17,695
(y^2 + (-1)) * (y^2 + (-1)) = (1 + y) ((-1) + y) ((-1) + y) \left(y + 1\right)
26,637
\binom{7}{2}\binom{3}{2}=63
6,539
2(-1) + z + 1 = z + (-1)
-4,443
\frac{-9\cdot z + 1}{(-1) + z \cdot z} = -\frac{5}{z + 1} - \dfrac{4}{(-1) + z}
41,168
\lceil \frac{1006^2}{2013} \rceil =503
29,746
C/x + \frac{1}{x^2}\cdot B = \tfrac{1}{x^2}\cdot (B + x\cdot C)
427
\mathbb{E}(R \cdot C) = \mathbb{E}(R) \cdot \mathbb{E}(C)
6,644
\binom{n + (-1)}{\left(-1\right) + k} + \binom{n + (-1)}{k} = \binom{n}{k}
22,280
2^i = 2 + 4 + 6 + \dots + 2\cdot i
20,468
(z + y)\cdot (z - y) = -y^2 + z^2
17,590
(y - \sqrt{2}) \cdot (y + \sqrt{2}) = y^2 + 2 \cdot (-1)
-3,023
13^{1 / 2}*5 = (3 + 2)*13^{\frac{1}{2}}
39,721
\frac{1}{2} = |-1|/2
-30,268
\dfrac{1}{y + 3}(y^2 + y + 6(-1)) = \dfrac{(y + 2\left(-1\right)) (y + 3)}{y + 3} = y + 2(-1)
26,793
4^k*2^k = 2^{k*3}
23,930
e^x = z \Rightarrow e^{2 \cdot x} = z^2
16,597
4\cdot \cos(\theta) = 3^{1/2}\cdot \sin(\theta)\cdot \csc^2\left(\theta\right) = 3^{1/2}\cdot \csc(\theta)
-17,170
2 = 2\cdot (-2\cdot q) + 2\cdot (-8) = -4\cdot q - 16 = -4\cdot q + 16\cdot (-1)
57
a + d - 2d = -d + a
-6,429
\frac{2}{2 p + 16 \left(-1\right)} = \frac{1}{(p + 8 (-1))\cdot 2} 2
17,115
( x, z) + ( x', e) := ( x + x', e + z)
7,969
d + \frac{1}{2} \left(h - d\right) = \dfrac{1}{2} (h + d)
12,301
\frac{\sqrt{2}}{2} = \sin\left(\pi/4\right)
32,260
(x y)^2 = y^2 x x
6,713
4*x*z = -(x - z)^2 + (x + z)^2
-441
-\pi\cdot 8 + \pi\cdot 26/3 = 2/3\cdot \pi
27,731
(n + (-1))^2 = 1 + n^2 - n*2
8,865
3 - f^2 + f\cdot 2 = -(f + 3\cdot (-1))\cdot \left(1 + f\right)
-22,243
21 + q \cdot q + 10 \cdot q = \left(3 + q\right) \cdot (7 + q)
-15,786
\dfrac{7}{10} \cdot 8 - 3/10 \cdot 5 = 41/10
8,855
3^{n + (-1)} = \dfrac{1}{13} \cdot (3^{1 + n} + 3^n + 3^{(-1) + n})
30,515
rs a = rsa
15,204
l^{l + q} = (-q + l + q)^{q + l}
-5,444
10^5*0.4 = 0.4*10^{(-4)*\left(-1\right) + 1}
11,485
\frac{1}{2}\cdot (2 + 3) = \frac52