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ddrg
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math_formulas

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int64
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22,650
\left(f + d\right)^2 = d^2 + d \cdot f \cdot 2 + f^2
4,194
1/27*4/\left(8*\pi\right) = 1/(\pi*54)
-1,868
-\pi \cdot \frac{19}{12} + \pi \cdot \frac{19}{12} = 0
42,649
1000 = 0 + 0(-1) + 1000
-11,641
-10 + 10\cdot i = -4 + 6\cdot \left(-1\right) + 10\cdot i
28,396
\frac{36}{120} = \frac{1}{10} 3
3,734
i = s*h*e = s*e*h
23,698
\frac{1}{6^3} \cdot \binom{6}{3} = \tfrac{20}{216} = \frac{5}{54}
2,053
\arcsin{-a} = -\arcsin{a}
-24,755
\cos{\pi \cdot 7/12} = \frac14 \cdot (-6^{1 / 2} + 2^{\frac{1}{2}})
18,637
c*2 + \frac23*a \Rightarrow a = -c*3
-28,967
3 = 15 \times (-1) + 18
172
(S + 2(-1)) (1 + S) = 2(-1) + S^2 - S
20,051
R^2*X = R^2*X
15,206
z^2 + 72 - 13\cdot n^2 = 6\cdot 2^{1/2}\cdot n \cdot n + 12\cdot 2^{1/2}\cdot z = 2^{1/2}\cdot (6\cdot n^2 + 12\cdot z)
-5,923
\frac{1}{4 \cdot (6 \cdot (-1) + k)} \cdot 3 = \tfrac{3}{24 \cdot \left(-1\right) + 4 \cdot k}
-425
(e^{7i\pi/4})^{13} = e^{i\pi \cdot 7/4 \cdot 13}
12,925
\dfrac{a}{y} = \tfrac{a}{y}
8,456
(-8\cdot a + 1)\cdot (1 + a)^2 = 1 - 8\cdot a^3 - 15\cdot a \cdot a - 6\cdot a
34,586
m \cdot m/m! = \tfrac{1}{((-1) + m)!}\cdot m
21,015
ce - cb = c*(e - b)
26,424
2\times (1 + 2^n\times \left((-1) + n\right)) = 2 + 8 + 24 + 64 + \dotsm + 2^n\times n
25,073
0 + \gamma^2 = \gamma^2
11,623
4 - 7*(y^2 - y*4 + 4) = -y^2*7 + y*28 + 24*(-1)
-17,035
3 = 3(-4p) + 3 = -12 p + 3 = -12 p + 3
14,651
\tfrac{1}{k \cdot z^k} \cdot z^{k + 1} \cdot (k + 1) = (k + 1) \cdot z/k = \left(1 + \tfrac{1}{k}\right) \cdot z
23,497
\frac{1}{1}2 = 2 + \dfrac110
23,318
\int\limits_0^\pi \cos^{2\cdot k + 1}{t}\,dt = 0 = \int\limits_0^{2\cdot \pi} \cos^{2\cdot k + 1}{t}\,dt
-8,573
\dfrac{2}{3} - \dfrac{4}{12} = {\dfrac{2 \times 4}{3 \times 4}} - {\dfrac{4 \times 1}{12 \times 1}} = {\dfrac{8}{12}} - {\dfrac{4}{12}} = \dfrac{{8} - {4}}{12} = \dfrac{4}{12}
-22,371
(7 \cdot (-1) + p) \cdot \left(p + 6\right) = 42 \cdot (-1) + p^2 - p
-6,430
\tfrac{1}{t\cdot 3 + 27}\cdot 5 = \frac{5}{3\cdot (t + 9)}
12,659
|x - z| = z - x = \frac{z^2 - x^2}{x + z} \lt \frac{1}{2 \cdot x} \cdot (z \cdot z - x^2)
6,101
\tfrac13*2/3 = \frac29
26,907
14.7 = \frac{6}{6} + 6/5 + \tfrac64 + 6/3 + 6/2 + \dfrac11 \times 6
9,111
(x + c) \cdot (x + c) + d = c^2 + d + x^2 + 2\cdot x\cdot c
2,156
\dfrac{64^{1 / 2}}{8^{1 / 2}} = (\dfrac18 \cdot 64)^{\dfrac{1}{2}} = 8^{1 / 2} = 2 \cdot 2^{\frac{1}{2}}
-19,226
1/45 = \frac{1}{36\cdot \pi}\cdot A_s\cdot 36\cdot \pi = A_s
323
(i \cdot 16)^{-1} = (4 \cdot i)^{-1} - \frac{3}{16 \cdot i}
-6,396
\tfrac{1}{12 + 2\cdot p} = \frac{1}{2\cdot (6 + p)}
36,918
3^7 + 3\cdot (-1) = 2184
16,756
\frac{1}{n}*x = x/n
24,936
x^2 = (x + \left(-1\right) + 1)^2 = \left(x + \left(-1\right)\right)^2 + 2*(x + \left(-1\right)) + 1
28,461
26 = 5 * 5 + 1^2 = 4^2 + 3^2 + 1^2 = 3^2 + 3^2 + 2^2 + 2^2
36,626
|f - g| = -(f - g) = g - f
24,030
\dfrac{h}{c} \coloneqq h/c
11,177
\frac{1}{z^2 - z + 2\cdot (-1)}\cdot 2 = \frac{2}{(z + 2\cdot (-1))\cdot (z + 1)}
17,242
(1 + 1)\cdot \left(1 + 1\right)\cdot (1 + 2)\cdot \left(7 + 1\right) = 96
35,942
Y^2 + Y = 3*Y - I = Y^3 + I
-6,693
\frac{3}{100} + \frac{1}{10} \cdot 8 = \frac{80}{100} + \tfrac{1}{100} \cdot 3
18,247
\frac{\partial}{\partial y} \left(y^p G\right) = Gy^{\left(-1\right) + p} p
2,333
F = FF^0
-27,766
d/dz \left(3\tan(z)\right) = 3d/dz \tan(z) = 3\sec^2(z)
-22,083
\dfrac{6}{6}=1
21,467
x^2 + x \cdot k \cdot 2 + k^2 = (x + k) \cdot (x + k)
17,021
\cos{4 b} = \cos(b \cdot 3 + b)
24,678
-(-\cosh(x) + \sinh(x))*\left(\sinh(x) + \cosh(x)\right) = 1 \implies 1 = 5*(\cosh\left(x\right) + \sinh(x))
23,091
\left(n^3 - n^2 + n^2 - n + 1\right) \cdot (n^2 + n + 1) = (n^2 + n + 1) \cdot (1 + n \cdot n \cdot n - n)
49,422
(a+b+c)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})\geq \frac{3(a+b+c)}{\sqrt[3]{abc}}=\frac{2(a+b+c)}{\sqrt[3]{abc}}+\frac{(a+b+c)}{\sqrt[3]{abc}}\geq\frac{2(a+b+c)}{\sqrt[3]{abc}}+3
30,281
3^{20*j} = ((3^3)^6*3^2)^j = (27^6*9)^j
13,304
2\times \left(-1\right) + (\frac{1}{\xi} + \xi)^2 = \frac{1}{\xi^2} + \xi^2
48,542
8 = {8 \choose 1}
-10,396
-3/d \dfrac{4}{4} = -\frac{1}{4 d} 12
-9,614
30\% = 30/100 = 0.3
-22,636
\dfrac{1}{3} \times - \dfrac{5}{8} = \dfrac{1 \times -5}{3 \times 8} = \dfrac{-5}{24} = -\dfrac{5}{24}
13,216
4 \cdot 2 \cdot 3 + 5 \cdot 0 = 24
6,133
\left(-n + m\right)\cdot 3 = -3n + 3m
25,237
(\tfrac16*5)^2 = \dfrac{1}{6}*5*\frac56
23,708
l!*(1 + l) = (1 + l)!
-24,879
\frac{11}{12} = \frac{1}{12}\cdot s\cdot 12 = s
40,162
4 + x = 3 + x + 1 = 3\cdot (1 + (x + 1)/3)
-10,470
\frac{3}{3}\cdot \frac{1}{5\cdot q}\cdot 3 = \dfrac{9}{15\cdot q}
-4,127
\frac18\cdot 7 = \frac{1}{8}\cdot 7
2,067
\psi^4 + 4 = \psi^4 + 4\cdot \psi^2 + 4 - 4\cdot \psi^2 = \left(\psi^2 + 2\right)^2 - 4\cdot \psi^2 = (\psi^2 - 2\cdot \psi + 2)\cdot (\psi^2 + 2\cdot \psi + 2)
13,713
7 = 7/2 \times 2
18,672
Sy = yS + Sy
-3,052
10^{1 / 2} \cdot (1 + 4 + 5) = 10^{\tfrac{1}{2}} \cdot 10
-5,225
0.64*10^{10 + 5 (-1)} = 10^5*0.64
13,973
2 + 3^{1 / 2} = ((2^{1 / 2} + 6^{\frac{1}{2}})/2)^2
-6,169
\frac{1}{k * k + 5k + 36 (-1)}5 = \frac{1}{(k + 9) (4(-1) + k)}5
5,720
x_2/(x_1) \cdot x_1^2 = x_1 \cdot x_2
6,347
\left(x^2 + x + 1\right) \cdot (x + (-1)) = (-1) + x^2 \cdot x
17,103
(C' \times x/x)^3 = \frac{x}{x} \times C'^3
-28,785
\int z \cdot z\,\mathrm{d}z = \frac{1}{2 + 1} \cdot z^{2 + 1} + X = z^3/3 + X
-6,748
\frac{1}{100}\cdot 4 + 50/100 = 4/100 + \dfrac{5}{10}
13,364
48 = 50 + 3\cdot \left(-1\right) + 1
7,466
\sin{2\cdot \pi} + \sin{4\cdot \pi} = \sin\left(\pi\cdot 4 + \pi\cdot 2\right)
836
\left(2^5 + 5^6\right)^2 = 5^{12} + 2^{10} + 2\cdot 2^5\cdot 5^6
30,275
c + g_1 + g_2 = g_1 + g_2 + c
21,960
(3^{\left(-1\right) + x} + (-1))/2 = (3^{x + \left(-1\right)} + 3(-1))/2 + 1
818
\left(-X\cdot n + X\cdot n\right)/n = X - n\cdot X/n
403
T/I \times z = \dfrac{T}{I} \times z
-3,661
\frac{108}{60}*\tfrac{k^3}{k^5} = \frac{108*k^3}{60*k^5}
-29,096
(-2)*(-6) = 12
-3,988
k \cdot k\cdot 35/(k\cdot 30) = k \cdot k/k\cdot 35/30
-23,348
\dfrac{1}{9}*4*3/4 = \frac13
17,942
9^{91} \gt 9^{90} = (9^9)^{10} > \left(7^{10}\right)^{10} = 7^{100} \gt 7^{94}
33,121
h \cdot m = h_1 \cdot m_1 \Rightarrow h_1/h = \frac{m}{m_1}
18,146
\frac37 = \dfrac{9}{21}
-3,256
(4 + 2)\cdot 3^{1/2} = 6\cdot 3^{1/2}
13,471
8 = 4*k*j - k + j \Rightarrow \left(4*j + (-1)\right)*k + j = 8