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ddrg
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math_formulas

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int64
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|h_m\times a_m - a\times h| = |a_m\times h_m - a_m\times h + a_m\times h - h\times a|
11,500
\frac{1}{\Omega^{1/2} \cdot \Omega^{\frac12}} = \frac{1}{\Omega}
43,275
c = (1 + 1/4)\times \dfrac{p}{4} rightarrow \frac{5}{16}\times p = c
10,658
42 = \left((-1) + 7\right) \cdot 7
24,843
(7 + a) \times (7 + a) - 17 \times \left(a + 4\right) = a \times a - 3 \times a + 19 \times \left(-1\right)
33,788
h*H = H*h
35,539
\sin(g + b) = \sin{g} \cos{b} + \cos{g} \sin{b}
10,384
\sqrt{2} \approx 1.41\times \cdots < 1.44 = 1.2^2 = (5/4)^2
24,098
2^2 + 4^2 = 2^4 + 2^2
15,286
x^2 + \left(-1\right) = ((-1) + x) (1 + x)
6,505
h \cdot h + h\cdot g = d \cdot d \implies d^2 - h^2 = g\cdot h
21,695
120 \cdot (75 + 30 \cdot \left(-1\right)) = 5400
-3,659
5\times 1/6/p = 5/(p\times 6)
1,760
( -(2 \cdot a - x) + 2 \cdot b, z) = \left( (-a + b) \cdot 2 + x, z\right)
10,703
1/(2) + 1/(2\cdot 3) + \ldots + \frac{1}{(n + 1)\cdot n} = -\frac{1}{1 + n} + 1
11,781
1415934836 = 84\cdot 256 \cdot 256^2 + 101\cdot 256^2 + 256^1\cdot 115 + 256^0\cdot 116
-12,117
\dfrac{1}{6} = \tfrac{t}{6 \cdot \pi} \cdot 6 \cdot \pi = t
-4,146
8n^2 = n * n*8
39,255
2^4 \cdot 2 \cdot 2 = 2^3 \cdot 2^3
-20,174
\frac77 \frac{1}{(-8) q} (9 + q) = \frac{1}{q\cdot (-56)} (63 + q\cdot 7)
-6,140
\dfrac{1}{(s + 1) \cdot 2} = \frac{1}{2 + 2 \cdot s}
-3,882
\frac{1}{t^5} t^4 = \dfrac{t t t t}{t t t t t} = 1/t
10,056
\frac{1}{3}(3m + 3\left(-1\right)) + (3m^2 + 3m + 1)/3 = \frac{1}{3}\left(3m^2 + 6m + 2(-1)\right) = m^2 + 2m - 2/3
36,336
20 = 5 \cdot A \Rightarrow A = 4
8,422
\dfrac49 = 2/3 \cdot \frac13 \cdot 2
5,889
\pi\cdot 3/2 = \dfrac{\pi\cdot (-1)}{2} + \pi\cdot 2
6,191
12 \cdot \left(725760 + 986400 + 985824 + 967680\right) = 43987968
21,571
d = d \cdot x = x \Rightarrow d = x
-18,269
\frac{1}{-3 \cdot n + n^2} \cdot (15 \cdot (-1) + n^2 + 2 \cdot n) = \tfrac{\left(n + 5\right) \cdot (n + 3 \cdot (-1))}{n \cdot (3 \cdot \left(-1\right) + n)}
15,562
\frac{1}{x \cdot z} = \frac{1/z \cdot z}{x \cdot z}
39,242
1 = -\sin\left(\frac{\pi}{2}*3\right)
-10,281
\dfrac{\frac{1}{6}}{4*x + 2*(-1)}*6 = \frac{1}{24*x + 12*(-1)}*6
25,655
4^{100} - 3^{100} = 100 \cdot d^{99} = \dfrac{100}{d} \cdot d^{100}
15,364
1 + 3 + 3^2 + 3^3 + \dotsm + 3^k = \frac{1}{2} \times ((-1) + 3^{k + 1})
24,988
\frac{1}{(n + 1)^2} \cdot ((n + 1) \cdot (n + 1) + 1) = \dfrac{1}{(n + 1)^2} + 1
-5,935
\dfrac{1}{27*(-1) + y*3}*2 = \frac{2}{3*(y + 9*(-1))}
23,069
y^3 - 3y + 2(-1) = \left(y + 2(-1)\right) (y^2 + 2y + 1) = \left(y + 2(-1)\right) (y + 1)^2
-4,602
\frac{z \cdot 2 + 14 \cdot (-1)}{z^2 + 2 \cdot z + 15 \cdot (-1)} = -\frac{1}{z + 3 \cdot (-1)} + \frac{3}{5 + z}
-20,164
(-t\cdot 4 + 5)/(-7)\cdot \dfrac33 = \left(15 - 12\cdot t\right)/(-21)
29,500
\sqrt{3} + 2 = \frac{1}{\sqrt{3} + (-1)}(1 + \sqrt{3})
32,354
(x + y)^3 = (x + y) \cdot \left(x + y\right) \cdot \left(x + y\right) = \left(x + y\right) \cdot (x^2 + 2 \cdot x \cdot y + y^2)
21,126
8\cdot \left(2r \cdot r + 3r + 1\right) + 1 = 16 r^2 + 24 r + 9 = (4r + 3)^2
-1,165
\frac{1}{9}\cdot 5\cdot (-\frac98) = \dfrac{5\cdot 1/9}{\frac{1}{9}\cdot (-8)}
31,971
\frac{4}{52} \cdot 3/51 = 12/2652 = \dfrac{1}{221}
-11,908
\frac{1}{100} \cdot 1.601 = 1.601 \cdot 0.01
3,354
\dfrac{1}{\sqrt{2\cdot n} + \sqrt{2\cdot n + 2}} = \dfrac{\frac{1}{\sqrt{2\cdot n + 2} - \sqrt{2\cdot n}}}{\sqrt{2\cdot n} + \sqrt{2\cdot n + 2}}\cdot (\sqrt{2\cdot n + 2} - \sqrt{2\cdot n}) = (\sqrt{2\cdot n + 2} - \sqrt{2\cdot n})/2
560
(-1) + y^3 = (\left(-1\right) + y)*(y^2 + y + 1)
24,150
0 = m^2 - x \implies m = x^{1 / 2}
-18,968
\frac{9}{10} = \frac{D_t}{100 \cdot \pi} \cdot 100 \cdot \pi = D_t
4,358
(n + 2*(-1))! + (n + (-1))! + n! = n * n*(n + 2*(-1))!
6,598
z^2 - y^2 = 4 \cdot x^5 rightarrow (y + z) \cdot (z - y) = 4 \cdot x^5
21,576
a \cdot z = \frac12 \cdot (a \cdot z + z \cdot a) = z \cdot a
36,858
2^{3.14} = 2^{\frac{1}{100} \cdot 314} = \left(2^{314}\right)^{\tfrac{1}{100}}
4,850
\left(\frac{36}{100} = \frac4z \Rightarrow 400 = 36 \cdot z\right) \Rightarrow z = 11.11
26,168
x\cdot 2 \gt -x + 3\Longrightarrow 1 < x
-23,516
0.23\cdot 0.053 = 0.23\cdot 0.23\cdot 0.23 = 0.23 \cdot 0.23 \cdot 0.23
2,249
\dfrac{1}{(-1) + 1}*(1 + 1) = 2/0
5,711
b\cdot \lambda + a = b\cdot \lambda + a
11,476
\left(90 \cdot k = 9 \cdot (x - p) \implies -p + x = 10 \cdot k\right) \implies x = p + 10 \cdot k
-27,499
30 \cdot n^3 = 3 \cdot n \cdot n \cdot n \cdot 5 \cdot 2
11,522
2\cdot (-1) + H^3 = (H + 2)\cdot (H^2 - H\cdot 2 + 4) - 2\cdot 5
7,375
(c + b)/2 + y = \dfrac{1}{2}(c + b + 2y)
10,592
\frac{1}{99 \cdot 999} \cdot (((-1) + 100) \cdot 717 - 71 \cdot \left(1000 + (-1)\right)) = -\frac{71}{99} + 717/999
1,041
(g^n)^{12} = 1\Longrightarrow g^n
29,085
\left(1 + x\right)*\left(1 + x^2 - x\right) = x^3 + 1
14,217
n\cdot \left(m + 1\right) = n\cdot m + n
26,853
\sin(\pi/12) = \sqrt{(-\cos\left(\frac{\pi}{6}\right) + 1)/2}
14,637
\frac{1}{|z|^n + (-1)} = \frac{1}{(|z|^n + (-1)) \cdot |z|^n} + \frac{1}{|z|^n}
-3,040
-\sqrt{11} + \sqrt{25\cdot 11} = -\sqrt{11} + \sqrt{275}
-16,449
7 \cdot 4^{\frac{1}{2}} \cdot 7^{\frac{1}{2}} = 7 \cdot 2 \cdot 7^{1 / 2} = 14 \cdot 7^{1 / 2}
-10,093
0.875 = \frac{1}{8}7
37,816
0\times 0 = 0^2 = 0
-30,909
(32 - k)\cdot 470 = (-k + 32)\cdot 470
19,157
\int\limits_{-\pi}^\pi \sin^2(n \cdot x)\,\mathrm{d}x = \pi = \int\limits_{-\pi}^\pi \cos^2(n \cdot x)\,\mathrm{d}x
21,428
\frac{\sin\left(\frac{f}{3^k}\right)}{\frac{1}{3^k}} = 3^k \cdot \sin\left(\frac{f}{3^k}\right)
-20,893
\frac{1}{10 - k} \cdot (-k + 10) \cdot (-\frac12 \cdot 5) = \tfrac{1}{20 - k \cdot 2} \cdot (5 \cdot k + 50 \cdot (-1))
20,516
\cos{B}\cdot \sin{F} + \cos{F}\cdot \sin{B} = \sin(F + B)
2,752
(\left(-1\right) + n)/n = \frac{1}{n!} \times \left(-(n + (-1))! + n!\right)
30,842
\frac{a^2}{2} = a\cdot a/2
-5,319
10^{4 + 3} \cdot 7.8 = 7.8 \cdot 10^7
7,853
\tan\left(g\right) = \frac11*\tan(g)
-16,061
8\times 7\times 6\times 5 = \frac{8!}{(8 + 4\times (-1))!} = 1680
30,894
\mathbf{R} = \left]-\infty, \infty\right[
6,556
\left(4/3\right)^3 = \frac{4^3}{3^3} = \dfrac{64}{27}
239
\frac{1}{{5 \choose 2}}\cdot \frac{1}{2!^2\cdot 3!\cdot 1!^3}\cdot 10! = 15120
-12,099
1/36 = r/(12*π)*12*π = r
7,929
\left(3n\right)^2 = n \cdot n\cdot 9
-3,988
k^2\cdot 35/(k\cdot 30) = 35/30\cdot k^2/k
-19,064
1/5 = \frac{A_s}{25 \cdot \pi} \cdot 25 \cdot \pi = A_s
27,710
\frac{x + 1}{(x^2)^{1 / 2}} = \frac{x + 1}{(-1) \cdot x} = -1 - 1/x
16,840
(-p^2 + p^3)/2 = p^2 \cdot (p + (-1))/2
17,164
3/6\cdot 4/6/6 = 1/18
9,802
\frac{1}{-t^l + 1}*\left(1 - t^{2*l}\right) = 1 + t^l
32,878
(-1) + y^2 = (\left(-1\right) + y)\cdot (1 + y)
13,806
( t', x')*\left( t, x\right) \coloneqq t'*(-t) + x'*x
18,307
0 = D^2\Longrightarrow 0 = D
12,930
\tfrac{\left(-2\right)\cdot \pi}{3} = \pi/3 - \pi
25,647
300 - 90 + 180 \implies 300 + 280*(-1) = 20
-1,617
\pi \cdot 19/12 = 43/12 \cdot \pi - 2 \cdot \pi
-2,884
7^{1/2} = 7^{1/2}\cdot (2 + (-1))