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ddrg
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math_formulas

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int64
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6,170
\sin(\operatorname{atan}\left(z\right)) = \dfrac{z}{\sqrt{z \cdot z + 1}}
2,960
-(2*(-1) - \sqrt{5}) = 2 + \sqrt{5}
-15,531
\frac{1}{n^{10} \cdot \frac{n^{20}}{z^{10}}} = \dfrac{\dfrac{1}{n^{10}}}{\frac{1}{z^{10}}} \cdot \frac{1}{n^{20}} = \frac{z^{10}}{n^{30}} = \frac{1}{n^{30}} \cdot z^{10}
1,936
x + 1 = \frac{3}{2} \cdot \pi + \cos(\frac{3}{2} \cdot \pi) \Rightarrow 2 \cdot (-1) + \pi \cdot 3/2 = x
13,335
10 = 5\cdot 2 = 5\cdot (3 + \left(-1\right)) = 5\cdot (\left(3^4\right)^{1/4} + (-1))
20,374
\cos(\pi - r) = -\cos{r}\cdot \sin(\pi - r) = \sin{r}
26,139
y^2 + \delta\cdot y\cdot 2 + \delta^2 = (\delta + y)^2
-27,498
5*7aa = 35 a^2
5,873
2^{f + b} = 2^b\cdot 2^f
6,154
fz^{(-1) + f} = \frac{\partial}{\partial z} z^f
-23,857
7 + 5\cdot 2 = 7 + 10 = 17
-18,935
31/36 = A_s/(81*\pi)*81*\pi = A_s
-511
(e^{\frac{i*\pi*11}{12}*1})^7 = e^{7*\frac{\pi*i*11}{12}}
-12,064
7/9 = \dfrac{s}{14 \pi} \cdot 14 \pi = s
-20,648
-\frac{1}{-60\cdot s + 24}\cdot 48 = \frac66\cdot (-\frac{8}{4 - 10\cdot s})
-4,494
y^2 + 2*y + 3*\left(-1\right) = \left(y + 3\right)*((-1) + y)
13,135
-(-y)^{m + 1} = -(-1)^{m + 1}*y^{m + 1} = (-1)^{m + 2}*y^{m + 1}
18,177
H_x \lt G_x \lt G\Longrightarrow \frac{1}{G_x}G \frac{1}{H_x}G_x = G/(H_x)
-20,068
((-5)*r)/(r*\left(-5\right))*9/4 = \left((-45)*r\right)/(\left(-20\right)*r)
-22,993
\frac{21}{27} = \frac{7\cdot 3}{9\cdot 3}
48,924
150 = 6 \cdot 6 + 114
18,569
\dfrac{1}{6! \cdot 2!} 8! = 28
34,842
35\cdot \left(3 + 6\right) = 315
28,111
\tfrac{2^{1/3}}{2} = 2^{-\frac{2}{3}}
442
\left(z + 2 \cdot (-1)\right)^2 = 4 + z^2 - 4 \cdot z
24,583
\left(1/2 + 1\right) \left(1 - 1/2\right) = 1 - \frac14
31,640
\left(y \cdot y = z \implies \sqrt{y^2} = \sqrt{z}\right) \implies \sqrt{z} = |y|
-10,043
-\frac12 = -4/8
23,781
\binom{100}{3} = \frac{100!}{97!*3!} = 161700
35,214
-\dfrac{\pi}{8} = \frac{1}{8}*((-1)*\pi)
34,643
p + m/n = (pn + m)/n
2,927
c^3 = -2\cdot c + (-1) = c + 2
-25,098
8 \cdot \tan(y \cdot 4) \cdot \sec^2(y \cdot 4) = d/dy \sec^2(4 \cdot y)
-4,683
\dfrac{-y + 18\cdot (-1)}{y^2 + y + 6\cdot (-1)} = \dfrac{3}{3 + y} - \tfrac{4}{2\cdot (-1) + y}
-7,927
\frac{-4\cdot i - 8}{-2 + 4\cdot i}\cdot \frac{-2 - 4\cdot i}{-4\cdot i - 2} = \frac{1}{i\cdot 4 - 2}\cdot \left(-8 - 4\cdot i\right)
31,527
(h_b - h_t) \cdot p \cdot g \cdot s^2 = s^2 \cdot (-h_t + h_b) \cdot g \cdot p
950
11 - k \cdot 4 = 3\Longrightarrow 2 = k
-8,011
(20 - 25 i - 16 i + 20 \left(-1\right))/41 = (0 - 41 i)/41 = -i
-10,419
\frac{200 (-1) + n*20}{20 n + 20} = \frac{1}{20} 20 \frac{1}{1 + n} \left(n + 10 (-1)\right)
36,007
\frac{15}{16} + \frac{1}{64}\cdot 3 = \frac{63}{64} = 1 - \frac{1}{64}
12,491
512 \left(-1\right) + 256 = -256
19,096
\cos{2t} = 1 - 2\sin^2{t} = 2\cos^2{t} + (-1)
10,818
217^{\frac13} = (1 + \frac{1}{216})^{1/3}*6
27,904
3*89*3^2*2*7 = 267*126
25,776
{3 \choose 1}\cdot {2 \choose 1}\cdot {5 \choose 3} = 60
-11,835
\frac{8.106}{10} = 8.106*0.1
20,466
1/\left(\frac{1}{1/\left(1/25\right)}\right) = 5^{-2\times (-(-1)\times (-1))} = 5^2 = 25
2,975
\frac{8}{81} = (\frac{2}{3})^3*1/3
9,586
\cos\left(x\right) = \cos(x + 2*\pi)
24,533
\frac{44}{2}\cdot 52\cdot 48 = 54912
23,099
-B^n + Y^n = (Y - B) \left(Y^{\left(-1\right) + n} + B Y^{n + 2 (-1)} + \cdots + B^{(-1) + n}\right)
-15,946
6\cdot 7/10 - 10\cdot 3/10 = 12/10
12,421
2\cdot R\cdot s^2\cdot \pi \cdot \pi = s^2\cdot \pi\cdot 2\cdot \pi\cdot R
13,265
\dfrac{f^{l_2}}{f^{l_1}} = f^{-l_1 + l_2}
-2,426
4 \cdot 6^{1/2} - 3 \cdot 6^{1/2} = 16^{1/2} \cdot 6^{1/2} - 6^{1/2} \cdot 9^{1/2}
6,122
\frac{1}{A C} = 1/(A C)
28,677
10000\cdot \left(1 + \frac{1}{100}\right) = 10000 + \frac{1}{100}\cdot 10000
15,880
b_g*b_a = b_g*b_a
7,418
x^2 + 4\cdot x + 3 = (x + 1)\cdot \left(x + 3\right)
13,022
\frac{6!}{2!\times3!}=60
121
\left(-1\right) + g \neq 0\wedge g g + (-1) = 0 \Rightarrow 0 = g + 1
17,478
d \cdot g - d \cdot g \cdot d = d \cdot (-d \cdot g + g)
-2,031
\pi \cdot \frac74 + \pi \cdot 2/3 = \pi \cdot 29/12
-11,903
\frac{9.797}{100} = 9.797 \cdot 0.01
26,427
-\dfrac12 = 7 - \dfrac{15}{2}
39,948
3^{\dfrac1k} = 3^{1/k}
27,779
\cos\left(z + y\right) = \cos{z}\cdot \cos{y} - \sin{y}\cdot \sin{z}
5,090
\cos(\frac{x}{2})\cdot \sin(x/2)\cdot 2 = \sin\left(x\right)
-20,578
\frac{9 \cdot (-1) - j}{3 \cdot (-1) + j} \cdot 4/4 = \frac{-j \cdot 4 + 36 \cdot (-1)}{4 \cdot j + 12 \cdot (-1)}
-7,190
\frac{5}{24} = \frac{5}{3} \cdot 1/8
-426
(e^{\frac{i \pi}{4} 3})^{11} = e^{11 \cdot 3 \pi i/4}
27,598
-2 \cdot x^2 + (1 + x \cdot x)^2 = x^4 + 1
-23,422
\frac42 \cdot 1/7 = \tfrac17 \cdot 2
32,852
\dfrac{1}{(1 - z^2)^{\frac{1}{2}}} = \frac{\mathrm{d}}{\mathrm{d}z} \operatorname{asin}\left(z\right)
15,854
\dfrac{120*6}{200} = 3.6
9,882
\cos(\pi/3) + \cos(2/3\cdot \pi) = 0
8,446
f = \left\{2, f, 1, \dots\right\}
-9,042
54.7\% = \dfrac{54.7}{100}
757
i^{\frac{1}{2}} \cdot i^{\frac{1}{2}} = i = 0 + i = \left(h + bi\right)^2 = h^2 + 2hbi + b^2 i^2 = h^2 - b^2 + 2hb i
26,670
\frac{1}{1 - \frac{t}{2}} \cdot (1 + t/2) = \dfrac{2}{-t/2 + 1} + (-1)
42,923
31\cdot 109 = 3379
-3,658
27 = 3\cdot 3\cdot 3
32,240
\frac{dx}{dx} = \dfrac{1}{1 - x}\cdot x - x = \frac{x^2}{1 - x}
-6,442
\dfrac{5 \cdot b}{b^2 - 13 \cdot b + 36} = \frac{5 \cdot b}{(b + 4 \cdot \left(-1\right)) \cdot (b + 9 \cdot (-1))}
6,745
(1/3)^2 + \left(\frac{2}{3}\right)^2 = \frac19 5 < 1 + 1
10,761
0 = 1 - P(A) + P(B) - P(A) \cdot P(B) = (1 - P(A)) \cdot (1 - P\left(B\right))
-10,299
-\frac{1}{15 r + 15 (-1)}5 = 5/5 (-\frac{1}{3\left(-1\right) + 3r})
-3,026
13^{1/2} = 13^{1/2}\times (3 + 2\times \left(-1\right))
22,478
\frac{1}{4!} \cdot (6 + 1)! = 210
3,523
\dfrac{M!}{(M + (-1))!} = M
-22,208
18 + x^2 - x*9 = (x + 3 \left(-1\right)) (x + 6 (-1))
25,392
\left(2\cdot m + 2\right)! = (2\cdot m + 2)\cdot (2\cdot m + 1)\cdot \left(2\cdot m\right)!
-16,418
5 \sqrt{208} = 5 \sqrt{16\cdot 13}
-7,158
\dfrac{3}{5} = \tfrac45\cdot \dfrac34
19,604
(k + x) \cdot w = k \cdot w + w \cdot x
-22,480
(\frac{1}{81})^{\frac12} = 81^{-\frac{1}{2}}
-4,272
\frac{5 / 6}{z^3}\cdot 1 = \frac{5}{6\cdot z^3}
6,096
x/x = x \cdot \frac{1}{x} \cdot 1 = (\frac{x}{x}) \cdot (\frac{x}{x})
23,033
(z^2 + y^2) (1 - \tfrac{y}{z}) = (1 - \tfrac{y}{z}) (\sqrt{y^2 + z^2})^2
-4,701
\tfrac{16 \cdot (-1) - z \cdot 6}{6 + z \cdot z + z \cdot 5} = -\frac{1}{2 + z} \cdot 4 - \frac{2}{z + 3}