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ddrg
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math_formulas

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\sinh z=\frac{e^z-e^{-z}}2=\frac{e^{(-i)iz}-e^{-(-i)iz}}2=-i\frac{e^{i\cdot iz}-e^{-i\cdot iz}}{2i}=-i\sin iz
21,749
-r + r^2 = ((-1) + r) r
4,091
\dfrac{1}{A^4} = (\frac1A)^4
4,825
(-\nu + Y) \cdot (X - \mu) = (X - \mu) \cdot Y - \nu \cdot (X - \mu)
13,619
\cos(z + y) = -\sin(y) \cdot \sin\left(z\right) + \cos\left(y\right) \cdot \cos(z)
-26,572
(9 - 2\cdot y)\cdot (2\cdot y + 9) = 9^2 - (y\cdot 2)^2
33,699
-(x^2 + 12\times x + 28\times (-1)) = -(6 + x)^2 + 64
-11,980
7/24 = s/(16\cdot \pi)\cdot 16\cdot \pi = s
25,151
\frac{1}{b}\times c = \dfrac{c}{b}
-21,051
4/6 = \tfrac23*\dfrac{2}{2}
-1,896
5/12*\pi + \frac{\pi}{6} = 7/12*\pi
5,502
(N + 2)^2 = N^2 + 4\times N + 4
21,468
t^2 + t \cdot 2 + 9 = (t + 1) \cdot (t + 1) + 8
21,647
\sin(x - s) = \cos{s} \sin{x} - \cos{x} \sin{s}
46,004
\frac{2}{3}\cdot 30 = 20
33,336
\frac{q \cdot 41 + 420}{q^2 - q + 20 \cdot (-1)} = \frac{1}{(q + 5 \cdot (-1)) \cdot 9} \cdot 625 - \frac{1}{(4 + q) \cdot 9} \cdot 256
-20,069
\frac{z \cdot 15}{27 + 24 \cdot z} = 3/3 \cdot \frac{z \cdot 5}{8 \cdot z + 9}
-2,093
\dfrac{\pi}{3} + 0 = \pi/3
-9,882
-\dfrac{10}{10} = -1^{-1}
32,879
\left(10^{75} + (-1)\right) \cdot (1 + 10^{75}) \cdot (10^{150} + 1) = 10^{300} + (-1)
21,651
\frac{1}{x} = d*x/d = d^2*\frac{1}{x*d^2}
-20,672
(24\cdot (-1) - t\cdot 9)/(-6) = 3/3\cdot (8\cdot (-1) - 3\cdot t)/\left(-2\right)
4,738
(h + d)\cdot d + h\cdot (d + h) = (d + h)\cdot (h + d)
-16,343
7\sqrt{25} \sqrt{5} = 7*5 \sqrt{5} = 35 \sqrt{5}
20,637
-2\cdot z^2 + 16\cdot z = -2\cdot (z^2 + 8\cdot (-1)) = -2\cdot (z + 4\cdot (-1))^2 + 32
-5,444
10^{1 - -4} \cdot 0.4 = 0.4 \cdot 10^5
-19,669
\frac{1}{5}*10 = 10/5
21,670
\mathbb{E}[X] = 0 \Rightarrow 0 = \mathbb{E}[X * X]
26,221
d \cdot z_2/(z_1) = \frac{z_2}{z_1} \cdot d
8,463
\overline{z} + \overline{u} = \overline{u + z}
20,620
(2*(-1) + x)*(x^2 + 2*x + 2) + 2*x + 5 = 1 + x^3
-4,552
-\frac{1}{\tau + (-1)} - \dfrac{5}{2 + \tau} = \dfrac{1}{2 (-1) + \tau^2 + \tau} \left(-6 \tau + 3\right)
-16,026
46/10 = -\frac{3}{10}\cdot 8 + 10\cdot \frac{7}{10}
-2,104
\dfrac{17}{12}\cdot \pi + 0 = \pi\cdot \frac{1}{12}\cdot 17
29,188
\alpha + x + 1 \coloneqq \alpha + x + 1
8,085
s*z = x \implies \frac{dx}{ds} = z + s*\frac{dz}{ds}
898
((X + Y)^2 - (-Y + X)^2)/4 = XY
7,435
H^{15} H^{15} = H^{30}
-7,061
2/9*\dfrac{3}{10} = \frac{1}{15}
20,304
y \cdot z - z \cdot 6 - y \cdot 6 + 36 = 36 \Rightarrow 36 = (z + 6 \cdot \left(-1\right)) \cdot (6 \cdot (-1) + y)
6,797
\tfrac{1}{1}\left(a - b\right) = -\frac{b}{1} + \frac11a
-4,056
\dfrac{1}{y}y^3 = \frac{y^3}{y}1 = y \cdot y
13,571
\cos{e_1}\cdot \sin{e_2} + \sin{e_1}\cdot \cos{e_2} = \sin(e_2 + e_1)
34,404
\cos(\cos{\theta}) = \cos\left(\cos\left(\pi + \theta\right)\right)
13,260
(y^6)^{36} + (-1) = \left(-1\right) + y^{216}
48,708
66-(3+6+10)=47
8,292
\cos(x) = (e^{i*x} + e^{-i*x})/2*\sin(x) = \frac{1}{2*i}*(e^{i*x} - e^{-i*x})
9,111
f + (x + c)^2 = c^2 + f + x^2 + c\cdot x\cdot 2
-23,813
\frac{36}{3 + 9} = 36/12 = \frac{1}{12}*36 = 3
-1,444
\frac{1}{1/8*\left(-9\right)}*(1/7*(-9)) = -8/9*(-9/7)
41,318
\frac{1}{z^o} = z^{-o}
-30,243
16\cdot (-1) + y \cdot y = (y + 4)\cdot (y + 4\cdot (-1))
-4,027
\dfrac{1}{x^2}x^3 = xx x/(xx) = x
-4,837
10^3 \cdot 0.46 = 0.46 \cdot 10^{3 \cdot (-1) + 6}
7,751
(\tan^{-1}{\infty} - \tan^{-1}{-\infty})\cdot 2 = \pi\cdot 2
-1,727
-5/6*\pi = \pi/3 - \pi*7/6
10,869
(\sqrt{-F + y})^2 = y - F
6,685
33 = 1^2 + 4^2*2
22,437
x + (-1) = 3\cdot (-1) + 2 + x
21,202
t\frac{g^{n_t}}{t} = g^{n_t}
37,495
360/8 = 45
6,001
-37^2 + s^2 = (s + 37\cdot \left(-1\right))\cdot (s + 37)
-29,962
8*y^3 + 3*y * y + 6*y = \frac{\mathrm{d}}{\mathrm{d}y} (2*y^4 + y^3 + 3*y^2)
-9,426
s^2*24 = 2*2*2*3 s s
13,976
((-1) + n)*n*(n + 1)*\dotsm*2 = (n + 1)!
3,972
B\cdot B^n\cdot H^k = B\cdot B^n\cdot H^k = B^{n + 1}\cdot H^k
6,199
m + (-1) = (-1) + 2m - m
2,270
x^2 - y^2 = x x - y y = \left(x + y\right) (x - y)
9,619
\sin\left(x + z\right) = \sin(x)\cdot \cos(z) + \sin(z)\cdot \cos(x) = \sin(x) + \sin\left(z\right)
22,226
\frac{1}{x} \cdot h \cdot \frac{c}{f} = \tfrac{h \cdot c}{x \cdot f}
-28,790
\int x^8\,dx = \dfrac{x^{8 + 1}}{8 + 1} + B = \frac19 \cdot x^9 + B
23,046
(\frac53)^x = \frac{1}{\frac{1}{5^x} \cdot 3^x}
-13,432
\frac{15}{8 + 5\cdot (-1)} = \frac{1}{3}\cdot 15 = \frac{15}{3} = 5
37,784
2x + (-1) + 2 = 2x + 1 = 2\left(x + 1\right) + (-1)
-22,153
\tfrac{30}{50} = \frac35
7,954
pk = a \Rightarrow p = a/k
20,520
1/3 = 20/30*10/29 + \frac{9}{29}*10/30
14,971
4 \cdot z + 2 \cdot z \cdot 2 = z \cdot 8
-1,171
\frac{6}{7}*5/3 = \frac{1}{7}*6/\left(\frac{1}{5}*3\right)
21,705
\frac{1}{6}\cdot \left(1 + 4 + 9 + 16 + 25 + 36\right) = 91/6
8,845
y^2 = y^2 + 2 + \frac{1}{y^2} > y^2 + 2
-6,342
\frac{4}{z^2 - z \cdot 13 + 42} = \frac{1}{(z + 6 \cdot (-1)) \cdot \left(z + 7 \cdot (-1)\right)} \cdot 4
1,610
x\cdot (f - x\cdot c) = -x^2\cdot c + f\cdot x
-20,987
\dfrac{n\cdot 70 + 28}{49\cdot \left(-1\right) - n\cdot 63} = 7/7\cdot \frac{10\cdot n + 4}{7\cdot \left(-1\right) - n\cdot 9}
7,999
a^{x + 2 \left(-1\right)} a = a^{(-1) + x}
14,948
\frac{1}{6} \cdot \frac{5}{36} = 5/216
7,661
a^{k \cdot n} = (a^k)^n = \left(a^n\right)^k
-141
6\cdot (-1) - 26 = -32
-8,042
\frac{1}{32}(48 - 80 i - 48 i + 80 (-1)) = \tfrac{1}{32}(-32 - 128 i) = -1 - 4i
1,320
\frac1y*\sin{y} = \frac{1}{y}*(y - y^3/6 + \dots) = 1 - \dfrac16*y^2 + \dots
-13,737
\frac{6}{3 + 2(-1)} = \frac{1}{1}6 = \dfrac116 = 6
25,394
\dfrac{x}{z} = \frac{1}{1} \cdot 1/z \cdot x
44,596
-(1-e^x) = -1+e^x
18,775
\sin(g) \cdot \cos(z) + \sin(z) \cdot \cos(g) = \sin(g + z)
9,702
x^2\cdot 3 + 11\cdot x + 4\cdot (-1) = \left(4 + x\right)\cdot ((-1) + 3\cdot x)
-22,368
10 + y^2 - 7*y = (y + 5*\left(-1\right))*(2*\left(-1\right) + y)
9,102
x\cdot W\cdot y \Rightarrow W\cdot x\cdot y
19,476
Y^6 - 2\cdot Y \cdot Y^2 + 1 = (Y^3 + \left(-1\right)) \cdot (Y^3 + \left(-1\right)) = (Y + (-1))^6
35,408
\frac{\sqrt{3}}{2^{1/3}} = 2^{\frac23}\cdot \sqrt{3}/2
27,066
\left(z - y\right) \cdot \left(z^{n + (-1)} + \dots + y^{(-1) + n}\right) = z^n - y^n