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ddrg
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math_formulas

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9,163
\frac14 \cdot 0 + 1/4 + \frac{1}{2 \cdot 2} = 1/2
6,329
(z^4 + 1 + z^2)*\left(1 - z^2\right) = 1 - z^6
9,179
(f + x)^2 = f^2 + x \cdot f \cdot 2 + x^2
21,152
\frac{31}{66} = \tfrac{1}{132} \cdot 62
36,185
\mathbb{E}(W_1) \cdot \mathbb{E}(W_2) = \mathbb{E}(W_1 \cdot W_2)
29,470
\frac45 = \frac{1}{20} 16
-9,534
\frac{2}{8} = 0.25
-11,965
\frac{9}{10} = \frac{p}{4 \cdot \pi} \cdot 4 \cdot \pi = p
21,659
(a + f)^2 = f \cdot f + a \cdot a + f \cdot a + f \cdot a
30,905
e^{a + g i} = e^{g i} e^a
1,875
2*l + 1 = (l + 1)^2 - l^2 = (l + 1) * (l + 1) - l^2 + 0 * 0
30,313
\sin(x)=\sin(x-2\pi)
17,804
10 = \left(16 + 4\right)/2
9,900
g_1 \cdot g \cdot y \cdot y + y \cdot (g \cdot g_2 + f \cdot g_1) + g_2 \cdot f = (y \cdot g + f) \cdot (g_1 \cdot y + g_2)
18,593
\dfrac{1}{B\cdot G} = \tfrac{1}{G\cdot B}
40,398
\frac12 \cdot (\sqrt{2} + 1) = 1/2 + \dfrac{\sqrt{2}}{2}
-22,764
\frac{5}{5 \cdot 9}4 = \dfrac{20}{45}
17,400
x^2 = x \cdot x + (-1) + 1
-29,596
d/dx (-3*x^3) = -3*\frac{d}{dx} x^3 = -3*3*x * x = -9*x^2
4,432
\sin(-x - \dfrac{\pi}{2}) = -\cos\left(x\right)
26,946
2 2*191 = 764
-22,155
\tfrac{24}{20} = \tfrac{6}{5}
6,642
f + x + f + x = 2\cdot (x + f)
1,381
A^k = A \cdot \ldots \cdot A/k
-405
35 = \tfrac{7!}{4!*3!}
16,819
\left(-5\right)\cdot (-23) = 5\cdot 23
28,217
120 = \dfrac{1}{1/30}4
25,885
\frac{r_2*x}{q_2*q_1} = \frac{r_2}{q_2}*x/(q_1)
23,600
\left(b h + a q\right)/(b q) = \frac1q h + a/b
42,628
(4/3)^3 = \frac{64}{27} \gt 2
-10,272
-5/(4\cdot r)\cdot 10/10 = -\dfrac{1}{r\cdot 40}\cdot 50
53,815
1+4=3+2
-183
\frac{10!}{(5(-1) + 10)!} = 10\cdot 9\cdot 8\cdot 7\cdot 6
4,682
(2/5)^{k + (-1)}*4 = \dfrac{2^{k + (-1)}}{5^{k + (-1)}}*2^2
-4,570
\dfrac{1}{6 + y \cdot y + 5 \cdot y} \cdot (7 + 3 \cdot y) = \dfrac{1}{y + 2} + \frac{2}{y + 3}
38,673
13^{(-1) + m}\times 2 = 13^{m + 2\times (-1)}\times 2\times 13
32,399
2^{n + 4} = 2^{2 \times \left(-1\right) + n} \times 2^6
19,197
a/\sin{a} = R*2\Longrightarrow \frac{a}{R*2} = \sin{a}
-4,976
0.97\cdot 10^4 = 10^{8 + 4\cdot \left(-1\right)}\cdot 0.97
17,932
f^2 + x \cdot f' \cdot f = f' \cdot c \Rightarrow -f' \cdot c/f + f + x \cdot f' = 0
10,081
\left(2\cdot x\cdot y\right) \cdot \left(2\cdot x\cdot y\right) = 2^2\cdot x \cdot x\cdot y^2 = 4\cdot x \cdot x\cdot y^2
-23,813
\frac{1}{3 + 9} \cdot 36 = \frac{1}{12} \cdot 36 = \tfrac{1}{12} \cdot 36 = 3
2,929
\cos{4\cdot z} = \cos\left(2\cdot \pi - 4\cdot z\right) = \cos{9\cdot z}
-23,109
-\frac19 = \frac13\cdot ((-1)\cdot 1/3)
6,919
\frac{1}{\varphi^z} = \varphi^{-z}
14,265
\left(6 \cdot (-1) + 3 \cdot x \cdot x \cdot x - x^2 \cdot 2 + x \cdot 9 = 0 \Rightarrow 0 = (x \cdot 3 + 2 \cdot (-1)) \cdot x^2 + 3 \cdot (x \cdot 3 + 2 \cdot (-1))\right) \Rightarrow 0 = (3 \cdot x + 2 \cdot \left(-1\right)) \cdot (3 + x \cdot x)
25,913
x_1^R \cdot x_2 = (A \cdot x_1)^R \cdot A \cdot x_2 = x_1^R \cdot A^R \cdot A \cdot x_2
9,525
30^{1/2}*2 + 31 = (30^{1/2} + 1) * (30^{1/2} + 1)
-4,804
0.23\cdot 10^1 = 10^{6 + 5 \left(-1\right)}\cdot 0.23
-10,721
-\frac{1}{36 \cdot n + 12 \cdot \left(-1\right)} \cdot (4 \cdot n + 4) = -\dfrac{1}{9 \cdot n + 3 \cdot (-1)} \cdot \left(1 + n\right) \cdot \frac44
-20,601
-7/5 \frac{s \cdot 6 + (-1)}{6s + (-1)} = \frac{-42 s + 7}{5(-1) + 30 s}
-7,093
3/8\cdot \frac{3}{7} = \dfrac{1}{56}\cdot 9
-22,195
(t + 2)\times (10 + t) = 20 + t^2 + 12\times t
2,567
z^4 + 2\cdot (-1) = z^4 + 4 = z^4 + 4\cdot z^2 + 4 - z^2 = z \cdot z + 2 - z^2 = (z^2 + 2 - z)\cdot (z^2 + 2 + z)
-2,025
-\pi + \pi \cdot \frac{17}{12} = \frac{1}{12} \cdot 5 \cdot \pi
21,365
g^x \cdot \frac{1}{0! \cdot x!} \cdot x! = g^x
9,556
\mathbb{E}[|Y|] + \mathbb{E}[|X|] = \mathbb{E}[|X| + |Y|]
8,042
-3*10 + 5*7 = 5
19,269
\dfrac{1}{x^2 + 1}\cdot (2\cdot x \cdot x + x\cdot |x| + 2) = \frac{x^2 + 2}{x^2 + 1} = 1 + \frac{1}{x \cdot x + 1}
20,598
X*Z = Z^{1/2}*X*Z^{\dfrac12}
29,750
\left(y^2 - z^2 + 4y + 4 = 0 \Rightarrow 0 = -z^2 + (y + 2)^2\right) \Rightarrow (z + y + 2) (-z + y + 2) = 0
35,322
\sqrt{\sqrt{z}} = \sqrt{\sqrt{z}}
9,950
( z - y, z + y) = ( z, z) - \left( y, z\right) + ( z, y) - \left( y, y\right) = ( z, y) - ( y, z)
4,094
\binom{m}{x} = 0 = \binom{m + (-1)}{x + \left(-1\right)} + \binom{m + (-1)}{x}
14,082
\frac{\frac{1}{17}*2}{1/17*5} = \frac{2}{5}
10
\frac{1}{-z^2 + 4\times z} = \frac{1}{4}\times (\frac1z + \tfrac{1}{-z + 4})
6,907
-2^{1 + n} + 2^{2 + n} = 2^{1 + n}
21,112
(10*(-1) + 62 + 26*(-1))^7*26 = 26*26^7
-10,432
4/4\cdot (-8/(20\cdot r)) = -\frac{32}{80\cdot r}
31,527
(x_b - x_q)\cdot p\cdot r^2\cdot g = r^2\cdot (x_b - x_q)\cdot p\cdot g
7,868
\frac{z}{e}\cdot e = z
-22,271
(6 \cdot (-1) + f) \cdot (4 + f) = f^2 - 2 \cdot f + 24 \cdot (-1)
19,138
t + \left(-1\right) = (-1) + q \Rightarrow q = t
10,337
-(z - y) + l + 1 = l + 1 - z + y
-17,417
33 = 62 + 29*(-1)
-15,056
\dfrac{1}{\vartheta^4 \frac{1}{n^3}}n^5 = \dfrac{1}{\frac{1}{n^5} \tfrac{1}{n^3}\vartheta^4}
-16,596
\sqrt{80}*7 = 7*\sqrt{16*5}
-7,820
\left(20 - 40*i + 15*i + 30\right)/25 = \frac{1}{25}*(50 - 25*i) = 2 - i
-19,192
\frac{7}{24} = \frac{A_q}{64 \cdot \pi} \cdot 64 \cdot \pi = A_q
1,911
42 = 17 \cdot 1/2/2 \cdot \dfrac{168}{17} \cdot 1
6,467
(n + (-1)) \cdot 2 + 1 = n \cdot 2 + (-1)
16,006
d/s*f/p = d*f/(p*s)
-18,306
\frac{1}{30\cdot (-1) + y \cdot y - y}\cdot \left(5\cdot y + y^2\right) = \frac{y}{\left(y + 5\right)\cdot (y + 6\cdot (-1))}\cdot (y + 5)
-7,108
\frac{6}{14}*6/15 = 6/35
-3,064
(16*7)^{1/2} - 7^{1/2} = -7^{1/2} + 112^{1/2}
-20,368
\tfrac88 \cdot \frac{1}{3 \cdot x} \cdot (9 \cdot (-1) - x \cdot 9) = \frac{1}{24 \cdot x} \cdot (72 \cdot \left(-1\right) - x \cdot 72)
24,004
x \cdot x x^2 = xx^3 = 3x^2 - x
1,190
\cos\left(x + \theta\right) = -\sin{\theta} \sin{x} + \cos{\theta} \cos{x}
28,265
665-53=2\cdot306
10,828
9^{20} = 1.215 \ldots\cdot 10^{19} > 10^{19}
25,465
x^2/2 - 8x + Y = e^{z\cdot 2}/2 \Rightarrow e^{2z} = x^2 - 16 x + 2Y
10,198
(xa)^{k + (-1)} = (xa)^k/(xa) = x^k a^k \cdot 1/\left(ax\right) = x^k \frac{1}{x}a^{k + (-1)}
10,005
\sin(t) = \tan(t)*\cos\left(t\right) = \tfrac{1}{(1 + \tan^2(t))^{\frac{1}{2}}}*\tan(t)
18,421
\left(k \leq n \cdot x - n \cdot x \lt k + 1 \Rightarrow 0 \leq n \cdot x - n \cdot x - k < 1\right) \Rightarrow n \cdot x = x \cdot n + k
6,514
\tfrac{1/36}{\frac{1}{36}*3} = \frac{1}{3}
31,982
-z\times 404 + z\times 1010 = z\times 606
32,914
\left(n + 1\right)! = (n + 1)*n! \lt (n + 1)*\frac{n^n}{2^n}
17,481
(h_2 + h_1)^2 = h_1^2 + h_1 \cdot h_2 \cdot 2 + h_2^2
32,190
(1 + z + \ldots + z^4)^{1 + k} = (1 + z + \ldots + z^4)^k \cdot (1 + z + \ldots + z^4)
-7,019
4/7\times \frac36\times 2/5 = \tfrac{4}{35}