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ddrg
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math_formulas

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\sum_{x=1}^j (d_x + e*h_x) = \sum_{x=1}^j d_x + (\sum_{x=1}^j h_x)*e
22,807
\arctan{0} = \dfrac{1}{1 + 0^2}0
7,121
|y^3| = |y|^2 \implies |y| = 1
10,733
\dfrac{1}{1 - 1 - r} = 1/r
19,684
\frac121 = \frac12
-4,950
1.11\cdot 10 = 1.11\cdot 10/100 = 1.11/10
38,116
\dfrac{16}{2}9 = 72
41,842
\frac16240 = 40
-199
\frac{1}{2!}\cdot 5!/(\frac{1}{5!}\cdot 8!) = \frac{\dfrac{1}{3!\cdot (5 + 3\cdot (-1))!}}{\tfrac{1}{3!\cdot (3\cdot (-1) + 8)!}\cdot 8!}\cdot 5!
39,721
1/2 = \frac12 \cdot |-1|
-356
\frac{4! \cdot \frac{1}{\left(3 \cdot \left(-1\right) + 4\right)! \cdot 3!}}{\frac{1}{(3 \cdot (-1) + 9)! \cdot 3!} \cdot 9!} = \dfrac{\frac{1}{1!}}{1/6! \cdot 9!} \cdot 4!
18,749
f*A = f*\frac{A*f}{f}
22,185
2*x + 1 + x^2 - x^2 = 2*x + 1
18,919
(1 + r)^3 - (1 - r) \left(1 - r\right)^2 = 2 (3 r + r^3) = 2 r*\left(3 + r^2\right)
21,687
A*9 = 9 rightarrow 1 = A
12,229
\frac{1}{\binom{38}{5}} = 5!\cdot 33!/38! = \dfrac{1}{501942}
-7,044
\frac{1}{11}\cdot 3\cdot \frac{3}{10} = \frac{1}{110}\cdot 9
21,665
c^3 + g^3 = (g^2 + c^2 - cg) (g + c)
12,565
\dfrac{1}{t^{1/2}} \cdot t^3 = t^{5/2}
46,791
-1 + 2^{1 / 2} = -1 + 2^{1 / 2}
-12,120
\frac{5}{18} = s/(6*\pi)*6*\pi = s
10,409
\frac49 = \frac{1}{(-1) + \left(-1\right) \times 2 + (-1)^2 \times 12} \times \left((-1)^2 + 3\right)
25,450
\left(1 + t^4\right)\cdot (1 + t^2)\cdot ((-1) + t)\cdot (1 + t) = t^8 + \left(-1\right)
-10,844
\frac{1}{10}110 = 11
22,163
0 = x \cdot 6 + 3 \Rightarrow x = -1/2
5,994
A^{\dfrac12} \cdot A^{\frac12} = A
30,053
m\cdot {n \choose m} = (n - m + 1)\cdot {n \choose m + (-1)} = n\cdot {n + (-1) \choose m + (-1)}
-28,412
x \times x - 6 \times x + 13 = x \times x - 6 \times x + 9 + 4 = (x + 3 \times \left(-1\right))^2 + 4 = (x \times (-3))^2 + 2^2
15,271
e\cdot x^2 - 2\cdot x\cdot e \cdot e = 1 + e\cdot 4 + 9\cdot e^2 + \cdots + x^2\cdot e^{x + (-1)}
27,569
a \cdot b \cdot c = a \cdot b \cdot c = \dfrac{1}{b \cdot c} \cdot a
-10,063
\frac18 5 = 0.625
29,548
(-1) + 2^{1092} = \left((-1) + 2^{273}\right)*\left(2^{546} + 1\right)*(2^{273} + 1)
23,160
\dfrac{1 + z^2}{z * z * z - z} = \frac{1}{z + (-1)} - 1/z + \frac{1}{1 + z}
25,445
a^3 + a^2\cdot h\cdot 3 + 3\cdot a\cdot h^2 + h^3 = (a + h)^3
33,367
\sqrt{2}\cdot 8 + 3 = 7\cdot \sqrt{2} + 3 + \sqrt{2}
-501
π\cdot \frac{52}{3} - π\cdot 16 = \dfrac{4}{3}\cdot π
24,158
x^3 = x^2 \cdot x = x \cdot x = x
25,345
\left(1 + x\right)^2 = 1 + 2 \times x + x^2 \gt 1 + 2 \times x
45,386
5 = \tfrac51
21,376
2\times 6^y = 2^{y + 1}\times 3^y
3,828
a \cdot b = c \implies c = a \cdot b,b = c \cdot a
12,471
d/dx \cos{\pi/x} = \tfrac{1}{x^2} \cdot \sin{\pi/x} \cdot \pi
39,414
1 + 100 + 2 + 99 + 3 + 98 = 1 + 2 + 3 + 4 + \dotsm + 97 + 98 + 99 + 100
13,093
\frac{d}{dx} (\frac{3}{x}) = 3 \cdot \left(-\frac{1}{x^2}\right) = -\frac{1}{x^2} \cdot 3 = -\frac{3}{x^2}
-6,383
\frac{6}{3 \cdot (8 \cdot \left(-1\right) + y) \cdot (y + 5)} = \frac{3}{3} \cdot \frac{2}{(5 + y) \cdot (y + 8 \cdot (-1))}
-4,487
(x + 4)*\left(x + 2*(-1)\right) = 8*\left(-1\right) + x^2 + x*2
20,484
(-t + 1)*(\mathbb{Var}[Z] + 1/t) = (1 - t)/t + t*0 + (-t + 1)*\mathbb{Var}[Z]
9,769
x^2 - h \cdot h = h^2 - x \cdot x \cdot x - h \cdot h = x - h^2
9,400
\dfrac{1}{y}((-1) + y) = -\frac{1}{y} + 1
-2,979
\sqrt{7} = \left(2(-1) + 4 + (-1)\right) \sqrt{7}
9,299
w = \operatorname{P}(w) + w - \operatorname{P}\left(w\right)
9,743
l^2 = l! \frac{1}{\left((-1) + l\right)!}l
15,714
\cos(\arctan\left(z\right)) = \frac{1}{\sqrt{1 + z^2}}
2,284
\frac{\sin\left(y\cdot \pi/2\right)}{y} = \pi/2\cdot \frac{\sin(\frac{\pi}{2}\cdot y)}{\pi\cdot y\cdot 1/2}
17,312
9/10 = 90/100
-19,428
\tfrac{1/5}{7\cdot \tfrac{1}{5}}\cdot 7 = \dfrac{7}{5}\cdot \frac{1}{7}\cdot 5
-1,201
-21/24 = \frac{(-21)\cdot \frac{1}{3}}{24\cdot 1/3} = -7/8
-17,725
19 + 2 \cdot \left(-1\right) = 17
-5,705
\dfrac{1}{\left(2 (-1) + t\right) (t + 9 \left(-1\right))*8} 24 = 8/8*\dfrac{1}{(t + 9 (-1)) (t + 2 (-1))} 3
7,693
x - -x^2 * x/3! + \tfrac{1}{2!}*x * x - -x^5/5! + x^4/4! - \dots = \sin{x}
11,368
\sin(\alpha)\cdot \cos\left(x\right) + \cos(\alpha)\cdot \sin(x) = \sin(x + \alpha)
6,975
n = 2n + (-1) - n + \left(-1\right)
-10,327
\tfrac{2 \cdot 1/2}{5 \cdot (-1) + 3 \cdot x} = \dfrac{2}{6 \cdot x + 10 \cdot (-1)}
13,023
\frac{1}{2!\cdot 2^2}4! = 3
3,958
\frac{2}{24} = \dfrac{2}{2 + 7 + 15}
39,684
\sqrt{-1} = (-\sqrt{2} + \sqrt{2} + \sqrt{-2})/\left(\sqrt{2}\right)
24,257
15/256 = 15 \cdot 1/16/16
28,348
(3 w) (3 w) + (4 w)^2 = 25 w^2
38,304
(2/3)^3 = \frac{1}{27}8
15,084
\frac1a\cdot (h + x) = x/a + h/a
-18,655
\frac{1}{14}\cdot 25 = \frac{1}{28}\cdot 50
-5,734
\frac{3}{5\cdot \left(p + 2\cdot \left(-1\right)\right)} = \frac{1}{5\cdot p + 10\cdot (-1)}\cdot 3
4,552
1 - \frac{7}{x^2} = \frac{1}{x^3} \times (x^3 - 7 \times x)
24,708
1 - \sin^2{x} = \cos^2{x} = (1 + \cos{2\cdot x})/2
13,857
1 + x^2 - x*2 = \left((-1) + x\right)^2
20,066
(z + (-1)) \left(y + (-1)\right) = z + (-1) + y + \left(-1\right) + (z + (-1)) (y + (-1)) = zy + (-1)
11,427
V[X+Y]=V[X]+V[Y]
758
\tfrac{1}{x^r} = x^{-r}
12,281
\cos\left(\tan^{-1}(y)\right) = \frac{1}{(1 + y \cdot y)^{1/2}}
3,852
(n + 1)^5 - n^5 = 1 + n^4*5 + n n^2*10 + n^2*10 + n*5
13,291
\sum_{k=1}^l (1 + k)*((-1) + k) = \sum_{k=1}^l (1 + k)*((-1) + k)
5,452
x^3 + 1 = x^3 + \left(-1\right) = (x + (-1)) \cdot (x^2 + x + 1) = (x + 1) \cdot (x^2 + x + 1)
-10,569
\frac{\frac{1}{3}}{z \cdot 25} 3 = 3/(75 z)
-8,033
(i\cdot 4 - 10)/\left(-2\right) = -10/(-2) + i\cdot 4/(-2)
1,499
3 = \left\lceil{\frac{1}{16} 33}\right\rceil
26,417
\left(b - c\right)^2 + b\cdot c = b^2 - c\cdot b + c^2
20,357
\frac{1}{3 + \left(-1\right)} \cdot ((-1) + 3^{n + 1}) = 3^n \cdot 2 \Rightarrow 0 = -3^n + (-1)
24,547
12\cdot l + 2 = 7\cdot l + 1 + 5\cdot l + 1
18,836
a - i = -(-a + i)
10,356
\left(1/A = 3*A \Rightarrow A^2*3 = x\right) \Rightarrow \frac{x}{3} = A^2
42,631
2000 + 1023 \left(-1\right) = 977
-12,112
14/45 = \frac{\delta}{12\cdot \pi}\cdot 12\cdot \pi = \delta
28,292
(a + h)^2 = 100 = a^2 + 2\times a\times h + h^2\Longrightarrow -\frac{1}{2}\times (a^2 + h^2) = h\times a
-28,966
4 = 13 + 9 \times \left(-1\right)
-21,442
\frac{1}{10}\cdot 3\cdot \frac{10}{10} = \dfrac{30}{100}
14,209
\dfrac{2}{2^m} = \frac{1}{2^{(-1) + m}}
2,671
2 \cdot 2 + 4^2 + 4^2 = 6 \cdot 6
33,381
3796 + 52*\left(-1\right) = 3744
-20,876
\left((-4)*i\right)/\left((-28)*i\right) = \frac{1/((-4)*i)*(-4*i)}{7}
17,626
X*W = X*W*\left(Z + Z'\right) = X*W*Z + X*W*Z'