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ddrg
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math_formulas

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int64
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4,091
(\frac1Y)^4 = \dfrac{1}{Y^4}
27,625
\pi/4 = y \implies \cos^5\left(y\right) - \sin^5(y) = 0 \neq \cos(5\times \pi/4)
6,820
\frac1Y*(J + I) = J/Y + I/Y
-7,950
\frac{1}{4} \cdot (-16 \cdot i - 20) = -20/4 - \frac{16}{4} \cdot i
28,362
x*(b + a) = bx + xa
273
-d^3 + c \cdot c \cdot c = \left(c^2 + d\cdot c + d^2\right)\cdot (c - d)
-29,824
l*x^{(-1) + l} = \frac{\mathrm{d}}{\mathrm{d}x} x^l
-20
4 + 3 \cdot (-1) = 1
-29,582
d/dx (-x*10 + x^4 - 4x^2) = 10 (-1) + 4x^3 - 8x
-20,335
\frac{8 - z\cdot 4}{14 (-1) + 7z} = -4/7 \frac{2\left(-1\right) + z}{z + 2(-1)}
-20,959
\dfrac{2}{2}\cdot (-\frac{1}{2}) = -\frac{2}{4}
38,568
2^2 = x \cdot x \Rightarrow 2 = x
12,718
\left(y + (-1)\right) (y + 4) = 4(-1) + y^2 + 3y
-12,106
25/72 = \dfrac{x}{12 \cdot \pi} \cdot 12 \cdot \pi = x
19,159
1 + b^2 \cdot b = (1 + b^2 - b)\cdot (b + 1)
-2,946
8 \sqrt{13} = (5 + 3) \sqrt{13}
31,563
\left(-2\right) \times (-2) = 4
1,362
e^{H + ...}\cdot e^E = e^E\cdot e^H
12,173
7^{\frac{1}{2}} = \left(4^2 - 3^2\right)^{\dfrac{1}{2}}
-7,291
\dfrac{1}{7} \cdot 2/2 = 1/7
15,295
\sin(-v + u) + \sin(u + v) = 2 \cdot \sin(u) \cdot \cos(v)
28,595
2\cdot \sin(y)\cdot \cos(y) = \sin(y\cdot 2)
-20,956
-10/9\cdot \frac{1}{x + 2\cdot (-1)}\cdot (x + 2\cdot (-1)) = \frac{20 - 10\cdot x}{x\cdot 9 + 18\cdot (-1)}
36,406
\frac{d}{dx} x^{\left\{2\right\}} = x + x = 2*x
21,189
1 = 8/35 + \frac{12}{35} + \frac17 + \frac17 \cdot 2
27,383
(-1) + a^k = (a + 1) (a^{k + (-1)} - a^{k + 2 (-1)} + a^{k + 3 \left(-1\right)} - \cdots + a + (-1))
4,913
s = p^{a \cdot m} \cdot s^{f \cdot m} = (p^a \cdot s^f)^m
39,246
2^J + 2^m = 2^J + 2^m
12,870
\tfrac{1}{e^m} = e^{-m}
1,836
A_D \cdot A_l = A_D \cdot A_l
20,581
-1 = a + b \Rightarrow -16 = a - b
7,262
\binom{p}{i} = \tfrac{1}{i! \cdot (-i + p)!} \cdot p!
17,368
\binom{2 \cdot x}{x} \cdot x!^2 = (x \cdot 2)!
13,003
n\cdot {n + (-1) \choose x + (-1)} = x\cdot {n \choose x}
22,733
z \gt 1 rightarrow 7 \cdot z > 7 = 7
7,263
(-(X - Y)^2 + (X + Y)^2)/4 = Y \cdot X
-4,419
\frac{-x + 11 \left(-1\right)}{5 + x^2 - x*6} = \tfrac{3}{(-1) + x} - \frac{4}{x + 5(-1)}
-9,322
2*3*3 - 2*3*7*r = -r*42 + 18
-1,626
-\dfrac{5}{4}\cdot \pi + 2\cdot \pi = 3/4\cdot \pi
18,478
x + y \cdot i = (1 - i)^{1/4} \Rightarrow 1 - i = \left(y \cdot i + x\right)^4
-4,509
(y + 5) \left(y + 1\right) = 5 + y^2 + y*6
-734
(e^{\pi\cdot i/4})^{14} = e^{14\cdot \pi\cdot i/4}
12,000
1 = A*a rightarrow A = 1/a
14,530
g_2^3 + g_1^3 + 3*g_2*g_1 * g_1 + 3*g_1*g_2^2 = \left(g_2 + g_1\right)^2 * (g_2 + g_1)
3,369
\frac{1}{1 - x}*(1 + x) = \dfrac{2 - 1 - x}{1 - x} = \dfrac{1}{1 - x}*2 + (-1)
4,622
\sum_{x=1}^\infty h \cdot x \cdot (2 \cdot (-1) + 5)^x = \sum_{x=1}^\infty 3^x \cdot x \cdot h
20,992
x^3 + 2 = x^3 + (-1) = (x + (-1)) \times \left(x^2 + x + 1\right)
-16,797
7 = 7\times 5\times x + 7\times 4 = 35\times x + 28 = 35\times x + 28
-7,655
\left(85 - 35 i - 17 i + 7 (-1)\right)/26 = \frac{1}{26} \left(78 - 52 i\right) = 3 - 2 i
13,467
2y^2 + 6y + 35 = 2\left(y^2 + 3y\right) + 35 = 2(y + \dfrac{3}{2})^2 + 61/2
-20,360
\frac{4\cdot x + 4}{9 + x}\cdot 10/10 = \frac{1}{x\cdot 10 + 90}\cdot (40 + 40\cdot x)
25,858
y^4 + F^4 = -(y\cdot F)^2\cdot 2 + (F^2 + y^2)^2
6,828
n\cdot \pi = r\cdot \pi/3 \implies n\cdot 3 = r
18,406
1 + \frac{\mathrm{d}y}{\mathrm{d}t} = y^2 + 1 \Rightarrow \frac{\mathrm{d}y}{\mathrm{d}t} = y^2
-10,321
(20 + 50 q)/(50 q) = \frac{1}{5q}(5q + 2)*10/10
-19,056
\frac15 \cdot 4 = \dfrac{A_r}{16 \cdot π} \cdot 16 \cdot π = A_r
39,061
1/4 + 1/6 = (3 + 2)/12 = \frac{1}{12}\cdot 5
12,787
(a + 12)\cdot \left(6 + a\right) = a^2 \implies -4 = a
3,121
\dfrac38 = \frac{1}{8}\cdot 3
18,932
x + 2 x + 4 x + 8 \cdots = x
17,655
45 = (2^4 + (-1))\cdot 3
16,195
(g + b) \cdot \left(g - b\right) = g \cdot g - b^2
16,122
u^2 - v v = (u + v) (u - v)
-20,334
-\frac{1}{-3 \cdot s + 8 \cdot (-1)} \cdot 2 \cdot \frac33 = -\tfrac{1}{-9 \cdot s + 24 \cdot (-1)} \cdot 6
13,649
\frac13 \cdot 210 = 70
22,486
1 = x^2 + 2 \cdot x \cdot y + 5 \cdot y^2 = \left(x + y\right) \cdot \left(x + y\right) + 4 \cdot y^2
15,092
\frac{c}{a^4} = \frac{1}{a^4} \cdot c
27,502
x^2 + (-1) = \left(x + 1\right)*\left(x + (-1)\right)
-20,124
9/8 \cdot \frac{(-2) \cdot n}{n \cdot (-2)} = \frac{1}{n \cdot \left(-16\right)} \cdot ((-1) \cdot 18 \cdot n)
11,541
\bar{f_x}\cdot E\cdot a\cdot g = g\cdot \bar{f_x}\cdot E\cdot a
17,251
h = \left(w/h + \dfrac{h}{w}\right) \cdot x = \frac{w \cdot w + h^2}{w \cdot h} \cdot x
15,565
0 = (5 \cdot (-1) + 5)/6
30,019
\cos(b)\times \sin(a) = \frac12\times (\sin(-b + a) + \sin(b + a))
14,255
31 + 8\cdot \sqrt{15} = (a + b\cdot \sqrt{15})^2 = a^2 + 15\cdot b^2 + 2\cdot a\cdot b\cdot \sqrt{15}
22,870
5^y - 4^y = ((-1) + (5/4)^y)*4^y
22,589
2 \cdot a + x + y = y + 2 \cdot a + x
6,608
2 + 4 + 6 + ... + 2*n = n*\frac{1}{2}*(2*n + 2) = n^2 + n
-20,086
\dfrac{8}{2} = 2/2\cdot 4/1
13,627
Y/\left(Y_0\right) = 1000 \implies Y_0 = Y/1000
24,889
\frac{1}{2^x}\cdot a_{x + (-1)}\cdot 8 = 4\cdot \frac{1}{2^{(-1) + x}}\cdot a_{(-1) + x}
12,517
-5\cdot b + 5\cdot a = (a - b)\cdot 5
6,863
-\dfrac{x}{1 + x} + 1 = \dfrac{1}{1 + x}
15,668
1/4\cdot \frac{\dfrac{1}{4}\cdot 4/4}{4}/4 = \frac{4}{4^5}
12,188
-2k + 2n \geq n + 1 \implies k \leq \left(n + (-1)\right)/2
2,450
\infty + 1 = \infty \implies \infty + \infty\cdot \left(-1\right) = \infty - \infty + 1 = -1
-22,794
\dfrac{60}{40} = \tfrac{3\cdot 20}{2\cdot 20}
-16,481
\sqrt{9\cdot 3}\cdot 8 = \sqrt{27}\cdot 8
29,735
gh^n = h^n g
-9,081
25.2\% = \frac{25.2}{100}
22,705
144^{1 / 2} = (10^2)^{\frac{1}{2}} + (2 * 2)^{1 / 2}
18,321
g^2 + h^2 + 2gh = \left(h + g\right)^2
16,609
(1 + 1 + 1)!/\left(1!*1!*1!\right) = 3! = 6
4,066
k + 1 = \dfrac{1}{1 + k}\cdot k + k + \frac{1}{1 + k}
17,574
6 \times (-1) + z^2 - z = 0 \Rightarrow z = 3
16,826
10 = 0\cdot 10^0 + 10^1
-12,379
10 \cdot \sqrt{2} = \sqrt{200}
2,751
2 - \frac{1}{2^{n + \left(-1\right)}} = \frac{1}{2^{n + (-1)}}\cdot (2^n + (-1))
-2,335
\frac{1}{16} = \frac{1}{16}2 - 1/16
25,476
1/9 + \tfrac{1}{15}\cdot 2 = 11/45
20,229
\frac{1}{w \times g} = \frac{1}{g \times w}