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ddrg
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math_formulas

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1
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int64
-30,985
55.9k
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437k
14,214
7290 = 1 \times 9 \times 9 \times 9 \times 5 \times 2
13,211
30 = (63 - 30 \cdot q) \cdot q + (63 - 30 \cdot q) \cdot q \cdot q \cdot q = 63 \cdot q - 30 \cdot q^2 + 63 \cdot q \cdot q \cdot q - 30 \cdot q^4
16,455
\mathbb{E}[\left(Z_1 \cdot Z_2\right)^2] = \mathbb{E}[Z_1^2 \cdot Z_2^2] = \mathbb{E}[Z_1 \cdot Z_1] \cdot \mathbb{E}[Z_2 \cdot Z_2]
-25,219
\frac{\mathrm{d}}{\mathrm{d}y} y^m = y^{(-1) + m} \cdot m
-22,221
\eta \cdot \eta + \eta\cdot 5 + 6\cdot (-1) = \left((-1) + \eta\right)\cdot (\eta + 6)
6,835
1 - 80 \times x^2 - x \times 120 + 45 \times (-1) = 1 - 5 \times \left(9 + x^2 \times 16 + x \times 24\right)
25,464
\tfrac{1}{n \cdot n + 4\cdot (-1)}\cdot 4 = \tfrac{1}{(n + 2)\cdot (n + 2\cdot (-1))}\cdot (n + 2 - n + 2\cdot \left(-1\right)) = \frac{1}{n + 2\cdot (-1)} - \dfrac{1}{n + 2}
2,132
\frac{16}{27} = \frac{2^4}{3^4} + \frac{1}{3^4} \cdot 2^3 \cdot 4
-30,713
x*20 + 5*(-1) = ((-1) + 4*x)*5
47,113
6^{65} = 3^{65}\cdot 2^{65}
16,614
(2 + k)/k = \left(1 + k\right)/k \dfrac{1}{k + 1}(k + 2)
11,570
7^{2l} + 208 l + \left(-1\right) = 48^2 c + 256 l = 256*(9c + l)
5,386
15/79 = 0.189873 \cdot \ldots \approx 0.19
21,012
(f \cdot z)^2 = (z \cdot f) \cdot (z \cdot f)
41,794
1 = 0.999 \times \cdots
525
\left(\left(0 = \|x\|_0 \Rightarrow \|\mathbb{P}(x)\|_2 = 0\right) \Rightarrow 0 = \mathbb{P}(x)\right) \Rightarrow 0 = x
-26,652
(p^4*9 + 10) (9p^4 + 10 (-1)) = 81 p^8 + 100 (-1)
11,058
\left(m + (-1)\right)/m = 1 - \frac1m
-1,756
π \cdot \frac{1}{12} \cdot 5 + π = \dfrac{1}{12} \cdot 17 \cdot π
14,477
z = 5 \Rightarrow z^2 = 25
1,268
(x^2 + k \cdot k)^2 - (x^2 - k^2) \cdot (x^2 - k^2) = (2 \cdot x \cdot k)^2 = 2 \cdot 2 \cdot x \cdot x \cdot k \cdot k
-25,273
\frac{\mathrm{d}}{\mathrm{d}y} \frac{1}{y^3} = -\frac{3}{y^4}
23,115
x \cdot x\cdot 2 - x\cdot 3 = 2((-1) + x^2) - 3(1 + x) + 5
3,181
k^9 - k^3 = (\left(-1\right) + k^3) k^3 \cdot \left(k \cdot k \cdot k + 1\right)
18,431
\left(6l + 3\cdot (2x + 1) = 9 = 6(l + x) + 3 \Rightarrow x + l = 1\right) \Rightarrow l = 1 - x
-1,717
\pi/6 - \pi/12 = \pi/12
23,098
\tfrac{1}{\frac1a + \frac1b} = a*\dfrac{b}{b + a}
7,388
-16 = \left(5 + 7*\left(-1\right)\right)*\left(5 + 3\right)
32,768
\dfrac{t^2+x^2-tx}{tx} = \dfrac76 \implies 6t^2-13tx+6x^2 = 0 \implies 6t^2 - 9tx - 4tx + 6x^2 = 0
-20,342
\frac33 \cdot \frac{(-2) \cdot i}{-3 \cdot i + 3 \cdot (-1)} = \dfrac{i \cdot (-6)}{-9 \cdot i + 9 \cdot \left(-1\right)}
15,191
1/(x b) = \dfrac{1}{x b} = x b^2
-23,551
\frac{3}{16} = \frac{\dfrac{1}{8}*3}{2}
-9,484
36\cdot (-1) + k\cdot 84 = 2\cdot 2\cdot 3\cdot 7\cdot k - 2\cdot 2\cdot 3\cdot 3
-13,922
\frac{42}{8 + 6} = \dfrac{42}{14} = \frac{42}{14} = 3
15,320
\frac{\frac{1}{k^3} \cdot \frac{1}{x^2}}{\frac{1}{k^5} \cdot x^6} \cdot 1 = \frac{k^5}{k^3 \cdot x^6 \cdot x^2} = \frac{k^2}{x^8}
-21,028
-\frac157 \dfrac{1}{x + 4}(4 + x) = \frac{1}{x*5 + 20}(28 (-1) - x*7)
25,270
CD^2 = CD^2
4,944
c\cdot c\cdot c\cdot c\cdot c\cdot c = (c\cdot c\cdot c)^2
12,632
\sin(z*2) = 2\cos\left(z\right) \sin\left(z\right)
20,324
WS = SW
22,189
(1/x + 1 + x)^2 = x^2 + x\cdot 2 + 3 + 2/x + \frac{1}{x \cdot x}
115
34/49 - \frac{18}{49} = \frac{16}{49}
-17,987
5 \cdot (-1) + 75 = 70
13,853
4 \cdot k \cdot k + 4 \cdot k + 1 = 1 + 4 \cdot \left(k^2 + k\right)
-7,820
(20 - 40 i + 15 i + 30)/25 = \dfrac{1}{25}(50 - 25 i) = 2 - i
3,598
-\tfrac{1}{x} = \frac{1}{x \cdot x}\cdot (x\cdot \left(-1\right))
927
10 + 6 \cdot i + (z - 3 \cdot i)^2 = 10 + 6 \cdot i + z^2 - 6 \cdot i + 9 \cdot (-1) = 1 + z \cdot z
54,425
1597 = 610 + 987
5,913
\left(Fy = \lambda y \Rightarrow Fy \lambda = F^2 y\right) \Rightarrow Fy = \lambda Fy = \lambda * \lambda y
40,739
2^{\frac14} = 2^{\dfrac{1}{4}}
-17,718
3 = 23 + 20 (-1)
-5,082
18.0 \cdot 10^2 \cdot 10 = 10^{1 + 2} \cdot 18
13,514
(t-2)^2 = t^2 - 4t + 4
32,761
\dfrac{1}{(-1)\cdot g} = -\tfrac1g
17,345
2/3 + 2 = 8/3
28,132
-V^2 + (V + C) * (V + C) - C^2 = C*V + V*C
16,085
b + a = a + b \Rightarrow [a, b]
15,712
n*4 + 2 = \left(2n + 1\right)*2
3,627
x\cdot u_{q\cdot q}\cdot C + (x\cdot G + C\cdot W)\cdot u_q + G\cdot u\cdot W = u_{q\cdot q}\cdot C\cdot x + W\cdot u_q\cdot C + x\cdot u_q\cdot G + W\cdot u\cdot G
1,053
z^2 + y \cdot y + y\cdot z\cdot 2 = \left(y + z\right)^2
33,788
e \cdot G = e \cdot G
5,935
y^3 \cdot z \cdot z \cdot z = (z \cdot y)^3
25,907
\left\lfloor{(a + b + \left(-1\right))/b}\right\rfloor = \left\lfloor{((-1) + b)/b + \frac{a}{b}}\right\rfloor
492
-2\cdot a = \frac{1}{-a - 1}\cdot (-b + 7) \Rightarrow 7 - b = a\cdot 2 + 2\cdot a^2
22,321
1 = 111 \cdot \dots
13,192
(n + 1)! + n! = \left(1 + n\right)\cdot n! + n!
36,896
X + E = E + X
-26,546
1^2 + 2 \cdot y + y^2 = 1 + y \cdot 2 + y \cdot y
-3,065
\sqrt{7} \cdot \sqrt{16} + \sqrt{25} \cdot \sqrt{7} = 4 \cdot \sqrt{7} + 5 \cdot \sqrt{7}
-21,613
1 = \cos\left(2 \cdot \pi\right)
-2,660
\sqrt{11} + 4 \cdot \sqrt{11} = \sqrt{11} \cdot \sqrt{16} + \sqrt{11}
33,591
3\cdot 4 + 3\cdot 3 = \left(3 + 4\right)\cdot 3
7,020
z \cdot z^2 + 8 \cdot (-1) = z^3 - z \cdot z \cdot 2 + z \cdot z \cdot 2 - z \cdot 4 + z \cdot 4 + 8 \cdot (-1)
5,589
\tfrac{17.4}{4} = 1/2\cdot \frac12\cdot 17.4
25,038
\dfrac{1}{g\cdot h} = \frac{1}{g\cdot h}
-15,957
-\frac{4}{10}\cdot 8 + 6/10\cdot 9 = \frac{1}{10}\cdot 22
-24,926
\sin(z) \cdot \cos(z) \cdot 2 = \sin\left(z \cdot 2\right)
31,027
3 \cdot m + 2 = n \implies \frac{n \cdot n}{3} \cdot 1 = 3 \cdot m^2 + m \cdot 4 + 1
26,063
n \cdot n \cdot n \cdot n \cdot n \cdot n \cdot n \cdot n = n^8
-15,212
\frac{1}{m^{16} \cdot \frac{1}{m^5 \cdot r^5}} = \dfrac{1}{\frac{1}{r^5 \cdot m^5} \cdot m^{16}}
-12,905
16 + 6\cdot (-1) = 10
25,512
d/dy \ln(y) = \dfrac{1}{e^{\ln(y)}} = \frac{1}{y}
9,864
m_1\cdot x - m_2\cdot x = (-m_2 + m_1)\cdot x
40,712
\tan\left(\theta\right) = \sin(\theta)/\cos\left(\theta\right)
17,626
x\cdot Y = x\cdot Y\cdot (A + Z') = x\cdot Y\cdot A + x\cdot Y\cdot Z'
-20,407
\frac{1}{p \cdot (-6)} \cdot (3 - p \cdot 10) \cdot \frac14 \cdot 4 = \frac{-p \cdot 40 + 12}{p \cdot \left(-24\right)}
36,464
\cos(22) \cdot \cos(38) - \sin(22) \cdot \sin(38) = \cos(22 + 38) = \cos(60) = \frac{1}{2}
16,186
\left(-C = -R + K \cdot R \implies R \cdot (-d \cdot I + K) = -C\right) \implies R = \dfrac{C \cdot (-1)}{-I \cdot d + K}
4,714
h = ( h, h\times 2, \dotsm)
13,662
c\cdot m\cdot \dfrac{1}{\xi}\cdot B = c\cdot B\cdot m/\xi
30,639
a^n \times a^x = a^{n + x}
25,029
\sum_{j_1=0}^{j_2 + 1 + (-1)} x^{j_1} = \sum_{j_1=0}^{j_2} x^{j_1}
2,677
x a^i = x a^i
-20,788
-\frac15*7*\frac{1 + l}{1 + l} = \frac{-7*l + 7*(-1)}{5 + 5*l}
-26,462
(-b + g)^2 = g^2 - 2 g b + b b
22,820
\tfrac{1}{2} = e^{-\log_e(2)}
-15,121
\dfrac{1}{m^{12}*\tfrac{m^5}{t^{20}}} = \dfrac{(\frac{1}{m^4})^3}{(\tfrac{m}{t^4})^5}
-13,131
62 \cdot \frac{1}{-5}/(-4) = \frac{62}{\left(-5\right) \cdot \left(-4\right)} = \frac{1}{20} \cdot 62
-5,025
53.2/1000 = \tfrac{1}{1000} \times 53.2
16,651
\sqrt{2} = -\sin(((-1) \pi)/4) + \sin\left(\pi/4\right)