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ddrg
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math_formulas

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int64
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23,553
(1 + y) \cdot (-y + 1) = 1 - y^2
15,072
\dfrac{4}{4!} \cdot 10 \cdot 8 \cdot 6 = 80
-20,753
\frac{14 \cdot i}{i \cdot 2 + 8 \cdot (-1)} = \dfrac{2}{2} \cdot \frac{7 \cdot i}{4 \cdot (-1) + i}
14,992
0 = (m \cdot m - h \cdot h)^2 + m^2 = (m^2 - i\cdot m - h^2)\cdot (m \cdot m + i\cdot m - h^2)
-12,173
1/5 = q/(10 \pi)\cdot 10 \pi = q
-3,541
2/100 = \frac{2}{2*50}
22,840
12 (x + (-1))^2 (1 + x) = (x + (-1)) \left(x + 1\right) (\left(-1\right) + x)*12
27,774
i\cdot i = i^2
32,036
b + 0 (-1) = b
24,119
(x + 2)^{1 / 2} \left(2 + x\right) = (x + 2)^{3/2}
41,442
9 = \left(-3\right)\cdot \left(-3\right)
26,193
-\frac{b^2}{4} + (x + \frac{b}{2})^2 + c = x \cdot x + b\cdot x + c
8,467
\pi\cdot 0 - \pi/8 = -\frac{\pi}{8}
14,682
4^3 + 4^2 = 4^2\cdot (4^2 + (-1))/3
-20,797
-1^{-1} \dfrac{1}{9s + 6}(6 + s*9) = \frac{-9s + 6\left(-1\right)}{9s + 6}
-20,021
\frac{9 - 9*q}{4*(-1) + 4*q} = -\dfrac94*\frac{1}{(-1) + q}*(q + (-1))
-1,702
\pi\cdot \frac{13}{12} + 5/6\cdot \pi = 23/12\cdot \pi
31,123
20^{1 / 2} = 5^{1 / 2} \cdot 2
9,544
x_n = x_{n + \left(-1\right)} + x_{2 \cdot (-1) + n} \Rightarrow x_{(-1) + n} = x_n - x_{2 \cdot (-1) + n}
25,595
|z_2 + 0\cdot (-1)| = |z_2|
12,043
2 \cdot 3^4 \cdot 1247527 = 202099374
17,257
(a - f) \left(f + a\right) = a^2 - f^2
4,263
3^3 - 3*3^2 + 3*(-1) + 3 = 3^3 - 3 * 3 * 3 + 0 = 0
17,823
\cos\left(\operatorname{acos}(2/z)\right) = \frac{1}{z}\cdot 2
-20,656
\frac{1}{(-1) + q}\left(2(-1) + q\right) \cdot 7/7 = \frac{14 \left(-1\right) + 7q}{q \cdot 7 + 7(-1)}
9,787
|x*\alpha| = |x|*|\alpha|
-10,747
3/3*(-\dfrac{1}{5*(-1) + t*3}*10) = -\dfrac{1}{15*(-1) + 9*t}*30
6,696
3^{2*n} + (-1) = ((-1) + 3^n)*(1 + 3^n)
3,208
11/19\times \frac{12}{20} = \dfrac{132}{380}
14,579
\left(z + 1\right)\cdot (z + 3\cdot (-1)) = \left(z + (-1) + 2\right)\cdot (z + (-1) + 2\cdot (-1)) = (z + (-1))^2 + 4\cdot (-1)
-26,137
-\frac{3}{2} - -\frac{1}{1}\cdot 3 = -1.5 + 3 = 1.5
34,825
d + z = z = z + d
-11,300
(z + a)^2 = (z + a)\cdot \left(z + a\right) = z^2 + 2\cdot a\cdot z + a \cdot a
-26,440
4 + x^2 - 5*x = \left(4*(-1) + x\right)*((-1) + x)
-6,014
\frac{5}{(r + 2)\cdot (3 + r)}\cdot r = \frac{r\cdot 5}{6 + r^2 + 5\cdot r}
1,343
\int_a^b \frac{1}{x}\,dx = \int_a^b 1/x\,dx
26,089
x_g\cdot x_i = x_g\cdot x_i
26,999
1/(G\cdot n) = 1/(n\cdot G)
2,455
A \times I = A \times I
-19,031
\frac{9}{20} = \dfrac{A_s}{25 \pi} \cdot 25 \pi = A_s
-24,579
5\cdot 8 + 3\cdot \frac{1}{10}10 = 5\cdot 8 + 3 = 40 + 3 = 40 + 3 = 43
29,711
-2\times \left(2 - 2\times z\right) + \left(-1\right) = 5\times (-1) + z\times 4
5,444
B/z = \frac{B}{z}
2,091
x + \alpha/2 + \alpha/2 = x + \alpha
18,226
(-1) + z^8 = (z^4 + 1) \cdot \left(z^4 + (-1)\right)
40,764
-\tfrac{1}{7} = -\tfrac17
-12,962
\frac{1}{20}\times 15 = \tfrac{1}{4}\times 3
-7,120
4/10\times 5/11 = \tfrac{1}{11}\times 2
22,311
D_i\times D_j = D_j\times D_i
27,403
-\frac{6}{20} + 1 = 7/10
-26,458
y^2 \cdot 9 + 4 - 12 \cdot y = (y \cdot 3)^2 + 2 \cdot 2 - 2 \cdot 2 \cdot y \cdot 3
8,583
\dfrac{(-1)^n}{\left(-1\right)^{2 \cdot n}} = \dfrac{1}{(-1)^n}
15,881
i = j \implies -i + j = 0
2,690
6 + 420 + 60*\left(-1\right) = 366
28,705
500000 = 5*10^5
28,853
1 + {5 \choose 2} = 11
-5,738
\dfrac{5}{q^2 - 10q + 16} = \dfrac{5}{(q - 8)(q - 2)}
-16,745
-6 = -6 \times (-p) - -48 = 6 \times p + 48 = 6 \times p + 48
-358
\frac{9!}{(3*\left(-1\right) + 9)!} = 9*8*7
-23,101
3/4\cdot 15/4 = \tfrac{45}{16}
20,957
x = \frac13 \cdot \left(2 \cdot x + x\right)
670
(a - b)^2 = (a - b)*(a - b) = a * a - 2*a*b + b^2
3,645
G_2 = G_1 \cap G_2 \Rightarrow \left\{G_2, G_1\right\}
-20,176
\frac{1}{8 \cdot (-1) + x} \cdot (-5 \cdot x + 2 \cdot (-1)) \cdot \frac{3}{3} = \frac{6 \cdot (-1) - 15 \cdot x}{3 \cdot x + 24 \cdot \left(-1\right)}
-1,679
-5/4 \times \pi = \pi \times 7/12 - 11/6 \times \pi
-20,622
\frac{1}{l\cdot 30}\left(-l\cdot 40 + 20 (-1)\right) = 5/5 (-l\cdot 8 + 4(-1))/\left(l\cdot 6\right)
-720
-24 \cdot \pi + \frac{299}{12} \cdot \pi = 11/12 \cdot \pi
18,219
Z^l*Z = Z^{l + 1} = Z*Z^l
8,570
-\frac{1}{\sqrt{3}} + 1 = 1 - \tfrac13\sqrt{3}
-4,915
\frac{0.74}{10} = \frac{0.74}{10}
55,095
0 = det\left(x^4\right) = det\left(x\right)^4
717
\dfrac1z = \bar{z} = z^n rightarrow z^{n + 1} = 1
-1,262
\frac{1}{(-7) \frac{1}{5}}(\left(-8\right) \dfrac13) = -\frac{5}{7} (-\frac138)
15,956
\sin{2*z} = \frac{2*\tan{z}}{1 + \tan^2{z}}
-12,224
2/3 = \dfrac{1}{10 \cdot \pi} \cdot p \cdot 10 \cdot \pi = p
-22,279
m \cdot m + 9\cdot m + 14 = (m + 2)\cdot (m + 7)
25,696
\cot(y + 2\pi) = \cot{y}
-23,017
\dfrac{77}{4 \cdot 11} \cdot 1 = 77/44
6,651
1/(5*49*17) = \frac{1}{4165}
9,601
(y/g*g)^i = y^i/g*g
921
15/51 = \dfrac{(-1) + 16}{52 + (-1)}
18,904
\frac{1}{(1 + 1) \cdot 2^1} \cdot (1 + 2) = \tfrac34 = 1 - 1/4 = 1 - \frac{1}{(1 + 1) \cdot 2^1}
7,608
(t\times x)^2 = x^2\times t \times t
907
8/216 = 2/6\cdot \frac{1}{36}\cdot 4
1,157
\frac{1}{d + b}\cdot (d^2 + b\cdot d + b^2) = d + b - \frac{b\cdot d}{d + b}
-1,721
\tfrac{7}{2}*\pi - \pi*2 = \pi*\tfrac32
25,338
2^2 + 3^2 + 6^2 = 7 * 7
-9,431
-2\times 3\times 5 - 3\times 3\times 3\times t = 30\times (-1) - 27\times t
-21,709
-34/11 = -34/11
-2,905
3^{1 / 2} + (16*3)^{\dfrac{1}{2}} = 3^{1 / 2} + 48^{1 / 2}
3,696
n\cdot x = 1\Longrightarrow x = 1/n
44,120
(-19600) (-1) - 19177 = 423
22,798
-\frac{1}{8}\cdot 9 = -9/8
20,129
19 = 2 \times \left(-1\right) + 164 + 82 \times (-1) + 38 \times (-1) + 18 \times (-1) + 5 \times (-1)
8,539
\frac{1}{27}\cdot 4/180 = \frac{1}{1215}
21,910
1008 + \left(2014 + 1008 \cdot (-1)\right)/2 = 1511
32,898
(\sigma^2 + 5*\sigma + 5)^2 - 1^2 = (\sigma^2 + 5*\sigma + 4)*\left(\sigma^2 + 5*\sigma + 6\right) = (\sigma + 1)*(\sigma + 4)*\left(\sigma + 2\right)*\left(\sigma + 3\right)
7,089
2*l + 1 = l^2 + 2*l + 1 - l^2 = (l + 1) * (l + 1) - l^2*\cdots
27,144
\frac{1}{4^2}\cdot (-1^2 + 2^2) = \frac{3}{16}
-11,082
(y + 5 \cdot (-1)) \cdot (y + 5 \cdot (-1)) + b = (y + 5 \cdot (-1)) \cdot (y + 5 \cdot (-1)) + b = y^2 - 10 \cdot y + 25 + b