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ddrg
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math_formulas

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int64
-30,985
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\frac{1}{z^2 + 1 - z*3}z = \frac{z}{-z^2 + (1 - 2z) (1 - z)}
-18,658
-\frac{1}{7}4 = -4/7
29,283
1 + \frac13\cdot (2 + 1 + 2) = \frac{8}{3}
32,110
i g = i h \implies h = g
16,174
(-B + A) \cdot (B + A) = -B^2 + A^2
2,910
\left(7^{m - n} + 1\right)\times 7^n = 7^m + 7^n
21,072
(3\cdot \left(-1\right) + z)\cdot (z + 2\cdot (-1)) = z^2 - 5\cdot z + 6
-158
\frac{9!}{(4 \cdot (-1) + 9)!} = 9 \cdot 8 \cdot 7 \cdot 6
-1,890
-\pi \frac{1}{3}4 + 2\pi = 2/3 \pi
27,724
g \cdot \alpha = g^x \cdot \alpha = \alpha^x \cdot g
13,888
(k - q)^2 = (q - k) (q - k)
-4,323
\tfrac{6}{z^2\cdot 5} = \frac{\frac{6}{5}}{z^2} 1
21,887
y^{B + w} = y^w \cdot y^B
-22,328
(9 + p)\cdot \left(p + 7\right) = 63 + p \cdot p + p\cdot 16
-29,109
3/10 \cdot 8 \cdot 10^2 = \frac{3}{10} \cdot 800
21,419
16 = (3 + 1)*(3 + 1)
20,053
\lim_{n \to \infty} \dfrac{1}{n}\cdot \left(10 + n\cdot 2\right) = \lim_{n \to \infty}(2 + \frac{1}{n}\cdot 10)
29,896
p = \frac1p \cdot p \cdot p
8,819
11 = \dfrac{1}{4}*\left(20 + 10 + 11 + 3\right)
29,562
1 + 2 + 4 + \dots + 2^U = 2^{U + 1} + (-1) = 2 \times 2^U + (-1)
757
(\sqrt{i})^2 = i = 0 + i = (a + b\cdot i)^2 = a^2 + 2\cdot a\cdot b\cdot i + b^2\cdot i^2 = a^2 - b^2 + 2\cdot a\cdot b\cdot i
-20,549
81\cdot y/(72\cdot y) = 9\cdot y/(y\cdot 9)\cdot 9/8
24,843
I^2 - 3\cdot I + 19\cdot (-1) = (7 + I)^2 - 17\cdot (I + 4)
12,185
( x^1, \cdots, x^n) = \left( x^1, \cdots, x^n\right)\cdot 11
19,384
h^k*h^k = h^{2*k}
4,370
\frac{d}{dz} (z e^z) = z e^z + e^z = z e^z + e^z
-3,578
x^5/x = \dfrac{1}{x}\cdot x^5 = x^4
22,193
Z^3 \times Z^4 = Z^7 = Z^2
1,598
{l \choose l - j} = \frac{1}{(l - j)! \cdot (l - l - j)!} \cdot l! = \frac{l!}{\left(l - j\right)! \cdot j!} = {l \choose j}
931
x = z \cdot e^z\Longrightarrow e^{-z} \cdot x = z
19,623
p/2 + 2\cdot (-1) \gt -1\Longrightarrow 2 \lt p
-19,394
\dfrac{\frac{1}{4} \cdot 5}{6 \cdot 1/7} = 5/4 \cdot 7/6
-20,937
\frac{g + \left(-1\right)}{(-7) g} \frac99 = (9g + 9\left(-1\right))/(g*\left(-63\right))
-9,979
-\frac{1}{5} \cdot (-1^{-1}) \cdot (-11/20) = \dfrac{\left(-1\right) \cdot (-1) \cdot (-11)}{5 \cdot 20} = -\frac{11}{100}
-1,718
\pi*7/4 + \dfrac{7}{12}*\pi = \frac{7}{3}*\pi
12,929
\cos^{-1}(\frac{1}{z^2 + 1}\times (z^2 + \left(-1\right))) = 2\times y rightarrow \cos(2\times y) = \frac{1}{1 + z \times z}\times \left(z^2 + (-1)\right)
17,252
f^2\cdot 2 + a^2 + f\cdot a\cdot 2 = f^2 + \left(a + f\right) \cdot \left(a + f\right)
25,330
80\% \cdot 30\% \cdot z = z \cdot 24\%
11,827
3 + \sqrt{2} = 3 + \sqrt{2}\cdot 8 - 7\cdot \sqrt{2}
9,932
6 \cdot 2 + 96 + 154 \cdot 0 = 108
5,166
\left(-1\right)^{3/2} = -(-1)^{\frac{1}{2}} = -i
8,440
c*x = \frac{1}{c*x} = x*c
25,219
2.4 = \frac1512
26,444
2^l - 2^{l + \left(-1\right)} = 2^{l + (-1)} \cdot (2 + (-1)) = 2^{l + (-1)} \cdot (\dotsm!)!
1,918
1 + 2 + 3 + 4 = 1 + 4 + 2 + 3 = (1 + 4)/2 + \frac{1}{2} \cdot (1 + 4) + \frac{1}{2} \cdot (2 + 3) + (2 + 3)/2 = 4 \cdot 5/2 = 10
-26,537
-d^2 + a^2 = (-d + a)\cdot (a + d)
20,806
c_1 + c_2 = ( c_1, c_2) ( 1, 1) \leq \left(c_1^2 + c_2^2\right)^{1/2}
38,739
2^2*149 = 596
22,234
\frac{1}{r \cdot s} = \frac{1}{r \cdot s}
1,246
\dfrac{1}{(-1)\times x}\times \sin{-x} = \frac1x\times \sin{x}
-3,324
-\sqrt{63} + \sqrt{7} + \sqrt{112} = -\sqrt{9\cdot 7} + \sqrt{7} + \sqrt{16\cdot 7}
5,459
y \cdot y - 2 \cdot b \cdot y + b^2 = (-b + y)^2
33,429
g_1 - g_2 + 1 = 1 + g_1 - g_2
46,140
50 = 2*5^2
16,450
|\dfrac{1}{b + f*i}| = \dfrac{1}{|b + f*i|}
-5,037
55.2*10^3 = 55.2*10^{1 + 2}
18,197
(z^2 + (-1))^3 = z^6 - z^4*3 + z * z*3 + (-1)
36,765
D^{7.4} = D^{-2.6}\cdot D^7\cdot D^4/D
-11,081
(z + 10 \times \left(-1\right))^2 + h = (z + 10 \times (-1)) \times (z + 10 \times \left(-1\right)) + h = z^2 - 20 \times z + 100 + h
13,101
g = b rightarrow 0 = -g + b
-17,427
8 \cdot \left(-1\right) + 47 = 39
21,765
(t^{\frac{k}{2}} + 1)\cdot (t^{\frac{k}{2}} + (-1)) = (-1) + t^k
28,911
\binom{20}{14} = \binom{20}{20 + 14 (-1)} = \binom{20}{6}
26,815
2*5^2 + 0^2 = 50
-1,339
\frac{1}{\frac15*4}*\left(\left(-1\right)*1/4\right) = -\dfrac{1}{4}*\frac54
9,089
1 + \sin{y} = 1 - \cos\left(\pi/2 + y\right) = 2\cdot \sin^2\left(\dfrac{\pi}{4} + \dfrac12\cdot y\right)
10,592
(717*\left(100 + (-1)\right) - (\left(-1\right) + 1000)*71)/\left(999*99\right) = \frac{1}{999}*717 - \frac{1}{99}*71
-26,011
(9 - 2\cdot i + 36\cdot i + 8)/17 = \dfrac{1}{17}\cdot (17 + 34\cdot i) = 1 + 2\cdot i
17,358
\sqrt{-\psi}\cdot \sqrt{-\psi} = -\psi
30,998
216 = 2^3\cdot 3^3 = 6^3
-22,139
\frac13\cdot 2 = \frac{1}{9}\cdot 6
12,872
\left(-q + 1\right)\cdot \left(1 + q\right) = -q^2 + 1
-22,912
\frac{4 \times 28}{5 \times 28} = \frac{1}{140} \times 112
-25,838
\frac{1}{z + 7}(z^3 + 5z^2 - z*9 + 30) = z * z - z*2 + 5 - \frac{1}{z + 7}5
52,524
70 = {8 \choose 4}
7,969
h + \frac12 \cdot (-h + c) = \dfrac{1}{2} \cdot \left(h + c\right)
21,252
-\cos^2(\alpha) + \sin^2(x) + 1 = -\cos^2\left(x\right) + \sin^2(\alpha) + 1
2,272
t_m - t < x \Rightarrow t_m < t + x
-18,974
\dfrac{1}{3} = \dfrac{1}{9 \cdot \pi} \cdot A_s \cdot 9 \cdot \pi = A_s
-20,685
-\dfrac{1}{12}\cdot 54 = \frac66\cdot \left(-\frac12\cdot 9\right)
-3,578
\dfrac{t^5}{t} = t \cdot t \cdot t \cdot t \cdot t/t = t^4
15,024
1 - \left(y + 1\right)/3 = (2 - y)/3
-22,341
\left(k + 10\right) (k + 8(-1)) = 80 (-1) + k^2 + k\cdot 2
13,413
s^2 - 2\cdot s + 3\cdot (-1) = (1 + s)\cdot (s + 3\cdot (-1))
17,927
(x - y)\cdot (y \cdot y + x^2 + x\cdot y) = x^3 - y^3
27,059
5625 = {6 \choose 4} {5 \choose 1} {5 \choose 1} {6 \choose 4}
-25,006
\frac15\cdot 94 = 18.8
-3,067
16^{1/2}\cdot 6^{1/2} - 6^{1/2} = 4\cdot 6^{1/2} - 6^{1/2}
40,741
23 = 2*6 + 11
6,436
30/121 = 5/11\times \frac{6}{11}
19,547
-2\cdot \pi\cdot r \cdot r \cdot r + 4\cdot \pi\cdot r\cdot R^2 = 2\cdot r \cdot r \cdot r\cdot \pi + 4\cdot \pi\cdot R^2\cdot r - 4\cdot r \cdot r \cdot r\cdot \pi
12,930
\pi/3 - \pi = \frac{\left(-2\right)*\pi}{3}
32,126
3s - 3s^2 + s^3 = s\cdot 2 - s^2 + s - 2s \cdot s + s^3
24,556
z^6 + \left(-1\right) = \left((-1) + z\right) (z^0 + z^5 + z^4 + z^3 + z z + z^1)
17,262
k^4 = k \cdot k \cdot k^2 > 6 \cdot k^2
-10,308
\frac{2}{2} \cdot \frac{1}{3 \cdot x + 3} \cdot \left(x + 7 \cdot (-1)\right) = \dfrac{1}{6 \cdot x + 6} \cdot (2 \cdot x + 14 \cdot (-1))
-2,960
\sqrt{3} = \sqrt{3}\cdot (2\left(-1\right) + 3)
43,617
\left(g^x\right)^1 = g^{x/1}
22,785
(1 + \psi)^q \cdot (1 + \psi)^x = (1 + \psi)^{x + q}
-20,474
\frac{6 + r}{r*8 + 48} = \tfrac{1}{6 + r} (6 + r)/8