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ddrg
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math_formulas

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int64
-30,985
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3,446
\frac{\frac{1}{9}*5}{2} = \frac{5}{18}
2,703
\left(x + 5 \cdot (-1) \geq 0\Longrightarrow 5 \cdot (-1) + x = 1\right)\Longrightarrow 6 = x
-8,755
13^2=169
8,743
0 = C^2 \implies 0 = C
-9,274
r^2 \times 21 + 3 \times r \times r \times r = r \times 3 \times r \times r + r \times 3 \times 7 \times r
8,954
z_2 z_1 = \frac{1}{z_2 z_1} = 1/\left(z_1 z_2\right)
12,931
-1 = 2\times (-1) + 1
-10,402
\frac{25}{20 y + 100} = \dfrac{1}{4 y + 20} 5*\tfrac{5}{5}
33,310
900 = 1 + 999 + 100 \cdot \left(-1\right)
-5,355
\frac{0.27}{1000} = \frac{1}{1000} 0.27
8,274
\frac{1}{4! \cdot 3! \cdot 2!} \cdot 9! = \frac{1}{24 \cdot 6 \cdot 2} \cdot 362880 = 1260
16,013
h\cdot 4 - e\cdot 2 + 1 = 1 + h\cdot 4 - 2e
-20,980
\frac{1}{10\cdot r + 100}\cdot \left(-9\cdot r + 90\cdot (-1)\right) = \frac{r + 10}{10 + r}\cdot (-\frac{1}{10}\cdot 9)
3,765
(z + 1)/z = 1/z + 1
18,707
(c - b)*(c * c + c*b + b^2) = c^3 - b^3
6,406
1 = \frac{1}{n!} (n + 1)! = (n + 1) (n + 1 + (-1)) (n + 1 + 2 (-1))!/n!
-1,245
-\frac{10}{12} = \frac{(-10) \cdot 1/2}{12 \cdot 1/2} = -5/6
-6,014
\frac{5 x}{(x + 2) (x + 3)} = \tfrac{5 x}{x^2 + 5 x + 6}
9,975
49*b^2 + 35*(-1) = b * b*49 + 35*(-1)
-26,083
\frac{i - 2}{i - 2}\cdot \frac{1}{-i - 2}\cdot \left(1 + i\cdot 8\right) = \frac{1}{-2 - i}\cdot (1 + 8\cdot i)
15,560
d^2 + e^2 + f^2 = (-f)^2 + (-d)^2 + (-e) \cdot (-e)
9,658
x^7 + \left(-1\right) = (x^6 + x^5 + x^4 + x \cdot x \cdot x + x^2 + x + 1) \cdot ((-1) + x)
21,664
i^2 = ( 0, 1) \times ( 0, 1) = [-1,0] = \overline{-1}
-7,480
\frac12\cdot 9 = \dfrac18\cdot 36
-17,219
-\frac67 = -\frac67
-19,113
1/20 = \frac{1}{100\cdot \pi}\cdot Z_s\cdot 100\cdot \pi = Z_s
11,242
\frac{9}{48} + 3/54 = \frac{3}{16} + 1/18 = \ldots
40,640
\frac{1}{4} = 3!/4!
-18,088
25 (-1) + 30 = 5
20,331
\mathbb{E}[Z^2] = Var[Z] + \mathbb{E}[Z]^2
11,189
s_{1 + x} = s_{1 + x}
2,423
5/216 = \dfrac{1}{6*6}*5/6
-1,364
9*\frac{1}{2}/\left(\frac15*(-2)\right) = 9/2*(-5/2)
15,540
\sin^2{A} = \sin^2{A}
-10,347
\frac{4}{4}\cdot \left(-(3\cdot (-1) + 4\cdot n)/(9\cdot n)\right) = -\dfrac{1}{36\cdot n}\cdot (12\cdot (-1) + n\cdot 16)
22,676
\cos(x^3) + \left(-1\right) = 1 + (-1) - \frac{x^6}{2} + \dots = \frac{1}{2} \cdot ((-1) \cdot x^6) + \dots
-178
{10 \choose 6} = \frac{10!}{(10 + 6(-1))! \cdot 6!}
22,206
(A - H)^2 = A^2 - A*H - H*A + H^2 = A^2 + H^2
1,345
n^2 - 7\cdot n + 10 = (n + 3\cdot (-1))\cdot (n + 4\cdot (-1)) + 2\cdot \left(-1\right)
-10,720
-\frac{1}{5 + r\times 2}\times (8\times \left(-1\right) + r)\times 2/2 = -\frac{1}{10 + r\times 4}\times \left(16\times (-1) + r\times 2\right)
3,831
\cos(-x + \beta) = \cos\left(-(-\beta + x)\right)
11,623
-7\cdot z^2 + 28\cdot z + 24\cdot (-1) = -\left(z^2 - 4\cdot z + 4\right)\cdot 7 + 4
18,122
22100 = 50\cdot 52\cdot 51/(3\cdot 2)
-23,205
-12 = -8*\dfrac{3}{2}
-28,761
-\dfrac{3\cdot 1/2}{z + 2} + \dfrac12 = 1/2 - \frac{1}{4 + z\cdot 2} 3
7,911
(\frac{1}{1 + 0}\times (1 + 0))^0\times \frac23 = \frac13\times 2
17,130
\frac{(m + \left(-1\right))!}{(m + 2\cdot (-1))!} = \frac{\left(m + (-1)\right)\cdot (m + 2\cdot \left(-1\right))!}{(m + 2\cdot (-1))!} = m + (-1)
-26,613
49 \cdot m \cdot m - 126 \cdot n \cdot m + 81 \cdot n^2 = (-9 \cdot n + 7 \cdot m) \cdot (-9 \cdot n + 7 \cdot m)
14,209
\dfrac{1}{2^l} \cdot 2 = \frac{1}{2^{\left(-1\right) + l}}
47,875
\frac{\frac{1}{x}-1}{x-1} = \frac{\frac{1}{x}-1}{1}\cdot\frac{1}{x-1} = \frac{\frac{1}{x}-\frac{x}{x}}{1}\cdot\frac{1}{x-1} = \frac{1-x}{x}\cdot\frac{1}{x-1}
-1,409
\frac{1}{2}\cdot 7\cdot 7/2 = \dfrac{7\cdot 1/2}{2\cdot 1/7}
-13,392
-\dfrac{30}{3 + 8*\left(-1\right)} = -\frac{30}{-5} = -\dfrac{30}{-5} = 6
-6,704
7/100 + \frac{2}{10} = \frac{1}{100}\cdot 7 + 20/100
-15,746
\dfrac{(t^5)^5}{\left(t^5 z\right)^2} = \tfrac{t^{25}}{z * z t^{10}}
-22,902
3\cdot 26/\left(4\cdot 26\right) = \frac{1}{104}\cdot 78
16,256
\frac{3}{14} = 3/7\cdot \dfrac18\cdot 4
12,714
\tfrac{1}{1 + q} = 1 - q + \dfrac{q^2}{q + 1}
-7,469
24/5 = \tfrac{1}{10}48
673
a^2 = \left\lceil{y}\right\rceil \implies a^2 \leq \left\lceil{y}\right\rceil < a^2 + 1
37,354
x^2 - z^2 = (x - z) \cdot (x + z)
-29,581
4 \cdot n^3 - 8 \cdot n + 10 \cdot \left(-1\right) = \frac{\mathrm{d}}{\mathrm{d}n} (n^4 - n^2 \cdot 4 - n \cdot 10)
4,676
\frac{1}{2!}{10 \choose 5} = 126
-20,226
3/7 \times (-\frac{3}{-3}) = -\tfrac{9}{-21}
4,255
x^9 + (-1) = \left(x^3 + \left(-1\right)\right) \cdot (x^6 + x^3 + 1) = (x + (-1)) \cdot (x^2 + x + 1) \cdot (x^6 + x^3 + 1)
-10,742
-30 = 5 x + 1 + 21 \left(-1\right) = 5 x + 20 \left(-1\right)
-22,075
\frac83 = \frac{1}{12} \cdot 32
-3,858
63/54 \frac{z^5}{z^5} = \dfrac{z^5*63}{54 z^5}
-19,253
8/15 = A_s/(100\cdot \pi)\cdot 100\cdot \pi = A_s
30,610
x*2*x^x = x*2*x^x
-5,088
10^{3 - -2}*0.9 = 0.9*10^5
26,344
m + x + 1 + 1 = x + 1 + m + 1
7,471
\frac{60}{1 \cdot 2 \cdot 3} \cdot 1 + 3 \cdot \left(-1\right) = 7
-11,473
-22 + 20\cdot i = 3 + 25\cdot \left(-1\right) + 20\cdot i
33,389
a_l \cdot a_l = a_l^2
-19,083
\dfrac16 = \dfrac{1}{9 \cdot \pi} \cdot A_s \cdot 9 \cdot \pi = A_s
13,724
9 = 8 + 1 \Rightarrow 1 = 9 + 8*(-1) = 60 - 3*17 - 4*17 + 60*\left(-1\right) = 2*60 - 7*17
14,677
\frac{\pi}{2} = \tan^{-1}{\frac{1}{2^{1 / 2}}\cdot \infty}
17,305
a^\theta = b^y = (a\times b)^{\theta\times y}
24,164
\frac{1}{3! \cdot 4!} \cdot 210 \cdot 4! = \frac{7!}{3! \cdot 4!}
-1,864
-7/4\cdot \pi = -\pi\cdot \frac{11}{6} + \frac{\pi}{12}
20,851
A^2 = (A^1)^2 = A^{1\cdot 2}
-19,422
\frac{9}{1/5 \cdot 2} \cdot 1/7 = \frac17 \cdot 9 \cdot \frac12 \cdot 5
-14,170
3\cdot 10 + 7\cdot \dfrac55 = 3\cdot 10 + 7 = 30 + 7 = 30 + 7 = 37
16,413
i^{30} = i^2 i^2 \dots i^2 = -1
15,470
\frac{2}{100 \cdot 100} \cdot (25 \cdot 25 + 25 \cdot 25) = 1/4
20,667
20/91 = \binom{10}{1} \cdot \binom{5}{2}/(\binom{15}{3})
194
(\omega + N) \cdot (\omega + N) - (N - \omega)^2 = N\cdot \omega\cdot 4
11,981
\sin{x\cdot 3} = \sin{x}\cdot 3 - 4\cdot \sin^3{x}
27,114
i + 2 + 2(-1) = i
20,865
2 \cdot x \cdot a + x \cdot x + a^2 = (x + a) \cdot (x + a)
54,645
36 = 36
5,343
1 + \omega_0 + (-1) = \omega_0
15,770
\left\lfloor{\dfrac{1}{2} \cdot (n + 2 \cdot (-1))}\right\rfloor + 1 = \left\lfloor{\frac12 \cdot n}\right\rfloor
3,601
x^4 - x^2 = (2*x - x^2) * (2*x - x^2) = x^4 - 4*x^3 + 4*x^2
-7,049
\frac{4 / 9}{3}1 = \frac{4}{27}
-4,519
\frac{z\cdot 8 + 20\cdot \left(-1\right)}{5 + z \cdot z - 6\cdot z} = \frac{3}{z + \left(-1\right)} + \dfrac{1}{5\cdot (-1) + z}\cdot 5
-6,261
\tfrac{r}{(r + 10)*(7*\left(-1\right) + r)} = \frac{1}{70*(-1) + r^2 + r*3}*r
15,152
e^{\pi/2} = 4.8104 \cdot ... \approx 110^{\frac13} = 4.791
10,726
\frac{90}{3 \cdot 15} \cdot 4 = 8
26,094
\left(a + b\right) \times \left(a + b\right) = a^2 + b^2 + 2 \times a \times b = a^2 + b^2 + a \times b = a + b + a \times b = a \times b