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ddrg
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math_formulas

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int64
-30,985
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13,791
-\left(y + 1\right) \cdot (2 \cdot \left(-1\right) + y) \cdot 3 = -3 \cdot y^2 + 3 \cdot y + 6
-483
e^{\pi i*19/12*3} = (e^{i\pi*19/12})^3
-23,238
0.17 \cdot 0.029 = 0.17 \cdot (0.17 \cdot 0.17) = 0.17^3
25,000
2^k\cdot 2^z = 2^{z + k}
11,043
\mathbb{E}\left[V \cdot V\right] = \mathbb{E}\left[V\right] \cdot \mathbb{E}\left[V\right] + \mathbb{Var}\left[V\right]
22,589
z + 2\times a + x = z + a\times 2 + x
8,590
\cos{\frac{11}{7} \cdot \pi} = \cos{\frac{\pi}{7} \cdot 3}
-9,134
40\times (-1) + p\times 20 = -5\times 2\times 2\times 2 + p\times 2\times 2\times 5
-23,178
63/16 = 3/4 \cdot \frac{21}{4}
29,776
f + \left(-1\right) + \frac{1}{9} \cdot 99 = 10 + f
109
(-\cos\left(x\cdot 2\right) + 1)/2 = \sin^2(x)
40,222
\sqrt{(-1)^2} = 1
14,416
|x^3 + 3\cdot x^2\cdot h + 3\cdot x\cdot h^2 + h^3 - x^3| = |3\cdot x^2\cdot h + 3\cdot x\cdot h^2 + h^3| \geq 3\cdot x^2\cdot h
-8,457
-2 = (-1) \cdot 2
15,505
\dfrac{1}{2}*V = E \Rightarrow E \gt V
7,189
(-z)^{2/3} = ((-z)^2)^{\frac{1}{3}} = z^{\frac23}
228
f_1^l\cdot f_2/(f_2) = (\frac{f_1}{f_2}\cdot f_2)^l
-14,437
4 + (3 - 7*6) = 4 + (3 + 42*(-1)) = 4 - 39 = 4 + 39*(-1) = -35
422
\frac{3}{3\cdot 2} = \frac{1}{2}
-7,071
4/6*\frac{5}{7}*3/5 = \dfrac{2}{7}
34,186
84 = 3\binom{6 + 3 + (-1)}{3 + (-1)}
29,577
-21 = 27*(-1) + 30 + 24*(-1)
26,239
y \cdot x = 24\Longrightarrow y \cdot \frac{\mathrm{d}x}{\mathrm{d}t} + \frac{\mathrm{d}y}{\mathrm{d}t} \cdot x = 24
25,399
(d_1^2 + d_2^2) \cdot (r^2 + s^2) = (d_1 \cdot s + d_2 \cdot r)^2 + (d_1 \cdot r - d_2 \cdot s) \cdot (d_1 \cdot r - d_2 \cdot s)
-4,025
\dfrac{15 \cdot z^3}{3 \cdot z^5} \cdot 1 = \frac{1}{z^5} \cdot z^3 \cdot 15/3
41,569
2\cdot \left(1 + 3\right) = 8
30,820
a^m\cdot a^0 = a^m = a^{m + 0}
28,390
(m + 2)! = (m + 2) \cdot (1 + m) \cdot m \cdot \ldots
12,765
n*3 + 2 = n + (n + 1)*2
5,826
(a + b)/2 = a + \dfrac12 \cdot (b - a) = b - \tfrac12 \cdot \left(b - a\right)
-19,385
\frac{3}{\dfrac13*5}*1/8 = 3/5*3/8
-22,297
\left(k + 3\right) \cdot (k + (-1)) = 3 \cdot (-1) + k^2 + 2 \cdot k
13,068
\frac{\partial}{\partial x} |z\cdot x|^{0.5} = (x^2\cdot z^2)^{1/4}/\left(2\cdot x\right)
35,530
\frac{1}{6} ((-1) + 3) = \dfrac{1}{3}
32,412
2^n + 2 (-1) - 2 (\left(-1\right) + n) = 2^n - n \cdot 2
-12,445
200/5 = 40
27,145
(2 \cdot k^{1/2})^3 = k^{\frac32} \cdot 8
-25,964
48/0.24 = 48/0.24 = \frac{48 \cdot 100}{0.24 \cdot 100}
-18,606
3f + 5(-1) = 6*\left(3f + 4(-1)\right) = 18 f + 24 \left(-1\right)
-17,123
-5 = -5*\left(-4*x\right) - 40 = 20*x - 40 = 20*x + 40*(-1)
16,084
2 + z < 0 \Rightarrow z \lt -2
-22,907
\dfrac{15}{25} = \tfrac{3\cdot 5}{5\cdot 5}
16,609
\frac{1}{1!*1!*1!} (1 + 1 + 1)! = 3! = 6
4,347
4*z = 4*z + 1 = z + z + 1/4 + z + 2/4 + z + 3/4
8,732
\dfrac{\tau}{m} \cdot 1/y = \frac{1/m}{y} \cdot \tau = \dfrac{\tau}{y \cdot m}
9,171
det(A^2 - I) = 0 \Rightarrow det(A-I) = 0
31,382
\dfrac{6}{\left(2 \cdot \left(-1\right) + \nu\right)^3} = z \implies \left(\nu + 2 \cdot (-1)\right) \cdot \left(\nu + 2 \cdot (-1)\right) \cdot \left(\nu + 2 \cdot (-1)\right) = 6/z
-22,182
21/15 = \tfrac75
40,712
\frac{\sin{\theta}}{\cos{\theta}} = \tan{\theta}
17,058
u + w = v \Rightarrow v - u = w
17,597
168 = db \Rightarrow \frac1b168 = d
8,690
0 = x_3 - x_1 \cdot 7 - 11 \frac{1}{5}\left(2x_1 - x_2\right) \Rightarrow 0 = 5x_3 - x_1 \cdot 57 + x_2 \cdot 11
39,334
-15 = 37 \cdot \left(-1\right) + 22
11,825
(z + (-1))^2 + \left(-1\right) = -2\cdot z + z \cdot z
34,549
4\cdot i^2 = (2\cdot i)^2
28,804
t^H\cdot t^Z = t^{Z + H}
16,840
(p^3 - p^2)/2 = ((-1) + p)/2 \cdot p^2
-25,370
\frac{\mathrm{d}}{\mathrm{d}y} (\sin{y}/\cos{y}) = \sec^2{y}
37,103
16\times 6 + 4 = 100
7,074
{3 \choose 2} \cdot s_1 \cdot s_2^3 = 3 \cdot s_2 \cdot s_2 \cdot s_2 \cdot s_1
-27,167
\sum_{n=1}^\infty \tfrac{\left(0 + 4\right)^n}{n \cdot 4^n} = \sum_{n=1}^\infty \frac{4^n}{n \cdot 4^n} = \sum_{n=1}^\infty \frac{1}{n}
25,485
((-1) + s) \times (s^2 + s + 2) + 2 = s + s^3
28,554
\cos{2\cdot z} = (-1) + 2\cdot \cos^2{z}
21,415
3 + 2 \cdot 2 \cdot 2 = 11
30,352
\frac{1}{3 + 1}(3^2 + 3) = 3
-3,792
r^4*144/\left(r*36\right) = r^4/r*144/36
13,858
\left(1 + 1\right) (2 + 1) (1 + 1) = 12
8,455
\frac{1}{3} = 0.33333\cdot \dots
15,451
\int \frac{1}{u^2 + 1}\,\text{d}u = \arctan(u)
7,040
\frac{1}{18} = \tfrac{17}{18} \cdot \frac{16}{16} \cdot 1/17
-28,763
-\frac12 - \dfrac{4}{2 - 2 \cdot y} = \dfrac{5 \cdot \left(-1\right) + y}{2 - 2 \cdot y}
4,647
\frac{-x^3 + x^{n + 1}}{x + (-1)} = 0 \cdot x + x^2 \cdot 0 + x^3 + \dots + x^{(-1) + n} + x^n
3,632
n \cdot (n + (-1))/n = n + (-1)
-24,193
\frac{1}{6 + 5}*44 = 44/11 = \dfrac{1}{11}*44 = 4
-1,701
-2 \cdot π + π \cdot \frac{17}{6} = \frac56 \cdot π
21,080
6 \epsilon = 3 \epsilon + 3 \epsilon
21,471
\frac3x\cdot i\cdot V = w^2 \Rightarrow \sqrt{\dfrac1x\cdot i\cdot 3\cdot V} = w
-26,408
\frac{z^3}{z^4} = z^{-4 + 3} = \frac{1}{z}
30,302
\frac25 = \tfrac{1/9}{1/9 + 1/6}
29,673
2 \cdot \theta + \left(2 \cdot \theta + 1\right) \cdot (2 \cdot \theta + 1)^2 + 1 = 8 \cdot \theta^3 + 12 \cdot \theta \cdot \theta + 8 \cdot \theta + 1 = 4 \cdot (2 \cdot \theta^3 + 3 \cdot \theta^2 + 2 \cdot \theta + 1)
-26,394
\dfrac{1}{y^7 \cdot \frac{1}{y^{13}}} = y^{-7 - -13} = y^{-7 + 13} = y^6
-16,822
4 = 4 \cdot 2 \cdot y + 4 \cdot 5 = 8 \cdot y + 20 = 8 \cdot y + 20
-15,749
\tfrac{x^5}{\frac{1}{\tfrac{1}{x^{10}}\cdot z^6}} = \tfrac{x^5}{x^{10}\cdot \frac{1}{z^6}}
-9,317
b*5*b - 5*7*b = 5*b^2 - b*35
-12,747
18 + 3\left(-1\right) = 15
-29,356
x\times (-7)\times (x + 3\times \left(-1\right)) = x^2 - 3\times x - 7\times x + 21 = x^2 - 10\times x + 21
5,392
\frac{k!}{2^k} \geq \frac{1}{2^{\frac32 \cdot k}} \cdot k^{\frac{k}{2}} = (\frac{1}{2 \cdot 2 \cdot 2} \cdot k)^{k/2} = (k/8)^{k/2}
29,894
4 \cdot \pi \cdot r^2 = 2 \cdot r \cdot \pi \cdot 2 \cdot r
139
\frac{\dfrac{1}{3}*2*1/3}{3}*2 = 4/27
8,676
z^5 = 1 \cdot 1 \cdot z^1 \cdot z \cdot z \cdot z \cdot z = 1^1 \cdot z^3 \cdot \left(z^2\right)^1 = 1^0 \cdot z^5 \cdot (z^2)^0
-20,823
\frac{1}{30 \cdot x} \cdot \left(80 \cdot (-1) - 60 \cdot x\right) = \frac{1}{3 \cdot x} \cdot (-6 \cdot x + 8 \cdot (-1)) \cdot 10/10
2,132
4 \cdot \dfrac{2^3}{3^4} + \tfrac{2^4}{3^4} = \dfrac{1}{27} \cdot 16
36,429
5^2 + 6 \cdot 6 = 61
1,192
\cos(\alpha - \beta) = \sin{\alpha} \cdot \sin{\beta} + \cos{\beta} \cdot \cos{\alpha}
-20,737
7/7 \cdot \dfrac{1}{r + 5 \cdot (-1)} \cdot \left(r + 9 \cdot \left(-1\right)\right) = \frac{1}{35 \cdot (-1) + 7 \cdot r} \cdot (63 \cdot (-1) + r \cdot 7)
-15,944
\frac{1}{10}*4*7 - 10*\frac{6}{10} = -\frac{32}{10}
11,628
\frac{1}{2}*(1 - \cos\left(2*x\right)) = \sin^2\left(x\right)
114
\frac14\cdot \frac13/2 = 1/24
49,404
12^2 = 4! + 5!
33,376
x \cdot x \cdot x^2 = x^4