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ddrg
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math_formulas

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int64
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-3,243
(2(-1) + 3) \sqrt{10} = \sqrt{10}
18,235
d^3 = -2\cdot d + (-1) = d + 2
-18,460
-\frac{1}{10}15 = -3/2
-3,573
\frac{1}{z^4}\times z = \frac{z}{z\times z\times z\times z} = \dfrac{1}{z^3}
-25,857
yyyyyyy/(yy) = y^5
34,712
(4 + 12 + 2)(3!)3 = 324
22,847
f\cdot c\cdot f = f\cdot c\cdot f = f\cdot c\cdot f
7,711
c = I^2 \cdot 2 - 5 \cdot I + 2 \cdot (-1) rightarrow -c + 2 \cdot I^2 - 5 \cdot I + 2 \cdot (-1) = 0
23,039
\frac{1}{x^2} + x^2 = \left(\frac1x + x\right)^2 + 2\cdot (-1)
14,620
|z_0 - \frac1c \cdot ((-1) \cdot h)| = |z_0 + h/c|
18,537
\frac{1}{3}\cdot (a + 2) = 2\Longrightarrow 4 = a
36,525
10 = 40 + 30\cdot (-1)
31,311
N \times f_2 \times N \times f_1 = N \times f_1 \times N \times f_2
6,154
y^{c + (-1)} \cdot c = \frac{\partial}{\partial y} y^c
5,071
\left(1 + 1\right) \cdot (1 + 1) \cdot (2 + 1) = 12
20,392
-a^3 + x^3 = (-a + x) \left(x^2 + ax + a^2\right)
6,742
(-1)^3 = (-1)^{\frac{6}{2}} = ((-1)^6)^{1/2} = 1^{1/2} = 1
-29,002
0.125 = \left(0 (-1) + 0.25\right)/2
-735
(e^{\dfrac56 \cdot i \cdot \pi})^{19} = e^{19 \cdot i \cdot \pi \cdot 5/6}
-17,482
99 + 43 \cdot \left(-1\right) = 56
-27,727
\frac{d}{dz} (5\cdot \tan(z)) = 5\cdot \frac{d}{dz} \tan(z) = 5\cdot \sec^2(z)
2,240
B\times G = B\times G
43,231
d \cdot d = d^2
-22,035
36/40 = \frac{1}{10}\cdot 9
-22,343
6 + q \cdot q + q \cdot 7 = (6 + q) \cdot (q + 1)
-1,379
-7/9*7/2 = \frac{1/2}{\frac{1}{7}*(-9)}*7
9,960
\frac{n!}{(2\cdot (-1) + n)!\cdot 2} = \binom{n}{2}
1,301
(A - B) \cdot (A - B) = A^2 - 2\cdot B\cdot A + B^2
-20,217
\frac{1}{-3}\cdot (4 - 6\cdot l)\cdot \dfrac{1}{7}\cdot 7 = \frac{1}{-21}\cdot (28 - l\cdot 42)
-24,651
\frac16 \cdot 10 = \frac{5}{6} + 1/2 + 1/3
15,911
(f + d)^2 = f^2 + 2*d*f + d * d
-19,674
6\times 4/(7) = \frac{24}{7}
21,197
\cos(f_1) \cos(f_2) - \sin(f_1) \sin(f_2) = \cos(f_2 + f_1)
9,970
\binom{-k + N_2}{-k + N_1} = \dfrac{(-k + N_2)!}{\left(-k + N_1\right)! \cdot (N_2 - N_1)!}
-13,272
5 + 8\cdot 3 = 5 + 24 = 29
-7,220
2/7 \frac183*4/9 = 1/21
16,200
(x \cdot x + 1)\cdot (1 + x)\cdot (x + \left(-1\right)) = (-1) + x^4
14,322
H \cdot x \cdot f = f \cdot x \cdot H
20,898
x^2 = (\sqrt{l + \sqrt{l + \sqrt{l + \dotsm}}})^2 = l + x
-6,024
\tfrac{3 \cdot r}{\left(r + 10\right) \cdot \left(r + 4 \cdot (-1)\right)} = \frac{3 \cdot r}{40 \cdot (-1) + r^2 + 6 \cdot r}
13,422
(-1)\cdot 5 (-2) = (-1) (-10)
15,000
z^2 + 3z + 10 (-1) = \left(2(-1) + z\right)^2 + 7(2\left(-1\right) + z)
2,639
2\cdot 3=6=(1+\sqrt{-5})(1-\sqrt{-5})
50,962
6\cdot 5\cdot 4\cdot 3 - 4\cdot 3\cdot 4\cdot 3 = \dfrac{6!}{2!} - 4!/2!\cdot 4\cdot 3 = \frac{6!}{2!\cdot 4!}\cdot 4! - \frac{4!}{2!\cdot 2!}\cdot 4! = ({6 \choose 4} - {4 \choose 2})\cdot 4!
8,895
s = u \cdot (n - m) + h + j + \left(d - u\right) \cdot k \Rightarrow j = s - \left(-m + n\right) \cdot u - k \cdot (d - u) - h
-13,273
(5 + 6 - 8\cdot 8) = (5 + 6 + 64\cdot (-1)) = \left(5 - 58\right) = \left(5 + 58\cdot (-1)\right) = (-53) = (-53) = -53
30,082
\omega = \sin{\theta}\cdot 3\Longrightarrow \theta = \operatorname{asin}(\omega/3)
30,152
2 \cdot z = d/dz z \cdot z
41,087
5 \cdot 5 \cdot 5\cdot 2 = 3^5 + 7
-2,218
\frac{4}{19} = \frac{7}{19} - \frac{3}{19}
-8,531
7/10 - \frac{1}{10}*5 = 7/\left(10\right) - \frac{5}{10} = \tfrac{7}{10} - \frac{5}{10} = (7 + 5*\left(-1\right))/10 = 2/10
17,915
z*w = z*w
21,060
c \in H \Rightarrow H = H\cdot c
9,170
(H\cdot G - G\cdot H)^U = (H\cdot G)^U - (G\cdot H)^U = G^U\cdot H^U - H^U\cdot G^U
18,110
(-3d + 5)^2 - 4\left(d^3 - 2d^2 - 2d + 4\right) = -4d^3 + 17 d^2 - 22 d + 9 = (9 - 4d) (d + (-1))^2
-10,155
-0.68 = -7/10 = -\dfrac{1}{25} \cdot 17
-3,110
(3 + 5 + (-1))\cdot \sqrt{2} = 7\cdot \sqrt{2}
14,034
\left(10 \cdot z \cdot z - 6 \cdot z \cdot z = 16 \Rightarrow 16 = 4 \cdot z \cdot z\right) \Rightarrow z \cdot z = 4
27,596
\frac{\frac1m\cdot \left((-1) + m\right)}{m\cdot \frac{1}{1 + m}} = 1 - \frac{1}{m^2}
-1,331
\dfrac{1}{1/3\cdot 7}\cdot 7 / 5 = \frac{7}{5}\cdot 3/7
33,700
\binom{5 \cdot (-1) + x}{3} = \binom{(-1) + x + 8 \cdot (-1) + 4}{4 + (-1)}
8,575
-1^{-1} + 31/8 + 2 (-1) = 7/8
11,633
y \cdot y - 18\cdot y + 72 = (12\cdot (-1) + y)\cdot \left(6\cdot (-1) + y\right)
-28,890
3*x = x + 2 + x + 2*(-1) + x
8,320
1/2 \cdot \dfrac{1}{2}/2 = 1/8
16,762
\left((-1) + z\right)^4 = ((z + (-1))^2)^2
8,806
\left((-1) + x \times 2\right) \times p = 3 \times (x^2 + 1) \implies 0 = 3 \times x \times x - 2 \times p \times x + 3 + p
1,647
(25 + 7\times (-1))\times (25 + 7) = 18\times 32 = 576 = 24^2
19,282
y*F*x = x*F*y
12,236
(1 + 2 \cdot l) \cdot 3 = 6 \cdot l + 3
34,630
(x + w + \sqrt{x\cdot w})\cdot (x + w - \sqrt{x\cdot w}) = (x + w) \cdot (x + w) - x\cdot w = x^2 + w^2 + x\cdot w
10,053
\pi - 2 \cdot \arctan\left(1\right) = 2 \cdot \arctan(1)
-20,224
-7/2*\tfrac{1}{x + 1}*\left(1 + x\right) = \dfrac{1}{2 + x*2}*(-x*7 + 7*(-1))
-4,609
\tfrac{z \cdot 8 + 32}{z^2 + 8 \cdot z + 15} = \frac{1}{z + 5} \cdot 4 + \dfrac{1}{3 + z} \cdot 4
13,009
h^{l + x} = h^l \cdot h^x
2,104
100 + 19 \left(-1\right) = 81
-4,361
2j^2 \cdot j = j^3 \cdot 2
-3,685
12/8 \frac{z}{z^5} = \frac{z}{8 z^5} 12
8,492
s_2 s_3 s_1 = s_2 s_1 s_3
22,741
10^6 + 10 (-1) = 30*33333
-28,792
\int x^9\,\mathrm{d}x = \frac{1}{9 + 1}x^{9 + 1} + H = x^{10}/10 + H
37,368
\dfrac{\frac{1}{10^6}\cdot (1 - \frac{1}{10^9})}{\dfrac{1}{10^6}\cdot (1 - \frac{1}{10^9}) + \frac{1}{10^4}\cdot \frac{999999}{1000000}} = \frac{1}{101101001}\cdot 1001001 \approx 0.9901\%
-1,922
19/12 \pi + \dfrac{\pi}{2} = \dfrac{25}{12} \pi
-2,105
\frac{1}{6}*\pi - \tfrac{11}{6}*\pi = -5/3*\pi
20,627
x^4 - 6 \cdot x^2 + 1 - 7.2^y = 0 \implies x^2 = \frac12 \cdot (6 \pm \sqrt{-28.2^y + 32})
3,019
\frac{(2 + m)*m}{\left(m + 1\right)^2} = \dfrac{m^2 + 2*m}{(1 + m) * (1 + m)}
51,274
2^5 = 1*2*2*2*2*2
14,802
3^j - 3^{j + 1} = -3^j \cdot 2
-5,465
\dfrac{1}{s \cdot 3 + 9} = \tfrac{1}{3 \cdot \left(s + 3\right)}
-29,353
\left(-x + f\right)*\left(f + x\right) = -x^2 + f^2
-10,299
5/5 \times (-\frac{1}{3 \times q + 3 \times (-1)}) = -\dfrac{5}{15 \times (-1) + 15 \times q}
5,749
0.999886 = \dfrac{1}{\pi\cdot 4}\cdot \pi\cdot 2\cdot (0.999772 + 1)
18,915
\frac{10}{32} = 1/4*\frac12/4 + \frac{9}{32}
9,577
(7 + 1)^k = 2^{3k}
-22,197
(c + 1) \cdot (9 \cdot (-1) + c) = c^2 - 8 \cdot c + 9 \cdot (-1)
-8,372
(-6) \left(-7\right) = 42
34,585
2^5 \cdot 5^2 = 800
-5,455
\frac{1}{1000} 23.6 = 23.6/1000
-19,068
7/20 = \frac{1}{16 \pi}X_p*16 \pi = X_p
8,431
|y^{1/2}|^2 = (y^{1/2})^2 = y = |y|