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ddrg
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math_formulas

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int64
-30,985
55.9k
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437k
3,773
5/2 = 5/8 \cdot 4
31,919
13 = {2 \choose 2}\cdot {13 \choose 1}
-7,261
\frac{1}{7} 3 = \dfrac{6 / 7}{2} 1
-9,435
66*s + 88*\left(-1\right) = -11*2*2*2 + 2*3*11*s
2,493
\dfrac{(2n)!}{n!^2} = \binom{n*2}{n}
8,010
\operatorname{atan}(z) = z - \frac{z^3}{3} + z^5/5 \cdot \ldots \cdot \ldots \cdot \ldots
-6,252
\frac{4}{18\cdot \left(-1\right) + z^2 - 3\cdot z} = \frac{1}{(z + 3)\cdot (z + 6\cdot (-1))}\cdot 4
-1,119
5/6 \cdot (-\frac16) = \frac{\left(-1\right) \cdot \frac{1}{6}}{6 \cdot \frac{1}{5}}
2,348
2\cdot (-1) + (R + \frac{1}{R}) \cdot (R + \frac{1}{R}) = \dfrac{1}{R^2} + R \cdot R
18,671
\frac{1/5}{n} \cdot x \cdot x = \frac{0.2}{n} \cdot x^2
-17,563
28 \cdot (-1) + 39 = 11
27,905
(1 + p) \cdot (p^2 + 1) \cdot (p^4 + 1) \cdot (1 + p^{16}) \cdot (1 + p^8) \cdot (\left(-1\right) + p) = (-1) + p^{32}
-10,538
2/2*(-6/(r*8)) = -\frac{1}{r*16}*12
16,639
T_n - T_{n + 2(-1)} = 7 = T_{n + 2(-1)} - T_{n + 4(-1)} \Rightarrow 0 = T_{n + 4(-1)} + T_n - T_{n + 2(-1)}*2
-2,817
3^{\dfrac{1}{2}}\cdot 5 - 2\cdot 3^{\frac{1}{2}} = 25^{1 / 2}\cdot 3^{1 / 2} - 4^{\frac{1}{2}}\cdot 3^{\frac{1}{2}}
-4,454
-\frac{2}{x + 3} - \dfrac{2}{x + (-1)} = \frac{-4 \cdot x + 4 \cdot (-1)}{x^2 + 2 \cdot x + 3 \cdot \left(-1\right)}
-7,159
5/12\cdot \frac{2}{13} = 5/78
-22,764
\frac{4\times 5}{5\times 9} = 20/45
23,306
0.05 \cdot S = 0.02 \cdot x \Rightarrow \frac{x}{S} = \frac52
-21,040
\frac{1}{100}\cdot 20 = 2/10
24,891
(2 + (2 + (2 + ...)^{1 / 2})^{1 / 2})^{1 / 2} = y = (2 + y)^{1 / 2}
-11,694
\dfrac{1}{81} \cdot 256 = (4/3)^4
21,576
h*b = \frac{1}{2}*(h*b + b*h) = b*h
34,041
\frac{d}{dz} z^2 = 2 \cdot z
8,239
(x^2 - x + 1) \cdot \left(\left(-1\right) + x^3 + x^2\right) = x^5 + x + (-1)
-20,783
\frac{2}{-12} = -\frac{2}{-2} \cdot (-\frac16)
9,325
-d^3 + x x x = \left(-d + x\right) (d^2 + x^2 + d x)
2,365
\frac{y_x}{y} \times y = y_x
16,692
y^3 + 1 + y + y \cdot y = \left(y + 1\right) \cdot (1 + y^2)
32,653
M \cdot g = \frac{1}{g \cdot M} = g \cdot M
-7,706
\frac{1}{i + 5}(5 + i) \frac{-5 - 25 i}{5 - i} = \frac{1}{5 - i}(-25 i - 5)
-4,828
10^4\cdot 45.0 = 10^{-1 + 5}\cdot 45
10,014
8 \cdot (n_1 - n_2) = (-z_2 + z_1) \cdot 12 \Rightarrow 3 \cdot (-z_2 + z_1) = 2 \cdot \left(n_1 - n_2\right)
4,939
\frac{1}{2}(i*(-1)) \left(-1/6\right) = i/12
-20,447
8/8\cdot \left(-\dfrac{7}{2 + i}\right) = -\tfrac{56}{8\cdot i + 16}
-4,019
\frac{10\cdot p \cdot p^2}{60\cdot p^2} = \frac{p^3}{p^2}\cdot \frac{10}{60}
32,625
\frac12\left(1 + (2*178 + 1) * (2*178 + 1)\right) \pi = 63725 \pi \approx 200197.991850009574121
21,225
-40 = -27 + 13 (-1)
375
11 \cdot (y + 9) = y + 144\Longrightarrow 144 + y = 99 + 11 \cdot y
-1,426
\frac{1}{7} 4 (-\frac15) = ((-1)*1/5)/(1/4*7)
-20,424
\tfrac{1}{45}\cdot \left(5\cdot y + 25\right) = 5/5\cdot (5 + y)/9
2,179
x + ((-1) + x)*3 + 5*(x + 2*\left(-1\right)) + \dotsm + (x*2 + 3*(-1))*2 + 2*x + (-1) = 1^2 + 2^2 + \dotsm + x^2
18,226
y^8 + (-1) = \left((-1) + y^4\right)*(1 + y^4)
-643
(e^{23 \cdot \pi \cdot i/12})^4 = e^{\dfrac{1}{12} \cdot 23 \cdot \pi \cdot i \cdot 4}
21,767
y^2 + y \cdot 2 + 1 = (y + 1)^2
4,684
\left(-\frac12\right)^2 = 1/4
32,100
n\cdot a := --n\cdot a
3,729
(-1) + \frac{C^2}{4} = \frac14\left(C + 2\right) \left(2(-1) + C\right)
18,864
\sin{\frac{\pi}{2}} = \cos{2\cdot \pi}
2,856
\dfrac{A^g}{x} = A^g/x
28,697
15.75 = \frac{1}{6}*(27 + 4.5 + 9 + 13.5 + 18 + 22.5)
1,807
1985 = 5\cdot 397
12,818
1395 = 3\cdot \frac{30\cdot 31}{2}
18,639
z \cdot \theta^n = \theta^n \cdot z
-9,348
22 + 11\cdot q = 11\cdot q + 2\cdot 11
-3,347
3\sqrt{6} + \sqrt{6}*5 = \sqrt{6} \sqrt{25} + \sqrt{6} \sqrt{9}
9,681
(a+b)^2-(a-b)^2 = 4 ab
-122
11 = 7 + 4
-23,217
-\frac23\cdot (-\frac{1}{9}\cdot 8) = 16/27
28,687
\frac{100}{3} = 1000/30
462
2-\frac24=\frac32
-4,272
\frac{\dfrac16}{m^3}\cdot 5 = \frac{5}{m \cdot m \cdot m\cdot 6}
32,357
(2 \cdot 5)^k = 10^k
-29,064
P^8 = P^7 \cdot P
26,759
\dfrac{1}{4! \cdot 3! \cdot 3!} \cdot 10! = 4200
13,047
1/3 + \tfrac{1}{3} \cdot 0 + \frac{1}{2 \cdot 3} = 1/2
5,607
\frac{\partial}{\partial x} u^n = nu^{n + \left(-1\right)} \frac{\mathrm{d}u}{\mathrm{d}x}
27,240
(\sqrt{c} - \sqrt{f}) (\sqrt{f} + \sqrt{c}) = c - f
-4,244
\frac{63}{54}*\frac{n}{n^5} = \frac{63*n}{n^5*54}
748
Z - z = x + z \implies z\cdot 2 = Z - x
6,898
2 \cdot x + x = 3 \cdot x
-18,970
\frac{5}{24} = A_s/(64 \pi) \cdot 64 \pi = A_s
5,171
\sqrt{-\sqrt{2} + 2} = \frac{\sqrt{2}}{\sqrt{2 + \sqrt{2}}}
15,007
e^z - 6 \cdot e^{z \cdot 3} + e^{z \cdot 5} = 0\Longrightarrow 0 = 1 - e^{z \cdot 2} \cdot 6 + e^{4 \cdot z}
37,059
((-1) + 2 \cdot m) \cdot |6/m| = 10.5\Longrightarrow m = 4
-9,489
-U \cdot 2 \cdot 7 \cdot U + U \cdot 2 \cdot 2 = -14 \cdot U^2 + 4 \cdot U
-4,702
-\frac{3}{2\cdot \left(-1\right) + y} + \frac{1}{3\cdot (-1) + y}\cdot 2 = \frac{-y + 5}{6 + y^2 - y\cdot 5}
8,561
(2i\pi - \pi i*2)/(i*2) = 0
18,011
(w^2 + z^2 - w \cdot z) \cdot (w + z) = z \cdot z \cdot z + w^3
44,497
4^1-3^1=1^2
41,734
c + x + a + b = b + x + a + c
34,190
(a \cdot a)^{\dfrac{1}{2}} = 2 = -a
12,438
838721786045180184649^2 - 397 \cdot 42094239791738433660^2 = 1
-9,436
-27 r + 54 \left(-1\right) = -3*3*3 r - 2*3*3*3
12,714
\frac{1}{r + 1}\cdot r^2 + 1 - r = \frac{1}{r + 1}
3,575
y\cdot z^2 = z^6\cdot y = z^2\cdot y
18,842
9(-1) + x = (x^{\frac{1}{2}} + 3(-1)) (3 + x^{\tfrac{1}{2}})
28,016
\left\lfloor{2013/(3\times 5)}\right\rfloor = 134
1,872
\mathbb{P}(B) = \left(B + (-1) - 2i\right) (B + \left(-1\right) + 2i) = B^2 - 2B + 5
-1,887
\frac54*π - π = π/4
-9,325
32\cdot \left(-1\right) - k\cdot 36 = -2\cdot 2\cdot 3\cdot 3\cdot k - 2\cdot 2\cdot 2\cdot 2\cdot 2
18,209
3 = 14 \cdot (-1) + 31 + 14 \cdot (-1)
24,075
x*2 - x * x = 1 - \left(1 - x\right)^2
28,718
\{\left\{Y,B\right\};Y\} \Rightarrow Y = B
7,034
\sin\left(\pi*2\right) = \sin(\pi*10)
-18,933
1/8 = \tfrac{1}{16*\pi}*G_x*16*\pi = G_x
5,066
1/16 + 2/17 = \frac{1}{16} + \frac{1}{17} + \dfrac{1}{17}
552
e^u e^y = e^{y + u}
-11,794
9/16 = (\frac14\cdot 3)^2
34,780
|g|*|h| = |h*g|