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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
10,760
(1 + \alpha + \beta)\cdot 2 = \alpha\cdot 2 + 1 + 2\cdot \beta + 1
2,752
(m + (-1))/m = (-\left(m + (-1)\right)! + m!)/m!
43,854
\frac{5}{2} = \frac{1}{2} \times 5
48,236
0.125 = 8\cdot 0.25\cdot 0.25\cdot 0.25
-3,572
\frac{q}{q \cdot q} = \frac{1}{q \cdot q} \cdot q = \frac1q
33,093
\dfrac{1}{V \cdot R} = \dfrac{1}{R \cdot V}
26,280
1 + n \cdot n + n \cdot 2 = (1 + n)^2
20,751
S*T = S^{\frac{1}{2}}*S^{1/2}*T^{1/2}*T^{1/2}
11,346
I + T + T^2 + \cdots + T^k = \frac{1}{I - T}\cdot (1 - T^{k + 1})
35,526
\frac{1}{36}\cdot 5 = |\frac19 - \dfrac{1}{4}| \leq |\tfrac13 - \frac12|^2
34,560
2\cdot z/2 = 1/2\cdot 2\cdot z = z
10,854
10\cdot 8\cdot 6\cdot 7!/10! = \frac{6}{8\cdot 9}\cdot 8 = 2/3
8,752
3^{2 n} + (-1) = 9^n - 1^n = \left(9 + (-1)\right) (9^{n + (-1)} + 9^{n + 2 (-1)} + \ldots + 1) = 8*\left(9^{n + (-1)} + 9^{n + 2 (-1)} + \ldots + 1\right)
2,471
\frac{\partial}{\partial x} \operatorname{atan}(x \times b + a) = \frac{b}{(b \times x + a)^2 + 1}
10,685
1100 = 3600 - \tfrac12*50*50 - 1/2*50*50
20,373
(1 + y + y^2 + y^3 + \dotsm)^5 = \frac{1}{(1 - y)^5}
14,140
\left(1 + k\right)! = k! \cdot (k + 1)
2,672
\cos{u}\cdot \cos{w} - \sin{u}\cdot \sin{w} = \cos(u + w)
24,712
\frac{2 \cdot x}{x + 7 \cdot \left(-1\right)} = \dfrac{1}{7 \cdot (-1) + x} \cdot 14 + \frac{2}{x + 7 \cdot (-1)} \cdot (7 \cdot \left(-1\right) + x)
2,243
\sin^2(\theta)\cdot \sin^2\left(\theta\right) = \sin^4\left(\theta\right)
-2,103
\tfrac{5}{12} \pi = -\dfrac{\pi}{12} + \tfrac{1}{2} \pi
14,971
8 \cdot x = 2 \cdot 2 \cdot x + x \cdot 4
3,766
2\times (y + (-1)) + 2 = y\times 2
-5,161
10^{1 - -2}\cdot 0.97 = 10^3\cdot 0.97
28,687
\tfrac13100 = \frac{1000}{30}
-19,508
5/2 \cdot \tfrac92 = \frac{1/2 \cdot 9}{2 \cdot 1/5}
34,899
\dfrac1y \cdot \dfrac1y = \dfrac{1}{y^2}
14,488
z = y^3 \Rightarrow z = y^{1/3}
13,190
BC^2 = 16 + 9 - 6 = 19 \implies BC =\sqrt{19}
-3,118
12\cdot \sqrt{2} = \sqrt{2}\cdot (4 + 3 + 5)
17,147
x \cdot x - 5 \cdot x + 6 = \left(2 \cdot \left(-1\right) + x\right) \cdot (x + 3 \cdot (-1))
32,439
(3*3930^{1/2} + 176)^{\frac13} = (176 + 3*3930^{1/2})^{1/3}
12,645
1 + \dfrac{1}{5} = 6/5
-2,507
( 1 + 3 + 2 )\sqrt{10} = 6\sqrt{10}
-30,343
0 = (p\times s_0) \times (p\times s_0) + 3\times p\times s_0 + 18\times (-1) = \left(p\times s_0 + 6\right)\times (p\times s_0 + 3\times (-1))
4,495
-c + \frac1b \cdot a = \dfrac{1}{b} \cdot a - c
29,431
(a \cdot 2)^m = 2^m a^m
51,021
\frac{1}{16} \cdot 9 = 0.5625 \approx 0.56
6,109
\frac{1}{\lambda} \cdot 2 \cdot \lambda^3 = 2 \cdot \lambda \cdot \lambda
1,274
\dfrac{1}{a} = \frac1a \coloneqq 1/a
20,646
\binom{n + x + (-1)}{x + (-1)} = \binom{n + x + (-1)}{n} = \binom{n}{x}
5,190
\pi/12 = \operatorname{asin}\left(\dfrac{1}{2*\sqrt{2}}*(\sqrt{3} + (-1))\right)
7,888
(-a + v)/v = 1 - \frac1v*a
11,889
\dfrac{n^2}{5*(-1) + n^2 - n} = \frac{1}{1 - \tfrac1n - \tfrac{1}{n^2}*5}
6,659
\frac{1}{(3 + (-1))!}\left(4 + \left(-1\right)\right)! = 3!/2! = 6/2 = 3
-20,547
-\dfrac{8}{-3 \cdot l + 7 \cdot (-1)} \cdot \dfrac33 = -\frac{1}{-l \cdot 9 + 21 \cdot (-1)} \cdot 24
16,247
\frac{1}{4}*2 = \tfrac12
16,733
\tfrac56*(n^2 + n*2) = \frac{1}{6}*5*\left(\left(1 + n\right)^2 + (-1)\right)
-11,967
\tfrac12 = s/(6*\pi)*6*\pi = s
-30,256
\dfrac{z^2 + 36\cdot (-1)}{z + 6\cdot (-1)} = \frac{1}{z + 6\cdot (-1)}\cdot (z + 6)\cdot (z + 6\cdot (-1)) = z + 6
-20,148
\frac{-42 k + 28}{-k\cdot 21 + 49} = 7/7 \tfrac{4 - k\cdot 6}{-3k + 7}
10,083
\cos{x} = \cosh{i\cdot x} = \frac12\cdot (e^{i\cdot x} + e^{-i\cdot x}) = \frac{1}{2\cdot e^{i\cdot x}}\cdot (e^{2\cdot i\cdot x} + 1)
5,097
2\cdot \sin(l)\cdot \cos(l) = \sin(2\cdot l)
-1,857
-\pi\cdot 17/12 + 17/12\cdot \pi = 0
-578
e^{i\pi/3*14} = (e^{\dfrac{1}{3}i\pi})^{14}
-4,810
10^{6 - 1} \cdot 29.6 = 29.6 \cdot 10^5
20,533
96 \cdot π = 3 \cdot 2 \cdot π \cdot 16
-19,315
5 \cdot 1/2/\left(1/3\right) = \frac{3}{1} \cdot \dfrac52
2,804
(p^2 - 2 \cdot p + (-1)) \cdot (p + (-1)) = 1 + p^3 - 3 \cdot p^2 + p
-23,204
-3/2*9 = -\dfrac{1}{2}*27
-10,488
(4z + 1)/z \frac{3}{3} = \tfrac{1}{z*3}(3 + z*12)
35,393
122461/371293 = 1 - (1 - \frac{1}{13})^5
-1,642
π/4 = 7/4\cdot π - \frac32\cdot π
-900
949/10000 = \frac{9}{10000} + 0 + \dfrac{1}{10}\cdot 0 + \frac{9}{100} + 4/1000
34,371
\sin{x} = \cos(-x + \dfrac12\cdot \pi)
-12,569
\dfrac12\cdot 58 = 29
17,018
u^2 + \frac{1}{u \cdot u} + 1 = \left(u + \frac{1}{u}\right)^2 + (-1) = \left(u + \dfrac{1}{u} + 1\right) \cdot (u + \frac1u + (-1))
19,892
\sqrt{\frac{1}{64}100} = \frac{1}{8}10 = \dfrac{5}{4}
2,135
y^2 \cdot 2 + y \cdot 2 + 2 = 2 \cdot y^2 + 2 \cdot y + 2
2,857
4 \times k^2 = (k \times 2) \times (k \times 2)
4,808
(x + q)\cdot (x - q) = x^2 - q^2
8,283
a \cdot b = \frac{1}{\frac{1}{a \cdot b}} = \dfrac{1}{\tfrac1a \cdot \frac1b} = \frac{1}{\frac{1}{b} \cdot 1/a} = b \cdot a
-14,622
\frac{1}{9}828 = 92
25,839
\mathbb{E}\left[RC\right] = \mathbb{E}\left[C\right] \mathbb{E}\left[R\right]
-535
e^{5\cdot \pi\cdot i/4\cdot 18} = (e^{\dfrac{5}{4}\cdot \pi\cdot i})^{18}
28,974
3\cdot x \cdot x = 15 \implies x^2 = 5
34,362
9\times 16/2! = 72
26,610
9/7 = \frac{2}{7} + 1
22,785
(1 + y)^{t + s} = (y + 1)^t\cdot \left(1 + y\right)^s
5,908
(n + 8)^2 - n * n = 16*(4 + n)
5,063
4 \cdot b^2 - c \cdot a \cdot 4 = 0\Longrightarrow c^3 + a^3 + b^3 = 3 \cdot a \cdot b \cdot c
104
\frac16 + \frac{1}{12} + 1/24 + \frac{1}{48} = \dfrac{15}{48}
13,061
\frac{1}{2} \cdot a^2 + h \cdot h/2 = (a \cdot a + h^2)/2
4,358
n^2 \cdot \left(2 \cdot (-1) + n\right)! = (n + 2 \cdot \left(-1\right))! + (n + (-1))! + n!
1,849
x_1\cdot 2 + x_3 = -b + t^2 rightarrow -b + t^2 - 2\cdot x_1 = x_3
-3,174
\sqrt{2} \cdot 4 + \sqrt{2} \cdot 5 = \sqrt{16} \cdot \sqrt{2} + \sqrt{2} \cdot \sqrt{25}
-7,712
\dfrac{104 - 28i + 78i + 21}{25} = \dfrac{125 + 50i}{25} = 5+2i
51,870
|-D + x| = |D - x|
26,433
\frac{1}{2*(1/2 + \frac{1}{12})} = 6/7
19,338
7*142857 = 10^6 + \left(-1\right)
12,162
\sin(z) = \frac{1}{2*i}*\left(e^{i*z} - e^{-i*z}\right) = -i*\sinh(i*z)
1,112
-b + c = \dfrac{c^2 - b * b}{c + b}
-7,161
\frac{1}{10}2\cdot \frac{1}{11}5 = 1/11
-6,346
\frac{1}{\left(n + 7*\left(-1\right)\right)*5}*3 = \dfrac{3}{n*5 + 35*(-1)}
-683
e^{i\pi/6*19} = \left(e^{i\pi/6}\right)^{19}
18,328
(\frac{1}{2})^4 \cdot \binom{4}{3} = \frac14
24,959
\sqrt{3} \cdot \frac{1}{2} \cdot \sqrt{3}/2 = \frac14 \cdot 3
-20,311
\frac17\times (4 + x)\times \dfrac55 = (x\times 5 + 20)/35
5,938
4 - 4*(-x + 1) = x*4
28,361
E[Q + B] = E[Q] + E[B]