Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
36,786
z * z + I = z^2 + z^2 + z + I = z + I
33,761
\mathbb{E}(U) + \mathbb{E}(X) = \mathbb{E}(X + U)
-4,742
-\frac{1}{y + 4*(-1)}*2 - \dfrac{5}{y + 3*(-1)} = \frac{26 - y*7}{y^2 - 7*y + 12}
39,881
\frac{1}{\sqrt{11}} = \sqrt{11}/11
51,184
\left(-1\right)^2 = 1 \cdot 1
22,437
m + (-1) = 3*(-1) + 2 + m
-28,843
7.4*x + 8*x + 12*(-1) = 12*(-1) + x*7.4 + x*8
30,696
-(l + 1) + x + 1 = x - l
17,877
\left(x = -f \implies f^n = x^n\right) \implies f^n\cdot 2 = x^n + f^n
-26,752
\sum_{n=1}^\infty \dfrac{(-5)^n}{n\cdot 5^n} = \sum_{n=1}^\infty \frac{(-1)^n\cdot 5^n}{n\cdot 5^n} = \sum_{n=1}^\infty \tfrac{1}{n}\cdot (-1)^n
4,487
\frac{1}{π} \cdot \int \frac{1}{y + 2/π} \cdot y\,dy = \int \dfrac{1}{2 + y \cdot π} \cdot y\,dy
36,402
6\cdot q\cdot x = -x\cdot q + q\cdot 3\cdot x + x\cdot 2\cdot q\cdot 2
10,233
z^3 = 2 + 11 \times i + 2 - 11 \times i + 3 \times ((2 + 11 \times i) \times (2 - 11 \times i))^{1/3} \times z = 4 + 15 \times z
17,626
W_1 Y = W_1 Y \cdot (W_2 + x) = W_1 Y W_2 + W_1 Y x
27,121
1 + 0 \cdot (-1) + 2 = 3
20,710
\binom{l}{i} = \dfrac{1}{i! \cdot (l - i)!} \cdot l!
23,158
4 = 2 \cdot 2 = (1 + \sqrt{-3}) \cdot (1 - \sqrt{-3})
16,879
y^2 \lt 4 rightarrow 2 > |y|
31,954
11/36 = 1 - 25/36
6,181
\left(3\cdot (-1) + x\right)\cdot ((-1) + x\cdot 2) = 2\cdot x \cdot x - 7\cdot x + 3
-18,304
\dfrac{1}{(10 \left(-1\right) + z) z} \left(z + 10 (-1)\right) (z + 3 (-1)) = \dfrac{30 + z^2 - z\cdot 13}{z^2 - 10 z}
5,866
(3 + x) (x + 1) = x^2 + x\cdot 4 + 3
4,538
(m + x*k)/k = \frac{m}{k} + x
9,769
z^2 - a^2 = a \cdot a - z \cdot z^2 - a^2 = z - a^2
-16,501
9\cdot \sqrt{25\cdot 2} = 9\cdot \sqrt{50}
10,609
(z - x) (z + x) = -x^2 + z^2
29,437
x^4 \cdot 2 - 1 - 3 \cdot x^3 = (1 - x + 2 \cdot x^2) \cdot (-1 - x + x^2)
-554
(e^{\frac{13*i*\pi}{12}})^{13} = e^{13*\frac{13*\pi*i}{12}}
25,694
\sin\left(y\right) \cos(y) = \sin(2y)/2 = \frac{2\tan(y)}{2}\dfrac{1}{1 + \tan^2(y)}
13,867
x x + (-1) = (1 + x) \left((-1) + x\right)
21,679
d*a/b = \frac{a}{1/d*b}
25,116
(f + a)^2 = f^2 + a * a + 2*a*f
6,109
2\cdot \lambda^3/\lambda = \lambda^2\cdot 2
15,872
R = \frac12 \cdot R + Y/4 \implies \tfrac12 \cdot Y = R
8,415
(b*2)^2*0.25*n = b * b*n
21,978
(x + gi) (l + ki) = xl - gk + (xk + gl) i = xl - gk + i
9,106
3/8*\frac12 + \frac16*2*\frac{1}{2} = \frac{1}{48}*17
-1,380
\frac{(-9) \cdot 1/7}{1/7 \cdot (-9)} = -\dfrac19 \cdot 7 \cdot \left(-9/7\right)
23,229
4! = (6 \left(-1\right) + 10)!
-12,008
1/9 = p/(12*\pi)*12*\pi = p
-7,578
\frac{1}{(3 - i \cdot 5) \cdot (5 \cdot i + 3)} \cdot (3 - 5 \cdot i) \cdot (8 \cdot i - 2) = \dfrac{1}{-(5 \cdot i)^2 + 3^2} \cdot (-2 + i \cdot 8) \cdot (-5 \cdot i + 3)
18,358
|\sin{\frac{2}{m \cdot \pi}} \cdot \cos{\frac{\pi}{2} \cdot m}| = \sin{\frac{2}{m \cdot \pi}} > \frac{1}{m \cdot \pi}
-20,614
\frac14\cdot 7\cdot \frac{7\cdot (-1) - q\cdot 3}{7\cdot (-1) - q\cdot 3} = \dfrac{1}{28\cdot (-1) - 12\cdot q}\cdot (-21\cdot q + 49\cdot \left(-1\right))
35,095
\sin(2\alpha) = 2\sin(\alpha) \cos(\alpha)
-6,178
\frac{4 \cdot q}{25 + q \cdot q - 10 \cdot q} = \frac{q \cdot 4}{\left(5 \cdot (-1) + q\right) \cdot (q + 5 \cdot (-1))}
10,459
z \cdot z + z = -\dfrac14 + \left(1/2 + z\right) \cdot \left(1/2 + z\right)
16,246
y + 8\cdot (-1) = -4\cdot (x + 1) = -4\cdot x + 4\cdot (-1) \implies 0 = y + x\cdot 4 + 4\cdot \left(-1\right)
17,197
\alpha/(\bar{\alpha}) = \tfrac{1}{\alpha \cdot \bar{\alpha}} \cdot \alpha^2
25,551
\dfrac{1}{1/b} = b^{(-1)*\left(-1\right)} = b^1 = b
33,141
k^{2 \cdot 3} = k^6
-9,556
52\% = 52/100 = \frac{13}{25}
11,055
(y^{2\cdot a})^h = (y^a \cdot y^a)^h = (\tfrac{1}{y^a})^h = (y^a)^{h + \left(-1\right)}
18,613
3*3*3 = 3 \Rightarrow 3*3 = 1
-676
(e^{\frac{1}{12}\cdot i\cdot \pi\cdot 17})^7 = e^{7\cdot \frac{i\cdot \pi}{12}\cdot 17}
9,741
x^5 = 3 \cdot x^2 + 2 \cdot x = 5 \cdot x + 3
1,027
a + \frac{1}{(-1)*b} = a + (-1) + \frac{1}{\frac{1}{(-1) + b} + 1}
-23,090
-1/9 (-\frac13) = \tfrac{1}{27}
704
2^0 z = z
-6,294
\frac{2}{(d + 9\left(-1\right)) (d + 5\left(-1\right))} = \frac{2}{d^2 - 14 d + 45}
9,482
(1 + a)\cdot (1 + a)^k = (a + 1)^{k + 1}
5,412
\left( a + m \cdot l, l\right) = (a + m \cdot l) \cdot x + l \cdot z = a \cdot x + m \cdot l \cdot x + l \cdot z
-20,930
\frac{1}{(-1) \cdot 25 \cdot x} \cdot x \cdot 40 = \frac{x \cdot (-5)}{x \cdot \left(-5\right)} \cdot (-\frac15 \cdot 8)
5,814
\frac{10}{31} \cdot 2 \cdot V - \tfrac{21}{31} \cdot V = \dfrac{1}{31} \cdot ((-1) \cdot V)
-1,265
\frac{15}{72} = \frac{1/3}{72 \cdot \frac13} \cdot 15 = \tfrac{1}{24} \cdot 5
-456
\left(e^{\frac{1}{12} \cdot \pi \cdot i \cdot 5}\right)^{11} = e^{11 \cdot \tfrac{5}{12} \cdot \pi \cdot i}
13,756
5^x = 2 \cdot \left(3^{x + \left(-1\right)} + 1\right)\Longrightarrow 2 \cdot 3^{x + (-1)} + 3 = 5^x
17,318
\dfrac12x + \frac{1}{2}x = x
-7,177
0 = \tfrac25*0
8,377
z^2 - z = (z + 0 \cdot (-1)) \cdot (z + (-1))
-19,054
14/15 = \frac{A_s}{4\cdot \pi}\cdot 4\cdot \pi = A_s
22,100
15 \times f^2/2 = -f^2/2 + 8 \times f^2
10,009
1^2 + 4^2 + 3 \cdot 3 + 2 \cdot 2 = 30
-29,452
-\left(\frac{1}{6} \cdot (-5)\right)/6 = \frac{5}{36}
4,120
462 = \dfrac{1!\cdot 2!\cdot 0!}{4!\cdot 5!\cdot 6!}\cdot 12!
29,103
1 = b^0 = b^{1 + (-1)} = \frac{b^1}{b} = b/b
12,478
\dfrac{99}{70} - \sqrt{2} = \frac{1}{(70 \sqrt{2} + 99)*70}
2,769
\beta*\alpha + \gamma*\alpha = \alpha*(\beta + \gamma)
-20,708
\frac{-2 \cdot q + 3 \cdot (-1)}{-q \cdot 10 + 15 \cdot (-1)} = \frac{1}{5} \cdot 1
-6,701
\frac{2}{10} + 8/100 = 8/100 + \frac{1}{100}*20
16,314
a^2 + b*a*2 + b^2 = (a + b)^2 \Rightarrow -a*b*2 + \left(a + b\right) * \left(a + b\right) = b * b + a^2
41,608
3542 = 154*23
14,627
\tfrac{0 + 2}{1 + 0} = 2
-16,352
\sqrt{16 \cdot 5} \cdot 8 = \sqrt{80} \cdot 8
40,711
F_{1 + j} = F_{j + 1}
770
l^2\cdot 4 + l\cdot x\cdot 2 + f = l\cdot 2\cdot (x + l\cdot 2) + f
2,366
(2 + z)/((-1)*z) = \frac{1}{(-1)*(y + 4*\left(-1\right))}*y rightarrow y = z*2 + 4
25,802
\tfrac{y}{1 - y} = 1 + y + y^2 + y^3 + y^4 + \cdots
-28,999
\left((-1)*382.5 + 1096.5\right)/2 = 357
10,112
2^k\cdot (b + g) = b\cdot 2^k + 2^k\cdot g
8,376
\left(-1\right) - p = t \implies -1 = p + t
-7,739
\frac{1}{-4*i + 3}*(3 - i*4) = \frac{-i*4 + 3}{3 - i*4}*\frac{4*i + 3}{3 + 4*i}
37,733
i^2 \frac{\sin(i z)}{i z} = \sin(z i) i/z
-2,980
50^{\frac{1}{2}} + 8^{\frac{1}{2}} = (25*2)^{1 / 2} + (4*2)^{\frac{1}{2}}
14,928
\dfrac{1}{\cos{T}} = \sec{T}
-6,500
\tfrac{12 t}{6 ((-1) + t) (t + 7 (-1))} = \frac{2 t}{(t + (-1)) (t + 7 (-1))} \cdot 6/6
4,910
1 - \frac{2}{n + 1} = \frac{1}{n + 1}(n + \left(-1\right))
4,047
-X\cdot (X^2 + (-1)) + (X^3 + 1) = -X^2 \cdot X + X + X \cdot X \cdot X + 1 = X + 1
34,321
(G + I) \cdot (G + 1 + I) = G^2 + G + I = G^2 + 1 + G + (-1) + I = G + 1 + I
-26,122
\tfrac{1}{9} = 1/9
25,431
2^n*3 = 2^n + 2^n + 2^n