Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
28,456
|e\cdot b| = |b\cdot e|
30,825
(f + g)*0 = \sin\left(0\right) + \cos(0) = 0 + 1 = 1 + 0 = \sin\left(\pi/2\right) + \cos\left(\frac{\pi}{2}\right) = (f + g) \frac12\pi
11,747
\sin^4{z} + \cos^4{z} = (\sin^2{z} + \cos^2{z})^2 - 2\cdot \sin^2{z}\cdot \cos^2{z} = 1 - \sin^{22}{z}/2
37,519
C \backslash B = C \cap B^c = B \cup C^c^c
-3,981
\frac{a^5}{a^5}*44/55 = \frac{a^5}{a^5}*4*11/(11*5)
15,441
x^{16} \times x^2 \times x^{32} = x^{50}
22,996
-2/l + \frac{1}{(-1) + l} + \frac{1}{l + 1} = \frac{2}{-l + l^3}
27,123
x^{\frac14} \cdot x^4 = x^{\frac14 + 4} = x^{17/4}
-10,296
\dfrac{32}{40*(-1) + m*20} = \frac{8}{5*m + 10*(-1)}*\dfrac{4}{4}
40,300
169 = 2(61) + 47
682
(1/y)^6 = \tfrac{1}{y^6}
-9,950
0.01 \left(-25\right) = -\frac{1}{100}25 = -0.25
2,659
(1 + 164 + 5 \cdot \left(-1\right))/5 + 1 = 33
-3,072
\left(9 \cdot 6\right)^{1/2} + (16 \cdot 6)^{1/2} = 54^{1/2} + 96^{1/2}
14,710
(x^Y \times X \times x)^Y = x^Y \times X^Y \times x = -x^Y \times X \times x
6,049
n^4 + (-1) = (n^2 + \left(-1\right)) (1 + n^2)
11,000
\frac{1}{-B + A} = \frac{1}{A*(1 - B/A)}
25,326
z^2 + \nu \cdot \nu = -z \cdot \nu \cdot 2 + (z + \nu)^2
30,581
|e^{i \cdot q} - e^{-i \cdot q}| = |2 \cdot i \cdot \sin{q}| = |2 \cdot \sin{q}| = 2 \cdot \sin{q}
-22,272
(d + 5)\cdot \left(d + 3\cdot (-1)\right) = d^2 + 2\cdot d + 15\cdot (-1)
4,899
(-a + y)*(y * y + a*y + a^2) = y * y * y - a^3
12,876
-d + c = (\sqrt{c} + \sqrt{d}) (\sqrt{c} - \sqrt{d})
-4,438
y^2 + (-1) = (y + 1)\cdot ((-1) + y)
27,971
1080 = 3^3\cdot 2 \cdot 2^2\cdot 5
8,816
h_1 + h_2 = \frac{h_1}{h_2} + \dfrac{h_2}{h_1} \lt h_1 + h_2
8,742
\left(1 - y^{18}\right)^2 = (1 - y)^2 y^{17} = y^{19} - 2y^{18} + y^{17}
20,327
\frac{1}{\frac{1}{H}} = H
13
\left(\frac{5}{6}\right)^2 \cdot 3/6 = 75/216
16,850
\sin(-3t + 4) = \sin\left(\pi + 3t + 4(-1)\right)
-15,955
-\frac{75}{10} = 6/10 - 9 \cdot \frac{9}{10}
16,000
2 + 7 + 12 + 17 + ... + 5\cdot k + 3\cdot (-1) = ((-1) + 5\cdot k)\cdot \frac{1}{2}\cdot k
20,286
y\cdot R\cdot x \Rightarrow x\cdot R\cdot y
30,183
-\arctan{x} + (1 + x^2)\cdot \arctan{x} = \arctan{x}\cdot x^2
7,219
\mathbb{N} = \left\{0, 2, 1, \dots\right\}
8,591
r^2\times \pi = r\times r\times \pi
1,857
\dfrac{1}{100} \cdot 15 \cdot 250 = 37.5
21,115
\cos{X}*\sin{A} + \cos{A}*\sin{X} = \sin(X + A)
696
4 \cdot \left(u^2 + 27 \cdot v^2\right) = (2 \cdot v)^2 \cdot 27 + (2 \cdot u)^2
-3,807
\dfrac{18}{t*42}*t^5 = \frac{18}{42}*t^5/t
-22,353
45 + s^2 + 14 \cdot s = (9 + s) \cdot (5 + s)
-7,117
\frac{3}{10}\cdot \frac29 = 1/15
-7,489
\frac{28}{6} = \dfrac13*14
23,825
90^2 = k * k - y^2 = (k - y)*(k + y)
-7,934
\left(16 + 8i + 32 i + 16 (-1)\right)/20 = \frac{1}{20}(0 + 40 i) = 2i
26,402
1/2\cdot \frac32/2 = 3/8
1,435
41 = 14\%\cdot z \Rightarrow z\cdot 0.14 = 41
14,844
F \cdot 26 + L + 27 = L + 1 + 26 \cdot (F + 1)
22,101
L + f + e = f + e + L
7,081
\int \sin{k}\,\text{d}k = -\cos{k}
26,175
\dfrac{1}{5 + 7 + 3} \cdot (2 + 4 + 2) = \frac{8}{15}
-11,504
-5 + 5 \times i = i \times 5 - 5 + 0 \times (-1)
23,082
I*2 = I + (-2)^{1 / 2} + I - (-2)^{\tfrac{1}{2}}
12,775
\mathbb{E}[A]\times \mathbb{E}[B] = \mathbb{E}[B\times A]
-20,094
\dfrac{1}{15 \cdot x} \cdot (15 \cdot x + 10 \cdot (-1)) = \frac55 \cdot \frac{1}{3 \cdot x} \cdot (3 \cdot x + 2 \cdot (-1))
-3,736
\frac{8}{5} \cdot p = \frac{1}{5} \cdot 8 \cdot p
15,478
(3 + 7i)^5 = e^{i\phi} = \cos\left(\phi\right) + i\sin(\phi)
5,679
f/f \cdot g \cdot f \cdot g/g = g \cdot g \cdot f \cdot \frac{f}{f}/g
-8,909
-1^3 = \left(-1\right) \cdot (-1) \cdot \left(-1\right)
34,669
(-1)\times 1.0\times 10^{-6} + 1 = 0.999999
-15,906
-8 \cdot \frac{9}{10} + \frac{5}{10} = -\dfrac{67}{10}
7,344
3*m^2 + m*3 + 1 = -m^3 + \left(1 + m\right)^2 * (m + 1)
37,032
4 = (2\cdot (-1) + 4)\cdot 2
-26,502
\theta^2*25 - 30*\theta + 9 = 3^2 + (5*\theta)^2 - 2*5*\theta*3
9,446
\beta*5 + 12*z = 1 \Rightarrow -2 = z,\beta = 5
26,853
\sin{\dfrac{\pi}{12}} = \sqrt{\left(-\cos{\frac16 \times \pi} + 1\right)/2}
1,374
a\cdot b\cdot g = (a\cdot b + 1)\cdot g = (a\cdot b + 1)\cdot g + 1 = a\cdot b\cdot g + g + 1
9,223
1 = -4209 \cdot 7284 + 3539 \cdot 8663
3,212
F \cdot x \cdot F^W = F \cdot x \cdot F^W \cdot F \cdot x \cdot F^W = F \cdot x \cdot x \cdot F^W
9,545
\left(\left(-1\right) + x\right)^2 + (z + (-1))^2 = 1\Longrightarrow \sqrt{-\left(x + (-1)\right)^2 + 1} + 1 = z
7,598
3/7 = 8/35 + \frac{1}{35}\cdot 6 + 1/35
26,121
\left(\sec{2*x} + \left(-1\right)\right)/\tan{2*x} = \tfrac{1}{\sin{2*x}}*(1 - \cos{2*x}) = \tan{x}
27,498
x - f = x - f
-28,858
\frac{1881}{9}\cdot 1 = (109 + 100)\cdot (109 + 100\cdot (-1))/9
3,693
10 = k \cdot 4\Longrightarrow k = \frac{5}{2}
25,341
\cos(x) = \sin\left(π/2 + x\right)
18,764
x^{\frac{1}{m}} = x^{\frac{1}{m}}
1,089
-2 \cdot \pi + \dfrac{4}{3} \cdot \pi = -\tfrac{2}{3} \cdot \pi
27,620
\frac{3}{2} \cdot 1/4 = \tfrac38
36,731
11 = 6*\left(-1\right) + 17
8,500
\sin(x) = 2 \cdot \sin(\frac{x}{2}) \cdot \cos(x/2)
13,061
x \cdot x/2 + \frac{c^2}{2} = (x \cdot x + c^2)/2
-22,320
m^2 - 2 m + 24 \left(-1\right) = (m + 4) (m + 6 (-1))
712
a_n \cdot a_n + x^2 - 2 \cdot a_n \cdot x = (x - a_n)^2
43,679
2*\left(4 + 1\right) + 3*2*2 = 10 + 12 = 22
18,687
\frac{1}{-\frac{1}{1 - y} + 1} = 1 - \frac{1}{y}
14,393
(1/6)^7\cdot 5/6\cdot 8 + (1/6)^8 = 41/1679616
3,261
\dfrac{1}{1 + \cos{x}}*\sin{x} = \frac{1}{\sin{x}}*(-\cos{x} + 1)
28,977
\pi \gt 2 \cdot \sqrt{2} = 2.828 \cdot ... > 2.82
27,305
3 * 3*2 * 2*7*43 = 10836
-20,064
-1/2 \tfrac{2(-1) + 2x}{2(-1) + 2x} = \tfrac{1}{4(-1) + x\cdot 4}(2 - x\cdot 2)
20,416
41^4 + \left(-1\right) = 2825760 = 2^5\times 3\times 5\times 7\times 29^2
3,610
x \cdot z = (x + z) \cdot 1995 \Rightarrow (x + 1995 \cdot (-1)) \cdot \left(z + 1995 \cdot (-1)\right) = 1995^2 = \left((3^{25})^{27}\right)^{219} \cdot \left((3^{25})^{27}\right)^{219}
33,732
-1 = (\sin(-\pi)*i + \cos(-\pi))
-20,338
\frac{1}{2 \cdot x + 4 \cdot \left(-1\right)} \cdot (x \cdot 2 + 6 \cdot (-1)) = \frac{1}{x + 2 \cdot (-1)} \cdot (3 \cdot \left(-1\right) + x) \cdot \tfrac{2}{2}
28,909
2 + (-\frac1v + v)^2 = v^2 + \frac{1}{v^2}
28,832
5/8 = \frac18*3 + \dfrac{1}{8}*2
-24,009
9 + 7^2 = 9 + 7\times 7 = 9 + 49 = 58
-30,279
x + 5 + \frac{2}{2 + x} = \dfrac{1}{x + 2}\cdot \left(12 + x^2 + 7\cdot x\right)
-2,116
\pi\cdot 23/12 - \pi\cdot 5/4 = \frac23\cdot \pi
16,619
s*2^{x/2} = 2^{-x}*2^{\tfrac{x}{2}}*2^x s