ddrg/math_formulas · Datasets at Hugging Face

id int64 -30,985 55.9k	text stringlengths 5 437k
32,603	G_\pi \cdot U = G_\pi \cdot U
-1,909	13/4 \pi = \pi \frac134 + 23/12 \pi
-6,211	\frac{1}{(3(-1) + t)5} = \frac{1}{5t + 15(-1)}
97	i = \cos{\frac12 \pi} + \sin{\pi/2} i
44,256	(\dfrac{1}{2}\cdot n + 1)\cdot \left(n + 1\right) = \frac{1}{2}\cdot (n + 1)\cdot (2\cdot \tfrac12\cdot n + 2) = \frac{1}{2}\cdot (n + 1)\cdot (n + 2)
5,235	48 + x^2*24 + 72 x = 24 (2 + x) (x + 1)
-27,711	6 \cdot \sin{x} = \frac{\mathrm{d}}{\mathrm{d}x} (-6 \cdot \cos{x})
43,194	\binom{30}{27} = \frac{30!}{27! \cdot \left(30 + 27 \cdot (-1)\right)!} = 4060
21,101	\left(a^2 + f^2\right)\cdot 5 = (2\cdot f + a)^2 + (2\cdot a - f)^2
21,438	\dfrac{13}{204} = 13*\frac{1}{51}/4
-20,576	-\frac{1}{5} \cdot 8 \cdot \frac{2 \cdot n + 2 \cdot \left(-1\right)}{2 \cdot n + 2 \cdot (-1)} = \frac{-n \cdot 16 + 16}{n \cdot 10 + 10 \cdot (-1)}
21,607	123 \cdot 345 x = 123 \cdot 345 x
10,221	\frac{z + (-1)}{3 + z} = \frac{1}{z^2 + z + 6 \times \left(-1\right)} \times (2 + z^2 - z \times 3)
21,520	\left(4 + 8\cdot (-1)\right) \cdot \left(4 + 8\cdot (-1)\right) \cdot \left(4 + 8\cdot (-1)\right) = \left(-4\right)^3 = -64
13,239	(1 + z)^2 + (z + x)^2 + ((-1) + y)^2 = x^2 + y^2 + 2\cdot z^2 + x\cdot z\cdot 2 - y\cdot 2 + 2\cdot z + 2
6,835	1 - 5 \cdot (x^2 \cdot 16 + 24 \cdot x + 9) = 1 - 80 \cdot x \cdot x - 120 \cdot x + 45 \cdot (-1)
26,978	\frac{1}{2}\cdot (0 + 4 + 4) = 4
7,543	\tan{50} = \tan(45 + 5) = \frac{1}{1 - \tan{45}\tan{5}}(\tan{45} + \tan{5})
-12,182	4/45 = s/(18\pi)18*\pi = s
14,985	4x^2 + 4x + 5 = (2x + 1)^2 + (-1) + 5 = (2x + 1)^2 + 4
19,421	\cos\left(-L\right) = \cos(L)
24,780	6 + 4^x \cdot 3 = 3 \cdot (4^x + 2)
12,570	-x^9 + 1 - x - x^3 + x^4 - x^5 + x^6 + x^8 = (-x^3 + 1) \cdot (1 - x^5) \cdot \left(-x + 1\right)
24,986	\left(3/4\right)^n = \frac{3^n}{4^n}
6,225	\sin(\dfrac13\pi) = 3^{\frac{1}{2}}/2
-19,052	\frac{7}{24} = \tfrac{1}{81 \cdot \pi} \cdot A_x \cdot 81 \cdot \pi = A_x
-29,560	\dfrac2x x^3 + \frac7x = \dfrac1x \left(2 x x x + 7\right)
30,618	149/32 = \frac{8500 \cdot \left(-1\right) + 23400}{8500 \cdot (-1) + 11700}
4,662	\tfrac16 = \frac{1}{426} \cdot 71
-7,274	\dfrac27\cdot \dfrac{1}{5} = \frac{1}{35}\cdot 2
22,527	3 = \left(-1\right) (-3)
-10,755	\dfrac{1}{8 + 4\cdot x}\cdot (x\cdot 6 + 4\cdot (-1)) = \frac{3\cdot x + 2\cdot \left(-1\right)}{2\cdot x + 4}\cdot \frac{1}{2}\cdot 2
21,123	(1 + 2^q)\cdot 3 = 2^{1 + 2 n} + 1 \implies 2^{2 n} - 3\cdot 2^{(-1) + q} = 1
15,893	2 \cdot (n + (-1)) = 2 \cdot (n + 2 \cdot (-1)) + 2
-3,648	\frac{l^4120}{144l^3} = \dfrac{l^4}{l^3}*\frac{120}{144}
-22,261	(a + 3\cdot \left(-1\right))\cdot (4 + a) = 12\cdot (-1) + a^2 + a
2,603	0 = 1 + s + s^2 = s \cdot s \cdot (1 + \frac{1}{s} + \frac{1}{s^2})
7,799	\varnothing = [1, 2] = 2 \cdot ( 1, 1)
48,707	1 + 9 * 9 + 9 = 91
18,605	\dfrac{1}{2} \cdot ((-1) + 2011) = 1005
5,436	(5 - 1)! = 432*1 = 24
13,363	p_ip_k = p_kp_i
-20,914	5/5 \frac{1}{(-1)5 y} \left(-6 y + 9\right) = \frac{45 - y30}{(-25) y}
-20,285	\frac{x + 8 \cdot \left(-1\right)}{x + 8 \cdot (-1)} = \frac{1}{8 \cdot (-1) + x} \cdot \left(8 \cdot (-1) + x\right)/1
8,593	\frac13 = \tfrac{3}{3^2}
-24,370	\frac{1}{6 + 8} 70 = 70/14 = \frac{70}{14} = 5
21,364	24 = ((8*9^{\frac{1}{2}})^{10/5})^{\frac{1}{2}}
17,983	\sin{l} = \sin(\pi - l)
-23,271	1/4 = -\frac34 + 1
5,511	h'\cdot k'\cdot h\cdot k = k\cdot h\cdot h'\cdot k'
40,289	\dfrac{150}{10} = 15
18,744	3/4 + (-\frac{1}{2} + z^2)^2 = 1 + z^4 - z \cdot z
40,329	-80,000 - 220,000=-300,000
5,792	\Sigma_kx^k = \Sigma_kx^{(-1) + k}*x
22,417	s * s * s = s^2*s
17,179	v = (z\cdot 2 + (-1))^{1/3} \Rightarrow z\cdot 2 + (-1) = v^3
13,956	y_1 + f_1 \cdot y_0 = y_0 \cdot f_1 + y_1
48,163	e^x = z \implies x = e^z
-3,893	\dfrac{1}{t^4}\cdot t = \frac{1}{t\cdot t\cdot t\cdot t}\cdot t = \dfrac{1}{t^3}
-4,923	0.53 \cdot 10^2 = 0.53 \cdot 10^{1 - -1}
204	9\cdot x^2 = (x\cdot 3) \cdot (x\cdot 3)
-6,907	8\cdot 12\cdot 8 = 768
-6,306	5/5\cdot \frac{4}{(z + 6\cdot \left(-1\right))\cdot (z + 7\cdot (-1))} = \frac{20}{5\cdot (z + 7\cdot (-1))\cdot (z + 6\cdot (-1))}
12,145	a\cdot x = 18 \Rightarrow x = \frac{18}{a}
4,451	1 \neq t, n^{1 / 2} = r/t \Rightarrow n = \frac{r^2}{t^2}
27,496	\sin(\piy) = \cos(\piy/2)\sin(\frac{\piy}{2})*2
6,008	(\dfrac14 \cdot 2) \cdot (\dfrac14 \cdot 2) \cdot (\dfrac14 \cdot 2) = 1/8
17,410	-(2 \cdot (-1) + z) = -z + 2
-2,993	\sqrt{2} \cdot 2 = \sqrt{2} \cdot (1 + 5 + 4 \cdot (-1))
11,112	5\cdot 3 - 5\cdot 2 = 5\cdot (3 + 2(-1))
-20,959	2/2\cdot (-\frac12) = -\dfrac{1}{4}\cdot 2
-9,237	2\cdot 2\cdot 2\cdot 3 - q\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3 = -72\cdot q + 24
-26,135	7\left(e^7 - 1/exp(14)\right) = -7/exp(14) + 7e^7
4,542	\frac{y + 0(-1)}{x + 0(-1)} = y/x
23,883	\left(120 = 6 \cdot a + a \cdot 4 \Rightarrow 12 = a\right) \Rightarrow a \cdot a = 144
13,613	1 = 2.5 + \sin(x) \implies \sin(x) = -1.5
-569	(e^{\tfrac{11}{12}i\pi})^4 = e^{4\dfrac{11}{12}i\pi}
15,162	\sin(D + G) = \sin(D)\cdot \cos(G) + \cos(D)\cdot \sin(G)
47,591	-\|x\| = x = x
19,657	\left\{2, 1, 0, 4, 3, \ldots\right\} = \mathbb{N}
-12,338	3 \cdot 6^{1/2} = 54^{1/2}
-2,386	(-4)^3 = \left(-4\right) \cdot (-4) \cdot (-4) = 16 \cdot (-4) = -64
-16,700	-3 = -3 \cdot (-2 \cdot m) - 21 = 6 \cdot m - 21 = 6 \cdot m + 21 \cdot (-1)
18,562	a^5 = b^4 \implies a = \left(\frac{b}{a}\right)^4
27,890	0 = x^2 - x + (-1) \Rightarrow x = (1 ± \sqrt{5})/2
-1,349	-1/4\frac54 = \dfrac{(-1)5}{4*4} = -\dfrac{5}{16}
2,294	2^1\cdot 3^2\cdot 3^4\cdot 2^5\cdot 4^3 = 2^6\cdot 3^6\cdot 4^2 \cdot 4
16,934	1 + zy = 1 + yz
8,587	\tfrac{\left(\sqrt{24}\right)^2}{8^2} = \frac{24}{64} = 6/16
3,206	z \cdot z^2 + 6\cdot z^2 + 4\cdot z + 2 = z^3 - 2\cdot z + (-1) + 6\cdot z^2 + 6\cdot z + 3 = z \cdot z^2 - 2\cdot z + (-1)
12,195	2 = 10^{1/2} \cdot (h + b \cdot 10^{1/2}) = h \cdot 10^{1/2} + 10 \cdot b
-5,859	\dfrac{4}{x^2 - 5\cdot x + 14\cdot (-1)} = \frac{1}{(x + 2)\cdot (x + 7\cdot (-1))}\cdot 4
28,707	4 + 8 + 2 \cdot \left(-1\right) = 10
1,303	\sin(x2) = \frac{\tan(x)2}{\tan^2(x) + 1}*1
609	l=l-l^2\Rightarrow l=0
8,801	2 * 243 = 48
-3,265	-\sqrt{2}\cdot \sqrt{9} + \sqrt{2}\cdot \sqrt{25} = 5\cdot \sqrt{2} - 3\cdot \sqrt{2}
-20,474	\frac{6 + s}{s\times 8 + 48} = \frac18\times 1
11,291	10^{f_1}*10^{f_2} = 10^{f_2 + f_1}
21,361	\frac{z^2 + (-1)}{z + (-1)} = \dfrac{1}{z + (-1)}(z + 1)\left(z + (-1)\right) = z + 1

32,603

G_\pi \cdot U = G_\pi \cdot U

-1,909

13/4 \pi = \pi \frac134 + 23/12 \pi

-6,211

\frac{1}{(3*(-1) + t)*5} = \frac{1}{5*t + 15*(-1)}

97

i = \cos{\frac12 \pi} + \sin{\pi/2} i

44,256

(\dfrac{1}{2}\cdot n + 1)\cdot \left(n + 1\right) = \frac{1}{2}\cdot (n + 1)\cdot (2\cdot \tfrac12\cdot n + 2) = \frac{1}{2}\cdot (n + 1)\cdot (n + 2)

5,235

48 + x^2*24 + 72 x = 24 (2 + x) (x + 1)

-27,711

6 \cdot \sin{x} = \frac{\mathrm{d}}{\mathrm{d}x} (-6 \cdot \cos{x})

43,194

\binom{30}{27} = \frac{30!}{27! \cdot \left(30 + 27 \cdot (-1)\right)!} = 4060

21,101

\left(a^2 + f^2\right)\cdot 5 = (2\cdot f + a)^2 + (2\cdot a - f)^2

21,438

\dfrac{13}{204} = 13*\frac{1}{51}/4

-20,576

-\frac{1}{5} \cdot 8 \cdot \frac{2 \cdot n + 2 \cdot \left(-1\right)}{2 \cdot n + 2 \cdot (-1)} = \frac{-n \cdot 16 + 16}{n \cdot 10 + 10 \cdot (-1)}

21,607

123 \cdot 345 x = 123 \cdot 345 x

10,221

\frac{z + (-1)}{3 + z} = \frac{1}{z^2 + z + 6 \times \left(-1\right)} \times (2 + z^2 - z \times 3)

21,520

\left(4 + 8\cdot (-1)\right) \cdot \left(4 + 8\cdot (-1)\right) \cdot \left(4 + 8\cdot (-1)\right) = \left(-4\right)^3 = -64

13,239

(1 + z)^2 + (z + x)^2 + ((-1) + y)^2 = x^2 + y^2 + 2\cdot z^2 + x\cdot z\cdot 2 - y\cdot 2 + 2\cdot z + 2

6,835

1 - 5 \cdot (x^2 \cdot 16 + 24 \cdot x + 9) = 1 - 80 \cdot x \cdot x - 120 \cdot x + 45 \cdot (-1)

26,978

\frac{1}{2}\cdot (0 + 4 + 4) = 4

7,543

\tan{50} = \tan(45 + 5) = \frac{1}{1 - \tan{45}*\tan{5}}*(\tan{45} + \tan{5})

-12,182

4/45 = s/(18*\pi)*18*\pi = s

14,985

4*x^2 + 4*x + 5 = (2*x + 1)^2 + (-1) + 5 = (2*x + 1)^2 + 4

19,421

\cos\left(-L\right) = \cos(L)

24,780

6 + 4^x \cdot 3 = 3 \cdot (4^x + 2)

12,570

-x^9 + 1 - x - x^3 + x^4 - x^5 + x^6 + x^8 = (-x^3 + 1) \cdot (1 - x^5) \cdot \left(-x + 1\right)

24,986

\left(3/4\right)^n = \frac{3^n}{4^n}

6,225

\sin(\dfrac13\pi) = 3^{\frac{1}{2}}/2

-19,052

\frac{7}{24} = \tfrac{1}{81 \cdot \pi} \cdot A_x \cdot 81 \cdot \pi = A_x

-29,560

\dfrac2x x^3 + \frac7x = \dfrac1x \left(2 x x x + 7\right)

30,618

149/32 = \frac{8500 \cdot \left(-1\right) + 23400}{8500 \cdot (-1) + 11700}

4,662

\tfrac16 = \frac{1}{426} \cdot 71

-7,274

\dfrac27\cdot \dfrac{1}{5} = \frac{1}{35}\cdot 2

22,527

3 = \left(-1\right) (-3)

-10,755

\dfrac{1}{8 + 4\cdot x}\cdot (x\cdot 6 + 4\cdot (-1)) = \frac{3\cdot x + 2\cdot \left(-1\right)}{2\cdot x + 4}\cdot \frac{1}{2}\cdot 2

21,123

(1 + 2^q)\cdot 3 = 2^{1 + 2 n} + 1 \implies 2^{2 n} - 3\cdot 2^{(-1) + q} = 1

15,893

2 \cdot (n + (-1)) = 2 \cdot (n + 2 \cdot (-1)) + 2

-3,648

\frac{l^4*120}{144*l^3} = \dfrac{l^4}{l^3}*\frac{120}{144}

-22,261

(a + 3\cdot \left(-1\right))\cdot (4 + a) = 12\cdot (-1) + a^2 + a

2,603

0 = 1 + s + s^2 = s \cdot s \cdot (1 + \frac{1}{s} + \frac{1}{s^2})

7,799

\varnothing = [1, 2] = 2 \cdot ( 1, 1)

48,707

1 + 9 * 9 + 9 = 91

18,605

\dfrac{1}{2} \cdot ((-1) + 2011) = 1005

5,436

(5 - 1)! = 4*3*2*1 = 24

13,363

p_i*p_k = p_k*p_i

-20,914

5/5 \frac{1}{(-1)*5 y} \left(-6 y + 9\right) = \frac{45 - y*30}{(-25) y}

-20,285

\frac{x + 8 \cdot \left(-1\right)}{x + 8 \cdot (-1)} = \frac{1}{8 \cdot (-1) + x} \cdot \left(8 \cdot (-1) + x\right)/1

8,593

\frac13 = \tfrac{3}{3^2}

-24,370

\frac{1}{6 + 8} 70 = 70/14 = \frac{70}{14} = 5

21,364

24 = ((8*9^{\frac{1}{2}})^{10/5})^{\frac{1}{2}}

17,983

\sin{l} = \sin(\pi - l)

-23,271

1/4 = -\frac34 + 1

5,511

h'\cdot k'\cdot h\cdot k = k\cdot h\cdot h'\cdot k'

40,289

\dfrac{150}{10} = 15

18,744

3/4 + (-\frac{1}{2} + z^2)^2 = 1 + z^4 - z \cdot z

40,329

-80,000 - 220,000=-300,000

5,792

\Sigma_k*x^k = \Sigma_k*x^{(-1) + k}*x

22,417

s * s * s = s^2*s

17,179

v = (z\cdot 2 + (-1))^{1/3} \Rightarrow z\cdot 2 + (-1) = v^3

13,956

y_1 + f_1 \cdot y_0 = y_0 \cdot f_1 + y_1

48,163

e^x = z \implies x = e^z

-3,893

\dfrac{1}{t^4}\cdot t = \frac{1}{t\cdot t\cdot t\cdot t}\cdot t = \dfrac{1}{t^3}

-4,923

0.53 \cdot 10^2 = 0.53 \cdot 10^{1 - -1}

204

9\cdot x^2 = (x\cdot 3) \cdot (x\cdot 3)

-6,907

8\cdot 12\cdot 8 = 768

-6,306

5/5\cdot \frac{4}{(z + 6\cdot \left(-1\right))\cdot (z + 7\cdot (-1))} = \frac{20}{5\cdot (z + 7\cdot (-1))\cdot (z + 6\cdot (-1))}

12,145

a\cdot x = 18 \Rightarrow x = \frac{18}{a}

4,451

1 \neq t, n^{1 / 2} = r/t \Rightarrow n = \frac{r^2}{t^2}

27,496

\sin(\pi*y) = \cos(\pi*y/2)*\sin(\frac{\pi*y}{2})*2

6,008

(\dfrac14 \cdot 2) \cdot (\dfrac14 \cdot 2) \cdot (\dfrac14 \cdot 2) = 1/8

17,410

-(2 \cdot (-1) + z) = -z + 2

-2,993

\sqrt{2} \cdot 2 = \sqrt{2} \cdot (1 + 5 + 4 \cdot (-1))

11,112

5\cdot 3 - 5\cdot 2 = 5\cdot (3 + 2(-1))

-20,959

2/2\cdot (-\frac12) = -\dfrac{1}{4}\cdot 2

-9,237

2\cdot 2\cdot 2\cdot 3 - q\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3 = -72\cdot q + 24

-26,135

7*\left(e^7 - 1/exp(14)\right) = -7/exp(14) + 7*e^7

4,542

\frac{y + 0(-1)}{x + 0(-1)} = y/x

23,883

\left(120 = 6 \cdot a + a \cdot 4 \Rightarrow 12 = a\right) \Rightarrow a \cdot a = 144

13,613

1 = 2.5 + \sin(x) \implies \sin(x) = -1.5

-569

(e^{\tfrac{11}{12}i\pi})^4 = e^{4\dfrac{11}{12}i\pi}

15,162

\sin(D + G) = \sin(D)\cdot \cos(G) + \cos(D)\cdot \sin(G)

47,591

-|x| = x = x

19,657

\left\{2, 1, 0, 4, 3, \ldots\right\} = \mathbb{N}

-12,338

3 \cdot 6^{1/2} = 54^{1/2}

-2,386

(-4)^3 = \left(-4\right) \cdot (-4) \cdot (-4) = 16 \cdot (-4) = -64

-16,700

-3 = -3 \cdot (-2 \cdot m) - 21 = 6 \cdot m - 21 = 6 \cdot m + 21 \cdot (-1)

18,562

a^5 = b^4 \implies a = \left(\frac{b}{a}\right)^4

27,890

0 = x^2 - x + (-1) \Rightarrow x = (1 ± \sqrt{5})/2

-1,349

-1/4*\frac54 = \dfrac{(-1)*5}{4*4} = -\dfrac{5}{16}

2,294

2^1\cdot 3^2\cdot 3^4\cdot 2^5\cdot 4^3 = 2^6\cdot 3^6\cdot 4^2 \cdot 4

16,934

1 + z*y = 1 + y*z

8,587

\tfrac{\left(\sqrt{24}\right)^2}{8^2} = \frac{24}{64} = 6/16

3,206

z \cdot z^2 + 6\cdot z^2 + 4\cdot z + 2 = z^3 - 2\cdot z + (-1) + 6\cdot z^2 + 6\cdot z + 3 = z \cdot z^2 - 2\cdot z + (-1)

12,195

2 = 10^{1/2} \cdot (h + b \cdot 10^{1/2}) = h \cdot 10^{1/2} + 10 \cdot b

-5,859

\dfrac{4}{x^2 - 5\cdot x + 14\cdot (-1)} = \frac{1}{(x + 2)\cdot (x + 7\cdot (-1))}\cdot 4

28,707

4 + 8 + 2 \cdot \left(-1\right) = 10

1,303

\sin(x*2) = \frac{\tan(x)*2}{\tan^2(x) + 1}*1

609

l=l-l^2\Rightarrow l=0

8,801

2 * 2*4*3 = 48

-3,265

-\sqrt{2}\cdot \sqrt{9} + \sqrt{2}\cdot \sqrt{25} = 5\cdot \sqrt{2} - 3\cdot \sqrt{2}

-20,474

\frac{6 + s}{s\times 8 + 48} = \frac18\times 1

11,291

10^{f_1}*10^{f_2} = 10^{f_2 + f_1}

21,361

\frac{z^2 + (-1)}{z + (-1)} = \dfrac{1}{z + (-1)}*(z + 1)*\left(z + (-1)\right) = z + 1