ddrg/math_formulas · Datasets at Hugging Face

id int64 -30,985 55.9k	text stringlengths 5 437k
7,725	2\cdot (h + (-1)) + (h + \left(-1\right)) \cdot (h + \left(-1\right)) = h \cdot h - 2\cdot h + 1 + 2\cdot h + 2\cdot (-1) = h^2 + (-1)
-16,588	10 \sqrt{18} = \sqrt{9 \cdot 2} \cdot 10
-4,807	10^{4 + 1}28.5 = 10^528.5
11,469	2z + \frac{\mathrm{d}}{\mathrm{d}z} y^2 = 0 = 2z + \frac{\mathrm{d}}{\mathrm{d}y} (y * y*\frac{\mathrm{d}y}{\mathrm{d}z})
3,529	\dfrac{1}{2}(3 \pm \sqrt{-3 + 4i}) = \dfrac12(3 \pm \sqrt{9 - 4*\left(3 - i\right)})
161	\|f + \left(-1\right)\| + \|b + (-1)\| = f + (-1) - b + (-1) = f - b
41,322	0^{\tfrac{1}{-1}} = 0^{\frac{1}{-1}} = 0
-5,742	\frac{5 \cdot s}{((-1) + s) \cdot (s + 8 \cdot (-1))} = \frac{5 \cdot s}{s^2 - 9 \cdot s + 8}
23,847	a^{h_2^{h_1}} = a^{h_2^{h_1}}
-20,387	\dfrac37 \cdot \frac{5 + 10 \cdot q}{5 + 10 \cdot q} = \frac{30 \cdot q + 15}{35 + q \cdot 70}
22,305	x\times 6 = 0 \Rightarrow x = 0
-24,826	\left(-1\right) + 575 = 574
-5,398	4.13\cdot 10 = 4.13\cdot 10\cdot 10^1 = 4.13\cdot 10 \cdot 10
10,151	-\sin^2(\theta)2 + 1 = \cos(2\theta)
22,348	4176 = 6642 + 2466*(-1)
8,488	\cos^2(\theta) = \frac{1}{2} + \frac{\cos\left(\theta*2\right)}{2}
30,189	3/4 - \frac{15}{4\left(5 + \frac{4}{3}\right)} = \frac{1}{19}3
29,280	\frac{2\cdot \pi}{5}\cdot 1.25 = \dfrac{\pi}{5}\cdot 2\cdot \frac{5}{4} = \pi/2
7,688	\dfrac{1}{z} = 1/z*\overline{z}/\overline{z} = \dfrac{\overline{z}}{\|z\|^2}
-4,460	\frac{-z\cdot 2 + 1}{20 (-1) + z^2 - z} = -\tfrac{1}{z + 4} - \frac{1}{5(-1) + z}
32,564	h = -\frac{\partial}{\partial s} \left(2hx\right)\Longrightarrow -h2 - xh*2 = h
554	(x - y) (y - z) + y^2 = yx - zx + yz
19,783	\sin\left(f + \pi\right) = \sin{f} \cdot \sin{\pi} + \cos{f} \cdot \sin{\pi} = -\sin{f}
8,219	yH = yH
6,308	0 = 14 + x^2\cdot 3 - 13\cdot x \Rightarrow \left(x\cdot 3 + 7\cdot (-1)\right)\cdot \left(2\cdot \left(-1\right) + x\right) = 0
912	3(i2 + 1) = ((-6)(2i + 1))/(-2)
17,135	12 = 25 + 13\cdot (-1)
16,811	p\cdot r'\cdot x = r'\cdot p\cdot x
-2,516	6 \cdot \sqrt{5} = (4 + 5 + 3 \cdot (-1)) \cdot \sqrt{5}
3,889	\frac{1}{q \cdot 2 + 1} \cdot (2^q + 1) \cdot ((-1) + 2^q) = \dfrac{1}{1 + q \cdot 2} \cdot ((-1) + 4^q)
549	2 = \left(\sqrt{2}\right)^2 = (2^{\dfrac{1}{3}})^3 = \dotsm
-1,780	\pi \cdot \dfrac{1}{4} \cdot 7 + \pi \cdot 11/6 = \pi \cdot 43/12
-12,223	\dfrac25 = \frac{s}{6\times \pi}\times 6\times \pi = s
23,122	gx = -x*(-g)
33,329	\cos{π/4} = \sin{π/4}
33,048	1000 + (-1) + 193 \cdot \left(-1\right) + 298 \cdot (-1) = 508
33,249	30 = \tfrac{5!}{2! \cdot 2!}
30,751	(0 - 1) \cdot a = -a + a \cdot 0
-6,670	\frac{5}{2x + 10(-1)} = \dfrac{1}{2(x + 5(-1))}*5
30,562	\tfrac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}
485	(-1) + z^3 = \left(z^2 + z + 1\right) \left(z + (-1)\right)
9,925	x^{-(z + 1)} = \dfrac{1}{x^{1 + z}}
41,114	(\sqrt{33}3 + 17)^{\frac{1}{3}} = \left(3\sqrt{33} + 17\right)^{1/3}
-1,044	\dfrac{1}{4} = \frac{1}{4}
20,634	0 = z^2 + y^2 - 3 \cdot y\Longrightarrow (-3/2 + y)^2 + z^2 = (3/2)^2
-7,275	\frac{1}{42} \cdot 5 = \frac{1}{9} \cdot 5 \cdot \frac48 \cdot 3/7
18,759	18! \cdot \frac{20}{2} \cdot 19 = \frac{20!}{2}
4,818	c - g_2 + g_1 - e = -(g_2 + e) + g_1 + c
26,054	\frac{1}{6\cdot 2} = \dfrac{1}{12}
4,173	8 \cdot 8 - 7^2 = 4^2 - 1^2
3,772	-z*(-1) + x = z + x
20,649	m9 + 9(-1) = 3\left(m + (-1)\right)3
-23,041	\frac{8}{9} = \frac13\cdot 4\cdot 2/3
16,370	\left\lfloor{41 \cdot 13/57}\right\rfloor = 9
-11,556	2\cdot i + 3 + 0\cdot (-1) = i\cdot 2 + 3
4,581	6^2 + 12^2 + 12 * 12 = 49 9
-15,544	\dfrac{l^5 \cdot z^5}{\frac{1}{l^{10}} \cdot \frac{1}{z^6}} = \frac{z^5 \cdot l^5}{\frac{1}{l^{10} \cdot z^6}}
11,706	\cos{n \cdot \phi} = \cos{-\phi \cdot n}
-4,815	10^{4 + 0}29.2 = 10^429.2
16,272	(2n + 2)! = (2 + n2)\left(2n + 1\right)(2n)!
-5,460	\frac{1}{2\cdot n^2 + 98\cdot (-1)}\cdot \left(4\cdot (-1) + n\cdot 6 + 42\cdot (-1) - n + 7\cdot \left(-1\right)\right) = \frac{1}{2\cdot n^2 + 98\cdot (-1)}\cdot (5\cdot n + 53\cdot (-1))
22,190	\dfrac{1}{4\cdot (-1) + n^2}\cdot 4 = \frac{1}{2\cdot (-1) + n} - \frac{1}{2 + n}
-10,573	120 = 15\cdot x + 30 + 30\cdot \left(-1\right) = 15\cdot x = 15\cdot x
15,323	x \cdot e^z \approx dy = e^x - e^z \approx dx \Rightarrow e^z - e^x \approx dx + x \cdot e^z \approx dy = 0
6,357	x^2 \cdot 3 - x \cdot 7 + 2 = \left((-1) + 3 \cdot x\right) \cdot (2 \cdot (-1) + x)
28,150	\sqrt{64 r \cdot r S^4 + 4} = \sqrt{4\cdot \left(16 r \cdot r S^4 + 1\right)} = 2\sqrt{16 r^2 S^4 + 1}
20,323	7/24 = \frac{1}{24} \cdot 5 + \frac{1}{12}
-7,598	\dfrac{6 - 14\cdot i}{-i\cdot 2 + 2}\cdot \dfrac{1}{2 + 2\cdot i}\cdot (2 + i\cdot 2) = \frac{1}{2 - 2\cdot i}\cdot (6 - i\cdot 14)
9,896	a \cdot d \cdot a - a = \frac{1}{\dfrac{1}{a - 1/d} - \dfrac1a}
1,342	6^n\cdot 5 + 6^n + \left(-1\right) = (-1) + 6^n\cdot (1 + 5)
17,846	(x * x)^{1 / 2} = ((-x)^2)^{\frac{1}{2}} = \|x\|
8,432	2 + 2 \cdot y = 2 \cdot \left(y + 1\right)
3,971	\left(1 + 4^3 - 4^2 + 4 \cdot (-1)\right) \cdot 4^{2013} = 4^{2013} + 4^{2016} - 4^{2015} - 4^{2014}
2,119	\cos{\pi \cdot 2014/12} = \cos(\dfrac{\pi}{12} \cdot 2014 - 83 \cdot \pi \cdot 2)
-19,123	\dfrac{14}{45} = A_s/\left(9\times π\right)\times 9\times π = A_s
10,837	\frac{1}{2 \cdot 100} + \frac{1}{200 \cdot 2} = 3/400
43,236	4 \times (-1) + 7 = 3
29,078	\frac{1}{f_1 + f + f_2} = \frac{1}{ff_1f_2}\left(ff_1 + ff_2 + f_2f_1\right) \implies ff_2f_1 = (f_1 + f + f_2)(ff_1 + f_2f + f_2f_1)
19,151	(2 + l) \cdot \left(2 \cdot \left(-1\right) + l\right) = l^2 + 4 \cdot (-1)
-5,494	\frac{3}{5 \cdot (r + 6)} = \dfrac{1}{5 \cdot r + 30} \cdot 3
35,873	1 = e^{i\cdot 0} = e^{i\cdot 3\cdot π/2} = -i
-1,265	15/72 = \frac{15 \cdot 1/3}{72 \cdot \frac13} = \frac{5}{24}
21,446	\sin(\frac{\pi}{2}\cdot 3) = \sin(\pi + \frac{1}{2}\cdot \pi)
18,605	\frac{1}{2}\cdot (2011 + (-1)) = 1005
5,370	\frac{1}{(\tau_F \cdot x)^5} \cdot \left(x \cdot \tau_F\right)^9 = (x \cdot \tau_F)^4
-28,982	q\cdot 100\cdot q = 100\cdot q \cdot q
-1,382	-20/54 = \dfrac{(-20) \cdot 1/2}{54 \cdot \frac{1}{2}} = -\frac{10}{27}
-1,450	-\frac{1}{45} 5 = \frac{(-5) \cdot 1/5}{45 \cdot 1/5} = -\frac{1}{9}
-26,724	\sum_{n=1}^∞ \dfrac{1}{n7^n}\left(3 + 4\right)^n(n + 6) = \sum_{n=1}^∞ \frac{7^n}{n7^n}*(n + 6) = \sum_{n=1}^∞ (n + 6)/n
3,365	x * x * x - 5x^2 + hx + (-1) = (x + (-1)) (1 + x^2 - x4) + x(h + 5(-1))
26,753	\dfrac{1}{a\dfrac{1}{a}} = \dfrac{a}{a}
-26,576	2\cdot z^2 + 162\cdot (-1) = 2\cdot (z^2 + 81\cdot \left(-1\right)) = 2\cdot (z + 9)\cdot (z + 9\cdot (-1))
52,690	\|q_1\| + \|q_2\| = q_1 - q_2 = \|q_1 - q_2\|
1,450	\frac{(-1)\cdot \pi}{6} = -2\cdot \pi\cdot 84 + \frac{2014}{12}\cdot \pi
-20,314	9/4\cdot \tfrac{1}{5\cdot s + 7}\cdot (7 + 5\cdot s) = \frac{63 + 45\cdot s}{28 + 20\cdot s}
19,377	( d, i)( h', x) = ( h', x)( d, i)
-9,183	-130 \cdot k \cdot k = -k \cdot k \cdot 2 \cdot 5 \cdot 13
6,482	\left(\left(-1\right) + \frac{m\cdot x\cdot f}{h\cdot l\cdot o}\right)\cdot 100 = \frac{1}{o\cdot l\cdot h}\cdot (-o\cdot l\cdot h + x\cdot f\cdot m)\cdot 100
40,263	\cosh\left(x\right) + \sinh(x) = e^x
-11,578	-25 + 0(-1) + 20 i = i*20 - 25

7,725

2\cdot (h + (-1)) + (h + \left(-1\right)) \cdot (h + \left(-1\right)) = h \cdot h - 2\cdot h + 1 + 2\cdot h + 2\cdot (-1) = h^2 + (-1)

-16,588

10 \sqrt{18} = \sqrt{9 \cdot 2} \cdot 10

-4,807

10^{4 + 1}*28.5 = 10^5*28.5

11,469

2*z + \frac{\mathrm{d}}{\mathrm{d}z} y^2 = 0 = 2*z + \frac{\mathrm{d}}{\mathrm{d}y} (y * y*\frac{\mathrm{d}y}{\mathrm{d}z})

3,529

\dfrac{1}{2}(3 \pm \sqrt{-3 + 4i}) = \dfrac12(3 \pm \sqrt{9 - 4*\left(3 - i\right)})

161

|f + \left(-1\right)| + |b + (-1)| = f + (-1) - b + (-1) = f - b

41,322

0^{\tfrac{1}{-1}} = 0^{\frac{1}{-1}} = 0

-5,742

\frac{5 \cdot s}{((-1) + s) \cdot (s + 8 \cdot (-1))} = \frac{5 \cdot s}{s^2 - 9 \cdot s + 8}

23,847

a^{h_2^{h_1}} = a^{h_2^{h_1}}

-20,387

\dfrac37 \cdot \frac{5 + 10 \cdot q}{5 + 10 \cdot q} = \frac{30 \cdot q + 15}{35 + q \cdot 70}

22,305

x\times 6 = 0 \Rightarrow x = 0

-24,826

\left(-1\right) + 575 = 574

-5,398

4.13\cdot 10 = 4.13\cdot 10\cdot 10^1 = 4.13\cdot 10 \cdot 10

10,151

-\sin^2(\theta)*2 + 1 = \cos(2*\theta)

22,348

4176 = 6642 + 2466*(-1)

8,488

\cos^2(\theta) = \frac{1}{2} + \frac{\cos\left(\theta*2\right)}{2}

30,189

3/4 - \frac{15}{4*\left(5 + \frac{4}{3}\right)} = \frac{1}{19}*3

29,280

\frac{2\cdot \pi}{5}\cdot 1.25 = \dfrac{\pi}{5}\cdot 2\cdot \frac{5}{4} = \pi/2

7,688

\dfrac{1}{z} = 1/z*\overline{z}/\overline{z} = \dfrac{\overline{z}}{|z|^2}

-4,460

\frac{-z\cdot 2 + 1}{20 (-1) + z^2 - z} = -\tfrac{1}{z + 4} - \frac{1}{5(-1) + z}

32,564

h = -\frac{\partial}{\partial s} \left(2*h*x\right)\Longrightarrow -h*2 - x*h*2 = h

554

(x - y) (y - z) + y^2 = yx - zx + yz

19,783

\sin\left(f + \pi\right) = \sin{f} \cdot \sin{\pi} + \cos{f} \cdot \sin{\pi} = -\sin{f}

8,219

yH = yH

6,308

0 = 14 + x^2\cdot 3 - 13\cdot x \Rightarrow \left(x\cdot 3 + 7\cdot (-1)\right)\cdot \left(2\cdot \left(-1\right) + x\right) = 0

912

3*(i*2 + 1) = ((-6)*(2*i + 1))/(-2)

17,135

12 = 25 + 13\cdot (-1)

16,811

p\cdot r'\cdot x = r'\cdot p\cdot x

-2,516

6 \cdot \sqrt{5} = (4 + 5 + 3 \cdot (-1)) \cdot \sqrt{5}

3,889

\frac{1}{q \cdot 2 + 1} \cdot (2^q + 1) \cdot ((-1) + 2^q) = \dfrac{1}{1 + q \cdot 2} \cdot ((-1) + 4^q)

549

2 = \left(\sqrt{2}\right)^2 = (2^{\dfrac{1}{3}})^3 = \dotsm

-1,780

\pi \cdot \dfrac{1}{4} \cdot 7 + \pi \cdot 11/6 = \pi \cdot 43/12

-12,223

\dfrac25 = \frac{s}{6\times \pi}\times 6\times \pi = s

23,122

gx = -x*(-g)

33,329

\cos{π/4} = \sin{π/4}

33,048

1000 + (-1) + 193 \cdot \left(-1\right) + 298 \cdot (-1) = 508

33,249

30 = \tfrac{5!}{2! \cdot 2!}

30,751

(0 - 1) \cdot a = -a + a \cdot 0

-6,670

\frac{5}{2*x + 10*(-1)} = \dfrac{1}{2*(x + 5*(-1))}*5

30,562

\tfrac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}

485

(-1) + z^3 = \left(z^2 + z + 1\right) \left(z + (-1)\right)

9,925

x^{-(z + 1)} = \dfrac{1}{x^{1 + z}}

41,114

(\sqrt{33}*3 + 17)^{\frac{1}{3}} = \left(3*\sqrt{33} + 17\right)^{1/3}

-1,044

\dfrac{1}{4} = \frac{1}{4}

20,634

0 = z^2 + y^2 - 3 \cdot y\Longrightarrow (-3/2 + y)^2 + z^2 = (3/2)^2

-7,275

\frac{1}{42} \cdot 5 = \frac{1}{9} \cdot 5 \cdot \frac48 \cdot 3/7

18,759

18! \cdot \frac{20}{2} \cdot 19 = \frac{20!}{2}

4,818

c - g_2 + g_1 - e = -(g_2 + e) + g_1 + c

26,054

\frac{1}{6\cdot 2} = \dfrac{1}{12}

4,173

8 \cdot 8 - 7^2 = 4^2 - 1^2

3,772

-z*(-1) + x = z + x

20,649

m*9 + 9*(-1) = 3*\left(m + (-1)\right)*3

-23,041

\frac{8}{9} = \frac13\cdot 4\cdot 2/3

16,370

\left\lfloor{41 \cdot 13/57}\right\rfloor = 9

-11,556

2\cdot i + 3 + 0\cdot (-1) = i\cdot 2 + 3

4,581

6^2 + 12^2 + 12 * 12 = 4*9 * 9

-15,544

\dfrac{l^5 \cdot z^5}{\frac{1}{l^{10}} \cdot \frac{1}{z^6}} = \frac{z^5 \cdot l^5}{\frac{1}{l^{10} \cdot z^6}}

11,706

\cos{n \cdot \phi} = \cos{-\phi \cdot n}

-4,815

10^{4 + 0}*29.2 = 10^4*29.2

16,272

(2*n + 2)! = (2 + n*2)*\left(2*n + 1\right)*(2*n)!

-5,460

\frac{1}{2\cdot n^2 + 98\cdot (-1)}\cdot \left(4\cdot (-1) + n\cdot 6 + 42\cdot (-1) - n + 7\cdot \left(-1\right)\right) = \frac{1}{2\cdot n^2 + 98\cdot (-1)}\cdot (5\cdot n + 53\cdot (-1))

22,190

\dfrac{1}{4\cdot (-1) + n^2}\cdot 4 = \frac{1}{2\cdot (-1) + n} - \frac{1}{2 + n}

-10,573

120 = 15\cdot x + 30 + 30\cdot \left(-1\right) = 15\cdot x = 15\cdot x

15,323

x \cdot e^z \approx dy = e^x - e^z \approx dx \Rightarrow e^z - e^x \approx dx + x \cdot e^z \approx dy = 0

6,357

x^2 \cdot 3 - x \cdot 7 + 2 = \left((-1) + 3 \cdot x\right) \cdot (2 \cdot (-1) + x)

28,150

\sqrt{64 r \cdot r S^4 + 4} = \sqrt{4\cdot \left(16 r \cdot r S^4 + 1\right)} = 2\sqrt{16 r^2 S^4 + 1}

20,323

7/24 = \frac{1}{24} \cdot 5 + \frac{1}{12}

-7,598

\dfrac{6 - 14\cdot i}{-i\cdot 2 + 2}\cdot \dfrac{1}{2 + 2\cdot i}\cdot (2 + i\cdot 2) = \frac{1}{2 - 2\cdot i}\cdot (6 - i\cdot 14)

9,896

a \cdot d \cdot a - a = \frac{1}{\dfrac{1}{a - 1/d} - \dfrac1a}

1,342

6^n\cdot 5 + 6^n + \left(-1\right) = (-1) + 6^n\cdot (1 + 5)

17,846

(x * x)^{1 / 2} = ((-x)^2)^{\frac{1}{2}} = |x|

8,432

2 + 2 \cdot y = 2 \cdot \left(y + 1\right)

3,971

\left(1 + 4^3 - 4^2 + 4 \cdot (-1)\right) \cdot 4^{2013} = 4^{2013} + 4^{2016} - 4^{2015} - 4^{2014}

2,119

\cos{\pi \cdot 2014/12} = \cos(\dfrac{\pi}{12} \cdot 2014 - 83 \cdot \pi \cdot 2)

-19,123

\dfrac{14}{45} = A_s/\left(9\times π\right)\times 9\times π = A_s

10,837

\frac{1}{2 \cdot 100} + \frac{1}{200 \cdot 2} = 3/400

43,236

4 \times (-1) + 7 = 3

29,078

\frac{1}{f_1 + f + f_2} = \frac{1}{f*f_1*f_2}*\left(f*f_1 + f*f_2 + f_2*f_1\right) \implies f*f_2*f_1 = (f_1 + f + f_2)*(f*f_1 + f_2*f + f_2*f_1)

19,151

(2 + l) \cdot \left(2 \cdot \left(-1\right) + l\right) = l^2 + 4 \cdot (-1)

-5,494

\frac{3}{5 \cdot (r + 6)} = \dfrac{1}{5 \cdot r + 30} \cdot 3

35,873

1 = e^{i\cdot 0} = e^{i\cdot 3\cdot π/2} = -i

-1,265

15/72 = \frac{15 \cdot 1/3}{72 \cdot \frac13} = \frac{5}{24}

21,446

\sin(\frac{\pi}{2}\cdot 3) = \sin(\pi + \frac{1}{2}\cdot \pi)

18,605

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

5,370

\frac{1}{(\tau_F \cdot x)^5} \cdot \left(x \cdot \tau_F\right)^9 = (x \cdot \tau_F)^4

-28,982

q\cdot 100\cdot q = 100\cdot q \cdot q

-1,382

-20/54 = \dfrac{(-20) \cdot 1/2}{54 \cdot \frac{1}{2}} = -\frac{10}{27}

-1,450

-\frac{1}{45} 5 = \frac{(-5) \cdot 1/5}{45 \cdot 1/5} = -\frac{1}{9}

-26,724

\sum_{n=1}^∞ \dfrac{1}{n*7^n}*\left(3 + 4\right)^n*(n + 6) = \sum_{n=1}^∞ \frac{7^n}{n*7^n}*(n + 6) = \sum_{n=1}^∞ (n + 6)/n

3,365

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

26,753

\dfrac{1}{a\dfrac{1}{a}} = \dfrac{a}{a}

-26,576

2\cdot z^2 + 162\cdot (-1) = 2\cdot (z^2 + 81\cdot \left(-1\right)) = 2\cdot (z + 9)\cdot (z + 9\cdot (-1))

52,690

|q_1| + |q_2| = q_1 - q_2 = |q_1 - q_2|

1,450

\frac{(-1)\cdot \pi}{6} = -2\cdot \pi\cdot 84 + \frac{2014}{12}\cdot \pi

-20,314

9/4\cdot \tfrac{1}{5\cdot s + 7}\cdot (7 + 5\cdot s) = \frac{63 + 45\cdot s}{28 + 20\cdot s}

19,377

( d, i)*( h', x) = ( h', x)*( d, i)

-9,183

-130 \cdot k \cdot k = -k \cdot k \cdot 2 \cdot 5 \cdot 13

6,482

\left(\left(-1\right) + \frac{m\cdot x\cdot f}{h\cdot l\cdot o}\right)\cdot 100 = \frac{1}{o\cdot l\cdot h}\cdot (-o\cdot l\cdot h + x\cdot f\cdot m)\cdot 100

40,263

\cosh\left(x\right) + \sinh(x) = e^x

-11,578

-25 + 0(-1) + 20 i = i*20 - 25