ddrg/math_formulas · Datasets at Hugging Face

id int64 -30,985 55.9k	text stringlengths 5 437k
7,513	y/1 = \dfrac{1}{3}(1 - z) = q \Rightarrow y = q,1 - q3 = z
8,103	4z^2 - z z = 4z^2 - z z = (4 + (-1))z z = 3z z
-3,070	\left(2 + 1 + 5\right) \times \sqrt{3} = 8 \times \sqrt{3}
3,298	(((\left((((7^2)^2 \cdot 7)^2)^2 \cdot 7\right)^2)^2 \cdot 7)^2)^2 = 7^{340}
3,903	5 (-1) + 64 + 8 (-1) + 7 \left(-1\right) + 7 (-1) + 7 (-1) = 30
31,778	171615\dotsm2 = 17!
21,429	0.064 = (\frac{4}{10}) \times (\frac{4}{10}) \times (\frac{4}{10})
-593	-4 \cdot \pi + 35/6 \cdot \pi = \pi \cdot 11/6
-14,214	\frac{1}{6 + 5 \cdot \left(-1\right)} \cdot 4 = 4/1 = 4/1 = 4
20,566	165 = \binom{(-1) + 8 + 4}{4 + (-1)}
13,921	(2\left(-1\right) + y) (y + 2) + 4 = y^2
10,611	\frac{\mathrm{d}}{\mathrm{d}x} \sin(x \cdot x) = 2 \cdot x \cdot \cos(x^2)
29,129	8\cdot 7=56
5,063	0 = -ca4 + 4f^2 \Rightarrow c^3 + a^3 + f^3 = acf3
9,038	\frac{1}{2\cdot \left(-1\right) + x}\cdot (2\cdot x^3 - 10\cdot x + 4) = x^2\cdot 2 + 4\cdot x + 2\cdot (-1)
19,299	\left((-1) + 2^l\right)(1 + 2^l) = 2^{l2} + (-1)
26,208	m/(2m)! = \frac{m}{2m(2m + (-1))!} = \dfrac{1}{2(2m + (-1))!}
11,861	\frac{52!}{5! \cdot 47!} = \dfrac{1}{47!} \cdot 52!/5!
2,402	\pi2 = 4\pi2/13 + 9*2\pi/13
-10,616	-\dfrac{20}{10 \cdot x^3} = -\dfrac{4}{2 \cdot x^3} \cdot \frac15 \cdot 5
-20,772	-8/5 \dfrac{1}{l + 3(-1)}(l + 3(-1)) = \frac{1}{l \cdot 5 + 15 \left(-1\right)}(24 - 8l)
-5,567	\dfrac{1}{6 \cdot (-1) + r \cdot 3} = \frac{1}{3 \cdot (r + 2 \cdot (-1))}
-2,338	\frac{1}{14} = -\tfrac{1}{14} + \frac{2}{14}
35,971	\ldots \cdot \ldots = \ldots^2
3,340	0 = X \cdot (H_2 + H_1 i) \Rightarrow 0 = H_2 X,XH_1 = 0
7,599	6 - 10 - h = h + 4(-1)
42,563	1 + 75 + 15 = 91
-7,192	5/6 \cdot \dfrac23 = \frac{5}{9}
-17,606	75 = 78 + 3 \cdot \left(-1\right)
-23,225	\dfrac{1}{5}\cdot 2 = 1 - 3/5
1,171	\dfrac{1}{y^4} + (-1) = -\frac{1}{y^4} \cdot (y^4 + (-1))
21,460	x^4 + 1 = x^4 - 2\times x^2 + 1 - -2\times x^2 = (x^2 + (-1)) \times (x^2 + (-1)) - x \times x = (x^2 + (-1) + x)\times (x^2 + (-1) - x)
-10,680	-\frac{25}{5 \cdot m^3} = -\frac{1}{m^3} \cdot 5 \cdot 5/5
-20,978	\frac133 \frac{1}{4 - 7t}\left(5 - t\cdot 4\right) = \frac{1}{12 - 21 t}(15 - t\cdot 12)
38,287	10*\left(1 + 2 + 3 + 4\right) + 5 = 105
12,021	1 + \sin{y\cdot 2} = q^2 \Rightarrow q^2 + (-1) = \sin{2\cdot y}
5,599	x\cdot e\cdot b = x\cdot b = b\cdot x = b\cdot e\cdot x
42,653	\sum_{i=1}^n b_i + \sum_{i=1}^n x_i = \sum_{i=1}^n (x_i + b_i)
-30,897	8 \times (-1) + 3 \times c = 8 \times (-1) + c \times 3
3,698	8\pip = p24*\pi
-3,896	\frac1x \cdot x \cdot x = \dfrac{x}{x} \cdot x = x
-1,948	-0π + 3/4π = 3/4*π
6,892	(i + g_1 + g_2) \cdot (i^2 + g_1^2 + g_2^2 - i \cdot g_1 - g_1 \cdot g_2 - i \cdot g_2) = -3 \cdot i \cdot g_2 \cdot g_1 + i^3 + g_1^3 + g_2^3
7,959	-d + 1 - d = -2\cdot d + 1
16,211	(1 + y)^{1 + y} = 1 + (1 + y) \cdot y + ... = 1 + y + y^2 + ...
22,637	1 + \frac{21}{34} = \frac{55}{34}
-26,511	\left(6z\right)^2 = 36z^2
-5,209	0.98\cdot 10^1 = 0.98\cdot 10^{5(-1) + 6}
11,324	a \cdot d + a = a \cdot \left(d + 1\right)
-5,081	48.0 \cdot 10^{11} = 48.0 \cdot 10^{6 + 5}
203	(x^{\tfrac12})^2 = x^{2/2} = x
877	\left(1 + y\right)\cdot (y + 5) = y^2 + 6\cdot y + 5
6,948	\sqrt {1+t}=1+t/2+...
17,943	\sin{x} = \cos{x} \Rightarrow x = \frac14\pi
24,791	(2 \cdot f + 15 \cdot (-1)) \cdot 15 + 225 = 30 \cdot f
-18,928	\frac{14}{15} = \frac{1}{9 \cdot \pi} \cdot A_r \cdot 9 \cdot \pi = A_r
24,533	54912 = \tfrac{524844}{2}
53,258	\frac{\cos{\theta} - \sin{\theta}}{\cos{\theta} + \sin{\theta}} = \tfrac{1}{\cos{\pi/4}\cdot \cos{\theta} + \sin{\frac{1}{4}\cdot \pi}\cdot \sin{\theta}}\cdot (\sin{\frac{\pi}{4}}\cdot \cos{\theta} - \cos{\pi/4}\cdot \sin{\theta}) = \dfrac{\sin(\dfrac{\pi}{4} - \theta)}{\cos\left(\frac{1}{4}\cdot \pi - \theta\right)} = \tan\left(\pi/4 - \theta\right)
-27,692	-7 \sin(z) = \frac{\mathrm{d}}{\mathrm{d}z} \left(7 \cos\left(z\right)\right)
15,631	g'' + \left(x + (-1)\right) \cdot f = 0 \Rightarrow f = -\frac{1}{1 - x} \cdot g''
44,384	0.125 = \dfrac{0.25}{2} \cdot 1
-23,381	\frac{1/7*3}{5} = 3/35
-7,872	\dfrac{-18 - 13\cdot i}{-i - 4} = \dfrac{-18 - 13\cdot i}{-i - 4}\cdot \frac{1}{i - 4}\cdot (-4 + i)
5,054	\dfrac{1}{l_2\cdot Z_2} = 1/(Z_2\cdot l_2)
-26,627	81(-1) + 16y^6 = (4y y * y)^2 - 9^2
59	\frac{1}{(n - k + 1)^2} \cdot (n - n - k + 1) = \frac{\left(-1\right) + k}{(1 + n - k) \cdot (1 + n - k)}
18,406	1 + x^2 = 1 + \frac{\mathrm{d}x}{\mathrm{d}t} \Rightarrow \frac{\mathrm{d}x}{\mathrm{d}t} = x^2
14,078	21 = a + e + c + h + 5\cdot (-1) + 5 + h = a + e + c + 2\cdot h
31,993	\sigma \in E \implies \sigma \in E
19,817	\left(-1\right)^{a\cdot b} = (-1)^{a\cdot b}
16,766	\sqrt{-x}\sqrt{-x} = \sqrt{-x(-x)} = \sqrt{x * x}
1,376	1 = (y^2 + 1)(gy^2 + by + c) = gy^4 + by^3 + \left(g + c\right)y^2 + b*y + c
-7,219	\frac{3}{9} \cdot \frac{4}{10} = \frac{2}{15}
-15,816	-\dfrac{1}{10} \cdot 63 = \frac{9}{10} - 8 \cdot \frac{9}{10}
-1,868	19/12 \cdot \pi - 19/12 \cdot \pi = 0
8,848	k = \left(1 + x_k\right)^k \geq k \cdot x_k
12,662	4^{k + 1} + (-1) = 4\cdot 4^k + (-1) = 4\cdot (4^k + \left(-1\right) + 1) + (-1) = 4\cdot (4^k + (-1)) + 4\cdot 4 + (-1) = 4\cdot \left(4^k + (-1)\right) + 15
4,623	9 - (5 + 4(-1))^2 = 8
-30,541	\frac{\mathrm{d}y}{\mathrm{d}x} = 2x e^{-y} = \frac{2x}{e^y}
12,500	b^{\infty} \cdot b = b^{\infty}
-1,678	\pi \cdot \frac76 = 13/12 \cdot \pi + \dfrac{\pi}{12}
13,485	b \cdot e \coloneqq b \cdot e
3,478	6\cdot (-1) + z^2 + z = (2\cdot (-1) + z)\cdot (z + 3)
875	2 = C_1/(C_2) = \dfrac{1}{C_2\cdot x}\cdot C_1\cdot \frac{C_2}{C_2}\cdot x = \dfrac{1}{C_2\cdot x}\cdot C_1\cdot \|x\|
-3,023	\sqrt{13}\left(3 + 2\right) = \sqrt{13}5
10,039	(1 + k)! = (1 + k)k! \Rightarrow -k! + \left(1 + k\right)! = k!k
4,839	\vartheta^b \cdot \vartheta^a = \vartheta^{a + b}
41,815	2 + 0 (-1) = 2
16,238	6132 = {4 \choose 2}\cdot (2\cdot (-1) + 2^{10})
19,676	4\cdot x + 2\cdot c_1 = 0 \Rightarrow -x\cdot 2 = c_1
32,938	369 = 258\cdot 492 + 147\cdot (-861)
13,877	-\tfrac{1}{1 + x}*(1 + x^2) = \dfrac{x + (-1)}{1 + x} - x
12,380	\pi = 2 \cdot x \Rightarrow \frac12 \cdot \pi = x
6,056	\|z \cdot \omega\| = \|z - z \cdot \omega + z\|
-7,872	\frac{-18 - 13 \cdot i}{-4 - i} = \frac{-4 + i}{-4 + i} \cdot \frac{-18 - i \cdot 13}{-4 - i}
5,015	849 = 8410 + 84(-1) = 840 + 84\left(-1\right) = 800 + 44*(-1) = 756
11,210	x + A \cdot 2 - A = x + A
-5,826	\dfrac{1}{5\cdot (n + 10\cdot \left(-1\right))} = \frac{1}{50\cdot (-1) + n\cdot 5}
4,444	( x, x_1) \cap ( x_2, x_1) = ( x\cdot x_2, x_2\cdot x_1, x\cdot x_1, x_1) = ( x\cdot x_2, x_2\cdot x_1, x_1)
28,477	-\cos\left(y\right) = \cos\left(-y + \pi\right)

7,513

y/1 = \dfrac{1}{3}*(1 - z) = q \Rightarrow y = q,1 - q*3 = z

8,103

4*z^2 - z * z = 4*z^2 - z * z = (4 + (-1))*z * z = 3*z * z

-3,070

\left(2 + 1 + 5\right) \times \sqrt{3} = 8 \times \sqrt{3}

3,298

(((\left((((7^2)^2 \cdot 7)^2)^2 \cdot 7\right)^2)^2 \cdot 7)^2)^2 = 7^{340}

3,903

5 (-1) + 64 + 8 (-1) + 7 \left(-1\right) + 7 (-1) + 7 (-1) = 30

31,778

17*16*15*\dotsm*2 = 17!

21,429

0.064 = (\frac{4}{10}) \times (\frac{4}{10}) \times (\frac{4}{10})

-593

-4 \cdot \pi + 35/6 \cdot \pi = \pi \cdot 11/6

-14,214

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

20,566

165 = \binom{(-1) + 8 + 4}{4 + (-1)}

13,921

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

10,611

\frac{\mathrm{d}}{\mathrm{d}x} \sin(x \cdot x) = 2 \cdot x \cdot \cos(x^2)

29,129

8\cdot 7=56

5,063

0 = -c*a*4 + 4*f^2 \Rightarrow c^3 + a^3 + f^3 = a*c*f*3

9,038

\frac{1}{2\cdot \left(-1\right) + x}\cdot (2\cdot x^3 - 10\cdot x + 4) = x^2\cdot 2 + 4\cdot x + 2\cdot (-1)

19,299

\left((-1) + 2^l\right)*(1 + 2^l) = 2^{l*2} + (-1)

26,208

m/(2*m)! = \frac{m}{2*m*(2*m + (-1))!} = \dfrac{1}{2*(2*m + (-1))!}

11,861

\frac{52!}{5! \cdot 47!} = \dfrac{1}{47!} \cdot 52!/5!

2,402

\pi*2 = 4\pi*2/13 + 9*2\pi/13

-10,616

-\dfrac{20}{10 \cdot x^3} = -\dfrac{4}{2 \cdot x^3} \cdot \frac15 \cdot 5

-20,772

-8/5 \dfrac{1}{l + 3(-1)}(l + 3(-1)) = \frac{1}{l \cdot 5 + 15 \left(-1\right)}(24 - 8l)

-5,567

\dfrac{1}{6 \cdot (-1) + r \cdot 3} = \frac{1}{3 \cdot (r + 2 \cdot (-1))}

-2,338

\frac{1}{14} = -\tfrac{1}{14} + \frac{2}{14}

35,971

\ldots \cdot \ldots = \ldots^2

3,340

0 = X \cdot (H_2 + H_1 i) \Rightarrow 0 = H_2 X,XH_1 = 0

7,599

6 - 10 - h = h + 4(-1)

42,563

1 + 75 + 15 = 91

-7,192

5/6 \cdot \dfrac23 = \frac{5}{9}

-17,606

75 = 78 + 3 \cdot \left(-1\right)

-23,225

\dfrac{1}{5}\cdot 2 = 1 - 3/5

1,171

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

21,460

x^4 + 1 = x^4 - 2\times x^2 + 1 - -2\times x^2 = (x^2 + (-1)) \times (x^2 + (-1)) - x \times x = (x^2 + (-1) + x)\times (x^2 + (-1) - x)

-10,680

-\frac{25}{5 \cdot m^3} = -\frac{1}{m^3} \cdot 5 \cdot 5/5

-20,978

\frac133 \frac{1}{4 - 7t}\left(5 - t\cdot 4\right) = \frac{1}{12 - 21 t}(15 - t\cdot 12)

38,287

10*\left(1 + 2 + 3 + 4\right) + 5 = 105

12,021

1 + \sin{y\cdot 2} = q^2 \Rightarrow q^2 + (-1) = \sin{2\cdot y}

5,599

x\cdot e\cdot b = x\cdot b = b\cdot x = b\cdot e\cdot x

42,653

\sum_{i=1}^n b_i + \sum_{i=1}^n x_i = \sum_{i=1}^n (x_i + b_i)

-30,897

8 \times (-1) + 3 \times c = 8 \times (-1) + c \times 3

3,698

8*\pi*p = p*2*4*\pi

-3,896

\frac1x \cdot x \cdot x = \dfrac{x}{x} \cdot x = x

-1,948

-0*π + 3/4*π = 3/4*π

6,892

(i + g_1 + g_2) \cdot (i^2 + g_1^2 + g_2^2 - i \cdot g_1 - g_1 \cdot g_2 - i \cdot g_2) = -3 \cdot i \cdot g_2 \cdot g_1 + i^3 + g_1^3 + g_2^3

7,959

-d + 1 - d = -2\cdot d + 1

16,211

(1 + y)^{1 + y} = 1 + (1 + y) \cdot y + ... = 1 + y + y^2 + ...

22,637

1 + \frac{21}{34} = \frac{55}{34}

-26,511

\left(6*z\right)^2 = 36*z^2

-5,209

0.98\cdot 10^1 = 0.98\cdot 10^{5(-1) + 6}

11,324

a \cdot d + a = a \cdot \left(d + 1\right)

-5,081

48.0 \cdot 10^{11} = 48.0 \cdot 10^{6 + 5}

203

(x^{\tfrac12})^2 = x^{2/2} = x

877

\left(1 + y\right)\cdot (y + 5) = y^2 + 6\cdot y + 5

6,948

\sqrt {1+t}=1+t/2+...

17,943

\sin{x} = \cos{x} \Rightarrow x = \frac14\pi

24,791

(2 \cdot f + 15 \cdot (-1)) \cdot 15 + 225 = 30 \cdot f

-18,928

\frac{14}{15} = \frac{1}{9 \cdot \pi} \cdot A_r \cdot 9 \cdot \pi = A_r

24,533

54912 = \tfrac{52*48*44}{2}

53,258

\frac{\cos{\theta} - \sin{\theta}}{\cos{\theta} + \sin{\theta}} = \tfrac{1}{\cos{\pi/4}\cdot \cos{\theta} + \sin{\frac{1}{4}\cdot \pi}\cdot \sin{\theta}}\cdot (\sin{\frac{\pi}{4}}\cdot \cos{\theta} - \cos{\pi/4}\cdot \sin{\theta}) = \dfrac{\sin(\dfrac{\pi}{4} - \theta)}{\cos\left(\frac{1}{4}\cdot \pi - \theta\right)} = \tan\left(\pi/4 - \theta\right)

-27,692

-7 \sin(z) = \frac{\mathrm{d}}{\mathrm{d}z} \left(7 \cos\left(z\right)\right)

15,631

g'' + \left(x + (-1)\right) \cdot f = 0 \Rightarrow f = -\frac{1}{1 - x} \cdot g''

44,384

0.125 = \dfrac{0.25}{2} \cdot 1

-23,381

\frac{1/7*3}{5} = 3/35

-7,872

\dfrac{-18 - 13\cdot i}{-i - 4} = \dfrac{-18 - 13\cdot i}{-i - 4}\cdot \frac{1}{i - 4}\cdot (-4 + i)

5,054

\dfrac{1}{l_2\cdot Z_2} = 1/(Z_2\cdot l_2)

-26,627

81*(-1) + 16*y^6 = (4*y * y * y)^2 - 9^2

59

\frac{1}{(n - k + 1)^2} \cdot (n - n - k + 1) = \frac{\left(-1\right) + k}{(1 + n - k) \cdot (1 + n - k)}

18,406

1 + x^2 = 1 + \frac{\mathrm{d}x}{\mathrm{d}t} \Rightarrow \frac{\mathrm{d}x}{\mathrm{d}t} = x^2

14,078

21 = a + e + c + h + 5\cdot (-1) + 5 + h = a + e + c + 2\cdot h

31,993

\sigma \in E \implies \sigma \in E

19,817

\left(-1\right)^{a\cdot b} = (-1)^{a\cdot b}

16,766

\sqrt{-x}*\sqrt{-x} = \sqrt{-x*(-x)} = \sqrt{x * x}

1,376

1 = (y^2 + 1)*(g*y^2 + b*y + c) = g*y^4 + b*y^3 + \left(g + c\right)*y^2 + b*y + c

-7,219

\frac{3}{9} \cdot \frac{4}{10} = \frac{2}{15}

-15,816

-\dfrac{1}{10} \cdot 63 = \frac{9}{10} - 8 \cdot \frac{9}{10}

-1,868

19/12 \cdot \pi - 19/12 \cdot \pi = 0

8,848

k = \left(1 + x_k\right)^k \geq k \cdot x_k

12,662

4^{k + 1} + (-1) = 4\cdot 4^k + (-1) = 4\cdot (4^k + \left(-1\right) + 1) + (-1) = 4\cdot (4^k + (-1)) + 4\cdot 4 + (-1) = 4\cdot \left(4^k + (-1)\right) + 15

4,623

9 - (5 + 4(-1))^2 = 8

-30,541

\frac{\mathrm{d}y}{\mathrm{d}x} = 2x e^{-y} = \frac{2x}{e^y}

12,500

b^{\infty} \cdot b = b^{\infty}

-1,678

\pi \cdot \frac76 = 13/12 \cdot \pi + \dfrac{\pi}{12}

13,485

b \cdot e \coloneqq b \cdot e

3,478

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

875

2 = C_1/(C_2) = \dfrac{1}{C_2\cdot x}\cdot C_1\cdot \frac{C_2}{C_2}\cdot x = \dfrac{1}{C_2\cdot x}\cdot C_1\cdot |x|

-3,023

\sqrt{13}*\left(3 + 2\right) = \sqrt{13}*5

10,039

(1 + k)! = (1 + k)*k! \Rightarrow -k! + \left(1 + k\right)! = k!*k

4,839

\vartheta^b \cdot \vartheta^a = \vartheta^{a + b}

41,815

2 + 0 (-1) = 2

16,238

6132 = {4 \choose 2}\cdot (2\cdot (-1) + 2^{10})

19,676

4\cdot x + 2\cdot c_1 = 0 \Rightarrow -x\cdot 2 = c_1

32,938

369 = 258\cdot 492 + 147\cdot (-861)

13,877

-\tfrac{1}{1 + x}*(1 + x^2) = \dfrac{x + (-1)}{1 + x} - x

12,380

\pi = 2 \cdot x \Rightarrow \frac12 \cdot \pi = x

6,056

|z \cdot \omega| = |z - z \cdot \omega + z|

-7,872

\frac{-18 - 13 \cdot i}{-4 - i} = \frac{-4 + i}{-4 + i} \cdot \frac{-18 - i \cdot 13}{-4 - i}

5,015

84*9 = 84*10 + 84*(-1) = 840 + 84*\left(-1\right) = 800 + 44*(-1) = 756

11,210

x + A \cdot 2 - A = x + A

-5,826

\dfrac{1}{5\cdot (n + 10\cdot \left(-1\right))} = \frac{1}{50\cdot (-1) + n\cdot 5}

4,444

( x, x_1) \cap ( x_2, x_1) = ( x\cdot x_2, x_2\cdot x_1, x\cdot x_1, x_1) = ( x\cdot x_2, x_2\cdot x_1, x_1)

28,477

-\cos\left(y\right) = \cos\left(-y + \pi\right)