id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
18,163 |
\sin{z}*\cos{z} = 1/2*\sin{2*z}
|
51,260 |
576 = 24 \cdot 24
|
-21,114 |
\frac12*2*3/4 = 6/8
|
28,200 |
1 + \dfrac78 = 15/8
|
4,547 |
20 \cdot (3 + x^3) + 77 \cdot (-1) = 20 \cdot x^3 + 17 \cdot (-1)
|
7,325 |
0 < 1 - t + x \implies x \gt (-1) + t
|
15,985 |
2^m - 2^n = ((-1) + 2^{m - n})*2^n
|
-3,455 |
\sqrt{250} + \sqrt{160} - \sqrt{40} = -\sqrt{4 \cdot 10} + \sqrt{25 \cdot 10} + \sqrt{16 \cdot 10}
|
34,599 |
3 (1 + k) = 2 + k*3 + 1
|
-26,546 |
z^2 + 1 + 2 \times z = 1^2 + z \times 2 + z \times z
|
19,967 |
\frac1a*(u*(-1 + a) + 1) = (1 - u*\left(1 - a\right))/a
|
-25,244 |
\dfrac{1}{x^4}=x^{-4}
|
5,038 |
\tfrac{1}{C} \cdot C = \frac{C}{C}
|
25,768 |
1 + 360 + 240 \left(-1\right) + 72 + 12 (-1) = 181
|
21,646 |
\sin(x + \alpha) = \cos(x)\cdot \sin(\alpha) + \sin(x)\cdot \cos(\alpha)
|
6,390 |
(3 + \mathrm{i}*2) * (3 + \mathrm{i}*2) = 12 \mathrm{i} + 5
|
13,117 |
48 = (2 + 1)*(7 + 1)*\left(1 + 1\right)
|
38,557 |
12^2 - 10\cdot 12 + 22 \left(-1\right) = 2
|
-20,323 |
\tfrac14 \cdot 4 \cdot \dfrac{1}{-10} \cdot (2 \cdot y + 2) = (8 \cdot y + 8)/(-40)
|
37,808 |
4! = (8 (-1) + 12)!
|
9,861 |
7^5\cdot 5^3\cdot 3^3\cdot 2^2 = 226894500
|
-935 |
\dfrac32 = \frac32
|
-22,324 |
(z + 9)\cdot (z + 8\cdot \left(-1\right)) = z^2 + z + 72\cdot (-1)
|
16,242 |
(7! - 2\cdot 6!)/7! = \left(7 + 2\cdot (-1)\right)/7 = 5/7
|
5,227 |
\lambda^2 - \lambda*x*2 + x^2 = (-x + \lambda)^2
|
40,014 |
479 = -{4 \choose 4} + {12 \choose 4} - {6 \choose 4}
|
-23,104 |
-3\cdot (-\tfrac{1}{3}\cdot 4) = 4
|
21,765 |
(1 + p^{\tfrac{l}{2}})*(p^{l/2} + (-1)) = p^l + \left(-1\right)
|
-27,102 |
\sum_{n=1}^\infty \frac{1}{n \cdot 5^n} \cdot (-5)^n = \sum_{n=1}^\infty \frac{(-1)^n}{n \cdot 5^n} \cdot 5^n = \sum_{n=1}^\infty \frac1n \cdot (-1)^n
|
-7,346 |
5/18 = \frac{1}{8}\cdot 4\cdot \dfrac59
|
-23,681 |
\tfrac{1}{7}5*\dfrac{3}{8} = 15/56
|
36,406 |
\left. d/dx x^{\left\{2\right\}} \right|_{\substack{ x=z }} = z + z = 2z
|
54,343 |
\frac{\frac{1}{\sin{\frac{1}{2 \cdot n}}}}{\sin^2{\dfrac12} \cdot \frac{1}{\sin{\frac{1}{2 \cdot n}}}} \cdot \sin{1/2} \cdot \sin{\frac{n + 1}{2 \cdot n}} = \sin{\frac{1}{2 \cdot n} \cdot (n + 1)}/\sin{1/2} = (\sin{\dfrac{1}{2}} \cdot \cos{\dfrac{1}{2 \cdot n}} + \cos{\frac{1}{2}} \cdot \sin{\frac{1}{2 \cdot n}})/\sin{\dfrac{1}{2}}
|
5,151 |
(a\cdot q^{n + 2\cdot \left(-1\right)}\cdot a\cdot q^n)^{1/2} = \left(a^2\cdot q^{2\cdot (n + (-1))}\right)^{1/2} = a\cdot q^{n + (-1)}
|
16,993 |
\frac{\sin(x*y^2)}{y^2 + x^2} = \frac{y^2*x}{y^2 + x * x}*\frac{1}{y^2*x}*\sin(y^2*x)
|
24,703 |
z^{12} + \left(-1\right) = \left(1 + z^6\right) (\left(-1\right) + z^6)
|
8,374 |
2 - 2\cdot h \Rightarrow 2\cdot (-h + 1) = 0
|
8,511 |
\sin(x) + \sin(y) + \sin(q) = 0 = \cos(x) + \cos(y) + \cos(q)
|
27,100 |
d = d/3 + \frac{1}{3}*d + \frac{d}{3}
|
-6,749 |
\dfrac{4}{100} + \tfrac{1}{100}*10 = 10^{-1} + \frac{4}{100}
|
-8,803 |
π\cdot 9 + π\cdot 9 + 30\cdot π = π\cdot 48
|
3,954 |
c \cdot (h + a) = a \cdot c + c \cdot h
|
-10,605 |
\frac{16}{16 r + 12} = \frac{1}{4}4*\frac{1}{3 + 4r}4
|
-186 |
\frac{1}{5!*(8 + 5*(-1))!}*8! = \binom{8}{5}
|
30,573 |
-G \geq -C \Rightarrow C \geq G
|
-4,063 |
\dfrac{a^4}{a^2} = \frac{a^4}{a\cdot a}\cdot 1 = a^2
|
11,614 |
(b + c)*e = e*c + e*b
|
27,495 |
1 + 2^2 + 3^2 + \cdots \cdot n^2 = n/6 \cdot (n + 1) \cdot (2 \cdot n + 1)
|
6,700 |
\theta + 2\cdot (-1) + \theta + (-1) = 2\cdot \theta + 3\cdot (-1)
|
-1,244 |
(1/5 (-2))/(1/6 (-1)) = -6/1 (-2/5)
|
28,677 |
(1 + 1/100)\cdot 10000 = 10000 + 1/100\cdot 10000
|
3,046 |
k \cdot 4 = -(k + 2 \cdot (-1)) - 2 + 2 \cdot k + 3 \cdot k
|
-27,066 |
\sum_{n=1}^\infty 1/n = \sum_{n=1}^\infty \frac1n \cdot (3 - 2)^n
|
13,359 |
\left(1/2 + l\right)^2 = \frac14 + l l + l
|
21,879 |
(-1 + \sqrt{-3})/2 = \frac{\sqrt{3} i}{2} - 1/2
|
1,327 |
\sigma_\phi x = x\sigma_\phi
|
21,396 |
6 n + 3 = 3*(n*2 + 1)
|
-18,612 |
5 r + 6 (-1) = 6 (r + 2) = 6 r + 12
|
-657 |
e^{3\frac{7πi}{4}} = \left(e^{πi*7/4}\right)^3
|
-6,104 |
\frac{6 + 11*p}{p^2*10 + p*40 + 320*(-1)} = \tfrac{1}{p^2*10 + p*40 + 320*(-1)}*(10*(-1) + 6*p + 24*(-1) + 5*p + 40)
|
-20,151 |
-4/1 \cdot \frac{(-9) \cdot t}{(-9) \cdot t} = \tfrac{36 \cdot t}{t \cdot (-9)} \cdot 1
|
28,901 |
(5 * 5 + 5^2)*2 = 6^2 + 8^2
|
35,530 |
\left(3 + \left(-1\right)\right)/6 = \frac{1}{3}
|
18,852 |
2 \cdot 1 \cdot (100+100+100-2(10+10+10)+4\cdot 1^2) = 488
|
-22,291 |
\lambda^2 - 11 \cdot \lambda + 18 = (2 \cdot (-1) + \lambda) \cdot (\lambda + 9 \cdot (-1))
|
23,375 |
x^2 + x*3 - 5*x + 15*(-1) = \left(3 + x\right)*\left(x + 5*\left(-1\right)\right)
|
33,425 |
0 = A + B \implies -B^2 + A^2 = 0
|
42,313 |
(6 - 2\cdot 5^{1/2})^{1/2} = (-20^{1/2} + 6)^{1/2}
|
7,957 |
\cos{z} = \frac{\sin{2\cdot z}}{\sin{z}\cdot 2}
|
13,812 |
\sin{x} = \frac{2\cdot \tan{x/2}}{1 + \tan^2{\dfrac{1}{2}\cdot x}}
|
-4,765 |
-\dfrac{3}{y + 2} - \dfrac{1}{y + 4} \cdot 5 = \frac{1}{8 + y^2 + 6 \cdot y} \cdot (-8 \cdot y + 22 \cdot (-1))
|
-20,122 |
\dfrac{y + 6}{-8y} \times \dfrac{10}{10} = \dfrac{10y + 60}{-80y}
|
5,712 |
\left(4 - x*3 = z \implies -3 x = z + 4 (-1)\right) \implies x = \left(4 \left(-1\right) + z\right)/(-3)
|
46,235 |
[2]^2 = [4]
|
25,362 |
\left( d, h, e\right) = ( h, e, d) = ( e, d, h)
|
-20,207 |
-\frac{4}{5}\cdot \frac{1}{-8\cdot n + 4\cdot (-1)}\cdot (4\cdot (-1) - 8\cdot n) = \dfrac{32\cdot n + 16}{20\cdot (-1) - n\cdot 40}
|
3,261 |
\frac{1}{1 + \cos\left(x\right)}\cdot \sin\left(x\right) = \frac{1}{\sin(x)}\cdot \left(-\cos(x) + 1\right)
|
25,468 |
13\cdot \binom{4}{3}\cdot \binom{48}{4} = 10118160
|
18,953 |
29^{32} + \left(-1\right) = (1 + 29^{16}) ((-1) + 29^{16})
|
-10,623 |
\frac{10}{x\cdot 2 + 3}\cdot 12/12 = \frac{120}{x\cdot 24 + 36}
|
16,949 |
1 + 3 + 3^2 + \dots + 3^{k + \left(-1\right)} = \dfrac{1}{2}*(3^k + \left(-1\right))
|
26,584 |
(-1) + w \cdot w^2 = (w + (-1)) \cdot (1 + w^2 + w)
|
2,974 |
(1 + 4) \cdot \left(1 + 2\right) \cdot (6 + 1) = 105
|
13,177 |
3 + (m + (-1))*3 = m*3
|
-20,557 |
\left(2(-1) - x \cdot 18\right)/(\left(-10\right) x) = 2/2 \frac{1}{x \cdot (-5)}((-1) - x \cdot 9)
|
-30,913 |
3 + 4 \cdot m = 4 \cdot m + 3
|
25,200 |
-c^2 + h^2 = (h - c)\cdot (h + c)
|
30,032 |
1 = (z + 1)/(13*z) = \dfrac{1}{13} + 1/(13*z)
|
22,308 |
4^2\cdot (4^2 + \left(-1\right))/3 = 4^2 + 4 \cdot 4^2
|
-6,304 |
\frac{q*5}{(9 (-1) + q) (9 + q)} = \frac{q*5}{q^2 + 81 (-1)}
|
10,635 |
(\sin(\dfrac{z}{2}) + \cos(z/2))^2 = 1 + 2*\sin(z/2)*\cos\left(z/2\right) = 1 + \sin(z)
|
-13,941 |
\frac{35}{1 + 6} = \tfrac{35}{7} = \frac{35}{7} = 5
|
-16,502 |
2 \cdot 44^{\frac{1}{2}} = 2 \cdot (4 \cdot 11)^{1 / 2}
|
36,952 |
{(-1) + 2\cdot m - k \choose m} = {m + m - k + (-1) \choose m}
|
15,599 |
z^5 + x^5 = (z + x)*(x^4 - x^3*z + z^2*x^2 - z^3*x + z^4)
|
-11,528 |
-i \times 5 - 37 = -12 + 25 \times \left(-1\right) - 5 \times i
|
7,971 |
y^3 + 1 + y + y^2 = (1 + y)\cdot (1 + y^2)
|
38,634 |
U = \frac{\pi}{\pi} U
|
-1,885 |
\pi*23/12 = \frac14*7*\pi + \frac{\pi}{6}
|
36,175 |
\left(x + z\right)*\alpha = \alpha*x + \alpha*z
|
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