id
int64 -30,985
55.9k
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stringlengths 5
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|---|---|
-23,129 |
3/4\cdot (-1/2) = -3/8
|
28,804 |
x^{B + A} = x^A \cdot x^B
|
8,225 |
\dfrac{A_x}{Y_x} = \frac{A_x \cdot (-1)}{Y_x \cdot (-1)}
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29,360 |
-x*\left(-a\right) = a*x
|
37,511 |
23^2*4 = 6^2 + 28^2 + 36^2
|
31,655 |
789768 = 504 \times \left\lfloor{\frac{1}{504} \times 789999}\right\rfloor
|
15,969 |
g^b\cdot g^a = g^{b + a}
|
23,712 |
\frac{1}{10^{∞}} = \frac{1}{10^{2*∞ + 1}}
|
24,320 |
C_t + C_t = 2 \cdot C_t
|
29,804 |
\frac{x^2}{(-1) + x^2} = x^2/2 \cdot \left(\frac{1}{x + (-1)} - \tfrac{1}{1 + x}\right)
|
-23,244 |
4 \cdot \frac16/2 = 1/3
|
12,810 |
0 = ((-\pi\cdot 2 + \pi)/2 + \frac{\pi}{2})/2
|
18,790 |
x^d + z^d < x + z = 1 = (x + z)^d
|
12,228 |
z * z + x^2 + 4*r^2 = z^2 + 2*r^2 + x^2 + r^2*2
|
10,464 |
x \cdot h' \cdot l \cdot h = h \cdot h' \cdot \dfrac{h}{h} \cdot x \cdot l
|
51,273 |
2*4*5*6 = 240
|
5,240 |
1 = \dfrac{1}{4} + 3/4
|
36,995 |
-y \cdot 2 = \frac{d}{dy} (-y^2)
|
-25,492 |
\frac{\mathrm{d}}{\mathrm{d}z} (\sin\left(z\right) \times 5 + z^2) = 5 \times \cos(z) + z \times 2
|
-20,788 |
\frac{1}{n + 1} \cdot (1 + n) \cdot (-7/5) = \frac{1}{5 \cdot n + 5} \cdot (7 \cdot (-1) - 7 \cdot n)
|
-20,507 |
\frac{21 + k*3}{70 + k*10} = \frac{3}{10}*\frac{k + 7}{k + 7}
|
4,519 |
\sin\left(x + 90 \cdot (-1)\right) = -\sin\left(90\right) \cdot \cos(x) + \sin(x) \cdot \cos\left(90\right)
|
5,344 |
\left(-\cos{2\cdot x} + 1\right)/2 = \sin^2{x}
|
-13,356 |
\frac{1}{6 + 5\left(-1\right)}7 = 7/1 = 7/1 = 7
|
6,165 |
\mathbb{E}[X] - C = \mathbb{E}[X - C]
|
3,579 |
0 = 24 + 4\cdot z \Rightarrow -6 = z
|
21,214 |
\sin(A) \sin(B) = \frac{1}{2} (\cos\left(A - B\right) - \cos(A + B))
|
-20,711 |
\frac{1}{18\cdot (-1) - 8\cdot p}\cdot (p\cdot 28 + 63) = \frac{1}{-p\cdot 4 + 9\cdot \left(-1\right)}\cdot (9\cdot \left(-1\right) - 4\cdot p)\cdot (-\dfrac{1}{2}\cdot 7)
|
22,981 |
y + z = 2*y + z - y
|
19,496 |
A^2 - B * B = (A + B)*(A - B)
|
17,228 |
-u_{z*z}*f^2 + u_t = 0 \Rightarrow u*u_{z*z}*f * f = u_t*u
|
4,967 |
(7^2)^y*7 = 7^{1 + y*2}
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38,227 |
500 = 5\cdot 100 = 5\cdot 10\cdot 10 = 5\cdot 5\cdot 2\cdot 5\cdot 2 = 2 \cdot 2\cdot 5 \cdot 5 \cdot 5
|
21,174 |
x^2 + y \cdot y\cdot 4 + 9\cdot z^2 + 12\cdot y\cdot z + 6\cdot z\cdot x + 4\cdot y\cdot x = (x + y\cdot 2 + z\cdot 3) \cdot (x + y\cdot 2 + z\cdot 3)
|
14,976 |
\frac{z^2}{z^2 + \left(-1\right)} = \frac{z \times z}{(z + 1) \times (z + (-1))}
|
-15,136 |
\tfrac{1}{\frac{1}{q^{20}} \cdot n^5} \cdot \frac{1}{n^3} \cdot \frac{1}{q^4} = \frac{1}{q^4 \cdot \frac{1}{q^{20}}} \cdot \dfrac{1}{n^3 \cdot n^5} = \frac{1}{n^8} \cdot q^{-4 - -20} = \frac{1}{n^8} \cdot q^{16}
|
18,121 |
3 \cdot y + 2 - 2 \cdot y + 2 \cdot \left(-1\right) = y
|
-18,252 |
\frac{1}{c^2 - c\cdot 4}\cdot (c^2 - c + 12\cdot (-1)) = \frac{1}{c\cdot (4\cdot (-1) + c)}\cdot (c + 3)\cdot (c + 4\cdot (-1))
|
18,709 |
9 = 0! \times {4 \choose 4} + 4! - 3! \times {4 \choose 1} + {4 \choose 2} \times 2! - 1! \times {4 \choose 3}
|
23,627 |
(-((-1) + j) + x)\cdot (x + 1 - (-1) + j)/2 = \frac{1}{2}\cdot (x - j + 2)\cdot (1 + x - j)
|
30,045 |
\left\{0, 1, 2, 3, 4\right\} = \left\{0, 1, 2, 3, 4\right\} = \Z_{5}
|
27,007 |
\left(k + 1\right) \cdot 4 = k \cdot 4 + 4
|
19,802 |
2\cdot (2 + z) = 4 + 2\cdot z
|
22,767 |
\sin\left(-l^2 + \left(l + 1\right) \times \left(l + 1\right)\right) = \sin(2\times l + 1)
|
28,111 |
2^{-\frac23} = 2^{1/3}/2
|
-27,502 |
2*2*h*h*5 = 20*h^2
|
16,507 |
\left(n\cdot b\cdot a\right)^2 = (a\cdot b\cdot n) \cdot (a\cdot b\cdot n)
|
45,754 |
2^4*2*3*4 = 4!*2^4
|
-6,211 |
\tfrac{1}{t*5 + 15*(-1)} = \tfrac{1}{(3*(-1) + t)*5}
|
13,634 |
(2013 + 2012 \cdot \left(2013 + 2012 \cdot (2013 + 2012 \cdot \dots^{1/2})^{1/2}\right)^{1/2})^{1/2} = 2013
|
7,382 |
1/\left(3*5*4\right) = \frac{1}{60}
|
17,397 |
4(-1) + 2 = -4^{1/2}
|
-9,898 |
88\% = \dfrac{88}{100} = \tfrac{22}{25}
|
21,089 |
\frac{\sqrt{3}}{4} = \frac{g^2}{c^2} \Rightarrow \sqrt{3} = g, 2 = c
|
-26,633 |
36 - z^2 = 6 \cdot 6 - z^2
|
5,704 |
\frac{1}{x^a + x^{-a}} = \frac{1}{x^{2\cdot a} + 1}\cdot x^a \approx \frac{1}{x^a}
|
-1,581 |
\frac16 \cdot \pi + \pi \cdot \frac{1}{12} \cdot 23 = 25/12 \cdot \pi
|
879 |
\frac{2}{3} + 1/3*0 = \dfrac23
|
-9,286 |
3*7 - n*7*7 = -49 n + 21
|
5,639 |
-c = (-c^{\frac{1}{3}})^3
|
2,333 |
C = C*C^0
|
9,749 |
36 \cdot (-1) + y \cdot y = 2 \cdot (-1) + y \cdot y \Rightarrow y = 6,-6
|
-1,833 |
\frac{1}{6}7 \pi = \pi \frac23 + \pi/2
|
14,939 |
\sin(\pi/12) = \dfrac{1}{4}*(\sqrt{6} - \sqrt{2})
|
14,380 |
det\left(z\cdot I - A\cdot B\right)\cdot det\left(A\right) = det\left(z\cdot A - A\cdot B\cdot A\right) = det\left(A\right)\cdot det\left(z\cdot I - B\cdot A\right)
|
-25,869 |
\dfrac{5^{10}}{5 \times 5^2} = 5^7
|
551 |
y^j\cdot g_j + d_j\cdot y^j = (g_j + d_j)\cdot y^j
|
-28,764 |
1/3 - \dfrac{1}{6 + z\cdot 3}\cdot 4 = \dfrac{z + 2\cdot (-1)}{3\cdot z + 6}
|
18,830 |
1/a + (-1) = (1 + \left(1 + \dotsm\right)^{-1})^{-1} = a
|
24,479 |
\dfrac{1}{2520}7920 = \frac{22}{7}
|
18,991 |
2 + z - z \cdot z = (-z + 2)\cdot \left(z + 1\right)
|
-20,054 |
9/9 \cdot \frac{1}{x + \left(-1\right)} \cdot (9 + 2 \cdot x) = \dfrac{1}{9 \cdot (-1) + 9 \cdot x} \cdot (81 + 18 \cdot x)
|
8,075 |
\frac{1}{55} \cdot 89 = 1 + \frac{34}{55}
|
-16,622 |
-6 = -6 \times 5 \times f - 6 = -30 \times f - 6 = -30 \times f + 6 \times (-1)
|
10,799 |
\frac{1}{1 - v/2}*\left((-1)*\dfrac12\right) + \dfrac{1}{1 - v} = -\frac{1}{-1 + v} + \frac{1}{-2 + v}
|
9,011 |
\frac{\text{d}}{\text{d}h} \arcsin(h) = 1/\cos(\arcsin(h))
|
25,182 |
\dfrac{1}{4 \cdot a^2} \cdot (a \cdot x \cdot 2 + h)^2 = \left(x + \dfrac{h}{2 \cdot a}\right)^2
|
-23,451 |
\frac{2}{3}*\frac15 = \frac{1}{15}*2
|
-6,742 |
20/100 + \frac{1}{100} \cdot 3 = \dfrac{1}{100} \cdot 3 + 2/10
|
31,022 |
1 + x \cdot 2 = \left(1 + x\right)^2 - x^2
|
-7,873 |
\frac{1}{-3 - i} \cdot (-i \cdot 16 + 2) = \dfrac{-3 + i}{-3 + i} \cdot \dfrac{1}{-3 - i} \cdot (2 - i \cdot 16)
|
-18,401 |
\frac{(l + 3 \cdot \left(-1\right)) \cdot \left(3 \cdot (-1) + l\right)}{(l + 3 \cdot (-1)) \cdot l} = \frac{1}{-3 \cdot l + l^2} \cdot (l^2 - 6 \cdot l + 9)
|
9,607 |
\frac{x}{K} \times M = |x \times M| = \max{|x|\wedge |M|} = \max{\frac{x}{K}\wedge M/K} = \dfrac{x}{K} \times M/K
|
31,631 |
1/3 = 1/(1/2\cdot 6)
|
-22,067 |
\frac18 \cdot 12 = 3/2
|
8,084 |
\sin(y + \tfrac{1}{2}*\pi) = \cos{y}
|
25,132 |
\lim_{n \to \infty} 2^{\frac1n \cdot \left(n + \left(-1\right)\right)} = 2 = \lim_{n \to \infty} 2^{(n + 1)/n}
|
245 |
y = \frac{1}{2 + x} rightarrow x = \frac{1}{y}*(1 - y*2)
|
-11,515 |
9 + 13*i = -3 + 12 + i*13
|
22,022 |
-2 = b + (-1) \Rightarrow -1 = b
|
-29,351 |
a \times a - g \times g = (g + a)\times (a - g)
|
-22,915 |
40/64 = 8\times 5/(8\times 8)
|
22,808 |
y^{y^{y^{y^{\ldots}}}} = 2 \Rightarrow 2 = y^2
|
24,701 |
2^2 - 2*x + x^2 = (x + (-1))*(x + 2*(-1)) + x + 2 = x^2 - 3*x + 2 + 2 + x = x^2 - 2*x + 4
|
29,283 |
1 + (1 + 2 + 2)/3 = \frac83
|
-2,148 |
\pi\cdot \frac{13}{12} + \dfrac{1}{12}\cdot 23\cdot \pi = 3\cdot \pi
|
40,612 |
5 5 5 + 3 3 3 + 4^3 = 6 6^2
|
-3,200 |
\sqrt{10}*6 = (1 + 5) \sqrt{10}
|
33,413 |
a/b = \dfrac{1 + b^2}{a^2 + 1} \implies a = b
|
17,372 |
\frac{1}{(-y + 1)^2}\times \left(y^{n + 1}\times n - y^n\times (n + 1) + 1\right) = 1 + y\times 2 + 3\times y^2 + ... + y^{n + (-1)}\times n
|
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