id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
24,350 |
\dfrac{x}{z} = x/z
|
13,706 |
\tfrac{-B^4 + 1}{1 - B} = 1 + B + B^2 + B^3
|
-10,285 |
-\frac{25\cdot (-1) + 5\cdot q}{15\cdot (-1) + 15\cdot q} = 5/5\cdot (-\dfrac{5\cdot (-1) + q}{3\cdot \left(-1\right) + q\cdot 3})
|
34,843 |
e^z = \sinh(z) + \cosh\left(z\right)
|
4,318 |
2\times \sin(1) = 1.683\times \dotsm \gt \frac15\times 8
|
26,618 |
256\cdot (8\cdot \left(-1\right) + y) + 53\cdot (-1) = y\cdot 256 + 2101\cdot \left(-1\right)
|
-15,797 |
5/10\cdot 9 - 6\cdot \frac{5}{10} = \frac{1}{10}15
|
18,883 |
0.121 = 10^2\cdot 0.001212\cdot \ldots
|
20,281 |
O\cdot A/\sin(E) = O\cdot E/\sin(A) = A\cdot E/\sin(O)
|
5,419 |
1775 = 50\cdot \frac{1}{2}\cdot (11 + 60)
|
-18,701 |
0.4649 = (-1) \cdot 0.2266 + 0.6915
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-26,136 |
2 \cdot 3 - 2 \cdot 5 = 6 + 10 \left(-1\right) = -4
|
1,434 |
\cos(y + 999\cdot y) = \cos{y\cdot 1000}
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3,943 |
-3 = \frac{1}{0(-1) + 3}\left(-7 + 2(-1)\right)
|
8,652 |
\frac{5}{x^4} - \dfrac{5}{x^2} = \frac{1}{x^4}(5 - 5x^2) \gt \tfrac{15}{4x^4}
|
-1,287 |
8*1/3/\left(\frac12*(-7)\right) = -2/7*8/3
|
-24,848 |
\int \dfrac{1}{z^2}\,\mathrm{d}z = \frac{1}{z\cdot (-2 + 1)} + F = -\frac{1}{z} + F
|
39,004 |
(\pi \cdot (-1))/8 = -\pi/8
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-1,339 |
\frac{\frac14 \cdot (-1)}{\frac{1}{5} \cdot 4} = 5/4 \cdot (-\frac{1}{4})
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21,876 |
58 = 2 \cdot (-1) + 50 + 1 - 2 \cdot (-7) + 1^2 - 2 \cdot 2 \cdot (-1) + 2 \cdot (-7) + 2^2
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-20,365 |
5/5\cdot \dfrac{1}{s\cdot 6 + 1}\cdot (s + (-1)) = \tfrac{1}{30\cdot s + 5}\cdot (5\cdot s + 5\cdot (-1))
|
31,384 |
b \cdot 2 = b \cdot 2
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-21,006 |
\frac{1}{18 \cdot \left(-1\right) - z \cdot 3} \cdot (12 + 2 \cdot z) = \tfrac{6 \cdot (-1) - z}{-z + 6 \cdot (-1)} \cdot (-\frac23)
|
-15,831 |
-56/10 = -\frac{9}{10}\cdot 7 + \frac{7}{10}
|
23,938 |
1 = (-1)\cdot (-1) = (y + 1/y)\cdot (y^2 + \frac{1}{y^2}) = y^3 + y + \frac1y + \frac{1}{y^3} = y^3 + \left(-1\right) + \frac{1}{y^3}
|
25,855 |
1125-54= 1071
|
33,169 |
\frac{0}{2}\cdot (0 + 1) = 0
|
29,070 |
GYX = XG Y
|
17,595 |
1 = (a + f)\cdot \left(c + x\right) = a\cdot c + f\cdot c + a\cdot x + f\cdot x
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-22,219 |
\left(a + 6 \cdot (-1)\right) \cdot (a + 5) = 30 \cdot (-1) + a^2 - a
|
16,538 |
\frac{\eta^t}{2}\cdot A\cdot \eta = \dfrac{A}{2}\cdot \eta^t\cdot \eta
|
3,334 |
2g\omega = -\left(-g + \omega\right)^2 + \omega^2 + g^2
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-9,213 |
-r \times 2 \times 3 \times 3 \times 3 - 2 \times 3 \times 3 = 18 \times (-1) - 54 \times r
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-2,409 |
(4 + (-1) + 3) \cdot \sqrt{6} = 6 \cdot \sqrt{6}
|
28,098 |
\left(x\cdot z\right)^9 = x^9\cdot z^9
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32,314 |
a^a = a^{(-1) + a} a
|
9,082 |
2^m + i = 2\cdot 2^{m + \left(-1\right)} + 2\cdot i/2 = 2\cdot (2^{m + \left(-1\right)} + \frac{i}{2})
|
23,598 |
\tfrac{1}{36} \cdot \frac{1225}{36} \cdot 35/36 = (\frac{35}{36})^3
|
-5,276 |
1.68\cdot 10 = 1.68\cdot 10/100 = \dfrac{1.68}{10}
|
5,579 |
(2\cdot l + 1)\cdot 2 = 4\cdot l + 2
|
-22,253 |
24 \cdot \left(-1\right) + t^2 + t \cdot 5 = (8 + t) \cdot (t + 3 \cdot (-1))
|
34,714 |
4 = 2^2 + 0 \cdot 0 + 0^3
|
-1,253 |
54/56 = \frac{54\cdot 1/2}{56\cdot \tfrac{1}{2}} = 27/28
|
4,854 |
\dfrac{n!}{2^n} \cdot \dfrac{1}{(1 + n)!} \cdot 2^{1 + n} = \frac{2}{n + 1}
|
20,466 |
1/(1/(1/\left(\dfrac{1}{25}\right))) = 5^{-2\left(-(-1) (-1)\right)} = 5^2 = 25
|
36,481 |
\tfrac{1}{\sqrt{z + (-1)}}(z + (-1)) = \frac{1}{\sqrt{z + (-1)}}\sqrt{z + (-1)} * \sqrt{z + (-1)} = \sqrt{z + (-1)}
|
-2,002 |
\frac{1}{4} \cdot 5 \cdot \pi = \frac13 \cdot \pi + \frac{11}{12} \cdot \pi
|
19,956 |
\cosh{z} = (e^z + e^{-z})/2 \times \sinh{z} = \frac{1}{2} \times \left(e^z - e^{-z}\right)
|
45,346 |
(\sum_{l=0}^{k + (-1)} e^{\omega^l}\cdot \omega^{-m\cdot l})/k = \frac{1}{k}\cdot \sum_{l=0}^{k + (-1)} (\sum_{n=0}^\infty (\omega^l)^n/n!)\cdot \omega^{-m\cdot l} = \sum_{n=0}^\infty \dfrac{1/k}{n!}\cdot \sum_{l=0}^{k + (-1)} \omega^{(n - m)\cdot l}
|
36,141 |
x = x\cdot x^c \Rightarrow x^c \leq x
|
-1,505 |
\frac{\frac18 \cdot 7}{\frac{1}{7} \cdot 8} = \frac{1}{8} \cdot 7 \cdot \frac{7}{8}
|
10,997 |
1/k + \frac{1}{\sqrt{k}} = (\sqrt{k} + 1)/k
|
12,708 |
\mathbb{E}\left(\dfrac{1}{X}\right) = \mathbb{E}\left(X\right)^{-1}
|
12,273 |
-\frac{1}{(1 - \frac{x}{2})*2} = \dfrac{1}{2*(-1) + x}
|
10,379 |
\left(0 = 4 + x^2 - y^2 + x\cdot 4 \implies (x + 2) \cdot (x + 2) - y^2 = 0\right) \implies 0 = (x + 2 + y)\cdot (x + 2 - y)
|
13,518 |
z^k\cdot z^{\alpha} = z^{\alpha + k}
|
-25,223 |
lz^{(-1) + l} = \frac{\mathrm{d}}{\mathrm{d}z} z^l
|
-9,881 |
\phantom{ -\dfrac{7}{10} \times \dfrac{1}{4} } = \dfrac{-7 \times 1 }{10 \times 4 } = -\dfrac{7}{40}
|
14,452 |
NgK = KN g
|
21,473 |
\frac{y}{(-1) + y} = \frac{1}{(-1) + y} \cdot (1 + y + (-1))
|
54,076 |
18851684897584 = {49 \choose 19}
|
21,314 |
(x + a)^2 + (h + y)^2 + 2 + (x - a)^2 + (y - h)^2 = (x^2 + y^2 + 1 + a^2 + h^2)*2
|
7,225 |
\sin(\dfrac{2 \pi}{5}) = -\sin(8 \pi/5)
|
-23,331 |
\dfrac{2}{21} = \frac{\frac{2}{7}}{3} \cdot 1
|
1,287 |
1 = \dfrac{1}{-61^3 + 1049 * 1049^2}\left(1823^3 - 1699^3\right)
|
31,319 |
13/18 = 1 - \frac{1}{9} - 1/6
|
-16,599 |
4 \sqrt{9} \sqrt{11} = 4*3 \sqrt{11} = 12 \sqrt{11}
|
-4,294 |
\frac{1}{x \cdot 9} = \frac{1}{x \cdot 9}
|
24,582 |
\frac{1}{1 + 2} = 1 + 2*(-1) + 4 + 8*\left(-1\right) - \ldots = 1/3
|
10,661 |
(i + 1)!\cdot \left(i + 1\right) = (1 + i)!\cdot \left(i + 2 + (-1)\right)
|
30,478 |
\left(x = \frac{1}{2}\cdot (-x + 1)\cdot \sqrt{2} \Rightarrow x\cdot \sqrt{2} = -x + 1\right) \Rightarrow \sqrt{2} + (-1) = x
|
-7,161 |
1/11 = \dfrac{2}{10} \cdot \frac{5}{11}
|
12,659 |
|x - z| = z - x = \frac{1}{x + z} \cdot (z \cdot z - x \cdot x) < \frac{z^2 - x^2}{2 \cdot x}
|
-1,092 |
((-8) \frac{1}{3})/(5*\frac{1}{8}) = -8/3*\tfrac{8}{5}
|
7,970 |
z^3 - 1 + 3z - z^2*3 = (z + (-1))^3
|
29,441 |
2/3 = \frac{1}{3} + 1/3
|
20,941 |
p \times p - 2\times p + 2 = 1 + (\left(-1\right) + p)^2
|
20,040 |
Z^3 \cdot (-p + 1) - Z \cdot Z + p = ((-1) + Z) \cdot (-p + Z \cdot Z \cdot (1 - p) - Z \cdot p)
|
27,719 |
\cos(c + b) = \cos\left(c\right)\cdot \cos(b) - \sin(b)\cdot \sin\left(c\right)
|
19,117 |
g \cdot b + b \cdot r + (g + b) \cdot (b + r) = g \cdot b + b \cdot r + g \cdot b + g \cdot r + b + b \cdot r = g \cdot r + b
|
10,336 |
\int \sec^2{x}\,\text{d}x = \tan{2\frac{x}{2}} + C = \tan{x} + C
|
7,296 |
(x^2 + 1)\cdot (x^4 - x \cdot x + 1) = x^6 + 1
|
18,296 |
\frac1t \cdot s \cdot \binom{s + (-1)}{(-1) + t} = \binom{s}{t}
|
39,542 |
1 + y^2 + (-1) = y^2
|
10,021 |
\left(b + a\right)\times (a - b) = -b \times b + a^2
|
14,108 |
r/R = r/R
|
-18,139 |
50 - 29 = 21
|
16,393 |
-\dfrac{d}{z + d} + 1 = \frac{1}{d + z}*z
|
6,333 |
x \cdot d_1 \cdot d_2 = (x + d_1 + 2 \cdot x \cdot d_1) \cdot d_2 = x + d_1 + 2 \cdot x \cdot d_1 + d_2 + 2 \cdot x \cdot d_2 + 2 \cdot d_1 \cdot d_2 + 4 \cdot x \cdot d_1 \cdot d_2
|
2,015 |
\binom{l}{2}\cdot 2^2 = \binom{l}{2}\cdot 2^2 = \binom{l}{2}\cdot 1^{l + 2\cdot (-1)}\cdot 2^2
|
13,803 |
2/9 = (1 - \frac{1}{3})/3
|
11,847 |
|r| < 1 \Rightarrow \dfrac{1}{-r + 1} = 1 + r + r * r + r^3 + \dotsm
|
221 |
-\frac{1}{12} = 1 + 2 + 3\cdot \dots
|
-2,533 |
-\sqrt{7} \cdot 2 + \sqrt{7} \cdot 3 = \sqrt{7} \cdot \sqrt{9} - \sqrt{7} \cdot \sqrt{4}
|
-11,292 |
(x + 5(-1))^2 + b = (x + 5(-1)) \left(x + 5(-1)\right) + b = x^2 - 10 x + 25 + b
|
14,972 |
f*g*h = h*f*g
|
-28,858 |
209\cdot 9/9 = \dfrac{1}{9}\cdot (109 + 100)\cdot (100\cdot (-1) + 109)
|
21,994 |
\frac{\sin{Q}}{1 + \sin{Q}} = \frac{1}{\sin{Q} + 1} \cdot (1 + \sin{Q} + (-1)) = 1 - \frac{1}{1 + \sin{Q}}
|
-20,057 |
(-8\cdot c + 16\cdot (-1))/\left(24\cdot c\right) = \left(2\cdot \left(-1\right) - c\right)/(c\cdot 3)\cdot 8/8
|
-28,990 |
\frac{\pi}{5} = \frac{1}{20} \cdot \pi \cdot 4
|
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