id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
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
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-4,807 |
10^{4 + 1}*28.5 = 10^5*28.5
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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})
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3,529 |
\dfrac{1}{2}(3 \pm \sqrt{-3 + 4i}) = \dfrac12(3 \pm \sqrt{9 - 4*\left(3 - i\right)})
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161 |
|f + \left(-1\right)| + |b + (-1)| = f + (-1) - b + (-1) = f - b
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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}
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23,847 |
a^{h_2^{h_1}} = a^{h_2^{h_1}}
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-20,387 |
\dfrac37 \cdot \frac{5 + 10 \cdot q}{5 + 10 \cdot q} = \frac{30 \cdot q + 15}{35 + q \cdot 70}
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22,305 |
x\times 6 = 0 \Rightarrow x = 0
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-24,826 |
\left(-1\right) + 575 = 574
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-5,398 |
4.13\cdot 10 = 4.13\cdot 10\cdot 10^1 = 4.13\cdot 10 \cdot 10
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10,151 |
-\sin^2(\theta)*2 + 1 = \cos(2*\theta)
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22,348 |
4176 = 6642 + 2466*(-1)
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8,488 |
\cos^2(\theta) = \frac{1}{2} + \frac{\cos\left(\theta*2\right)}{2}
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30,189 |
3/4 - \frac{15}{4*\left(5 + \frac{4}{3}\right)} = \frac{1}{19}*3
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29,280 |
\frac{2\cdot \pi}{5}\cdot 1.25 = \dfrac{\pi}{5}\cdot 2\cdot \frac{5}{4} = \pi/2
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7,688 |
\dfrac{1}{z} = 1/z*\overline{z}/\overline{z} = \dfrac{\overline{z}}{|z|^2}
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-4,460 |
\frac{-z\cdot 2 + 1}{20 (-1) + z^2 - z} = -\tfrac{1}{z + 4} - \frac{1}{5(-1) + z}
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32,564 |
h = -\frac{\partial}{\partial s} \left(2*h*x\right)\Longrightarrow -h*2 - x*h*2 = h
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554 |
(x - y) (y - z) + y^2 = yx - zx + yz
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19,783 |
\sin\left(f + \pi\right) = \sin{f} \cdot \sin{\pi} + \cos{f} \cdot \sin{\pi} = -\sin{f}
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8,219 |
yH = yH
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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
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912 |
3*(i*2 + 1) = ((-6)*(2*i + 1))/(-2)
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17,135 |
12 = 25 + 13\cdot (-1)
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16,811 |
p\cdot r'\cdot x = r'\cdot p\cdot x
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-2,516 |
6 \cdot \sqrt{5} = (4 + 5 + 3 \cdot (-1)) \cdot \sqrt{5}
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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)
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549 |
2 = \left(\sqrt{2}\right)^2 = (2^{\dfrac{1}{3}})^3 = \dotsm
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-1,780 |
\pi \cdot \dfrac{1}{4} \cdot 7 + \pi \cdot 11/6 = \pi \cdot 43/12
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-12,223 |
\dfrac25 = \frac{s}{6\times \pi}\times 6\times \pi = s
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23,122 |
gx = -x*(-g)
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33,329 |
\cos{π/4} = \sin{π/4}
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33,048 |
1000 + (-1) + 193 \cdot \left(-1\right) + 298 \cdot (-1) = 508
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33,249 |
30 = \tfrac{5!}{2! \cdot 2!}
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30,751 |
(0 - 1) \cdot a = -a + a \cdot 0
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-6,670 |
\frac{5}{2*x + 10*(-1)} = \dfrac{1}{2*(x + 5*(-1))}*5
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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}
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-1,044 |
\dfrac{1}{4} = \frac{1}{4}
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20,634 |
0 = z^2 + y^2 - 3 \cdot y\Longrightarrow (-3/2 + y)^2 + z^2 = (3/2)^2
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-7,275 |
\frac{1}{42} \cdot 5 = \frac{1}{9} \cdot 5 \cdot \frac48 \cdot 3/7
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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
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26,054 |
\frac{1}{6\cdot 2} = \dfrac{1}{12}
|
4,173 |
8 \cdot 8 - 7^2 = 4^2 - 1^2
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3,772 |
-z*(-1) + x = z + x
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20,649 |
m*9 + 9*(-1) = 3*\left(m + (-1)\right)*3
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-23,041 |
\frac{8}{9} = \frac13\cdot 4\cdot 2/3
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16,370 |
\left\lfloor{41 \cdot 13/57}\right\rfloor = 9
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-11,556 |
2\cdot i + 3 + 0\cdot (-1) = i\cdot 2 + 3
|
4,581 |
6^2 + 12^2 + 12 * 12 = 4*9 * 9
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-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}
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-4,815 |
10^{4 + 0}*29.2 = 10^4*29.2
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16,272 |
(2*n + 2)! = (2 + n*2)*\left(2*n + 1\right)*(2*n)!
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-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))
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22,190 |
\dfrac{1}{4\cdot (-1) + n^2}\cdot 4 = \frac{1}{2\cdot (-1) + n} - \frac{1}{2 + n}
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-10,573 |
120 = 15\cdot x + 30 + 30\cdot \left(-1\right) = 15\cdot x = 15\cdot x
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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
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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}
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-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
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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
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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}
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-1,450 |
-\frac{1}{45} 5 = \frac{(-5) \cdot 1/5}{45 \cdot 1/5} = -\frac{1}{9}
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-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
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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
|
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