id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
24,871 |
y + 1 + y + (-1) = y\cdot 2
|
-3,659 |
5/(6\cdot q) = 5\cdot \dfrac{1}{6}/q
|
3,649 |
s_2\cdot x = x\cdot s_2
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3,572 |
z_2 = 0,z_1 \neq 0 rightarrow \frac{z_2 \cdot z_2\cdot z_1}{z_1^2 + z_2^4} = 0
|
7,784 |
\frac{1}{16 \cdot 8} = \dfrac{1}{128}
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-21,600 |
\sin{\pi \cdot \dfrac12 \cdot 5} = 1
|
-2,582 |
2 \cdot \sqrt{11} = (3 \cdot (-1) + 5) \cdot \sqrt{11}
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31,631 |
\frac{1}{1/2 \cdot 6} = 1/3
|
1,637 |
x + \beta + x + x = \beta + 3*x
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-17,989 |
50 + 21\cdot (-1) = 29
|
-1,332 |
5/9*\frac{7}{3} = 7*\frac13/(9*1/5)
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11,815 |
(2^{k + 1} + (-1)) \left(x + 1\right) = \left(2^{k + 1} + (-1)\right) (b + 1) \left(d + 1\right) = 2^k\cdot \left(x + bd\right)
|
14,772 |
-x_1 \cdot 2 + x_2 = 4\Longrightarrow x_1 \cdot 2 = x_2 + 4 \cdot \left(-1\right)
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24,246 |
g^2 g^2 = g^4
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27,679 |
2 = \frac42 = \dfrac{4}{4*1/2}
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8,902 |
-\frac{c \cdot d}{1 - c} + 0 = \frac{d \cdot c}{c + \left(-1\right)}
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20,337 |
(a + a) \cdot 0 = a \cdot 0
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35,414 |
5 - \dfrac{1}{7} = ((-1) + 35)/7
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39,974 |
1/16 = \dfrac{1}{4} \cdot \dfrac14
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-4,444 |
\frac{1}{x^2 - x \cdot 2 + 3 \cdot (-1)} \cdot (-5 \cdot x + 7) = -\dfrac{2}{x + 3 \cdot \left(-1\right)} - \frac{1}{x + 1} \cdot 3
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19,585 |
r^{\frac12\cdot n}\cdot f = f\cdot r^{\frac{1}{2}\cdot ((-1)\cdot n)} = f\cdot r^{\frac{n}{2}}
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-2,338 |
-\frac{1}{14} + \frac{2}{14} = 1/14
|
51 |
2 \cdot (-1) + y^3 - 3 \cdot y = \left(1 + y\right)^2 \cdot (y + 2 \cdot (-1))
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31,506 |
\frac{1}{2*k}*(k + (-1)) = (1 - \tfrac1k)/2 = \frac{1}{2} - 1/(2*k)
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14,011 |
\left(u*(-1)\right)/(v*\left(-1\right)) = \frac{u}{v}
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23,775 |
\frac{456}{\left((-1) + 10 \cdot 10^2\right) \cdot 10^4} + 1.3245 = \frac{456}{10000 \cdot 999} + 1.3245
|
9,890 |
\sin{x}\cdot \tan{x} = \frac{\sin^2{x}}{\cos{x}} = \dfrac{1}{\cos{x}}\cdot \left(1 - \cos^2{x}\right)
|
17,657 |
tz^{(-1) + t} = \frac{\partial}{\partial z} z^t
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32,734 |
-80 = -4\times (-4)\times (-4) + 2\times 2\times 2 + 3\times 2\times (-4)
|
4,790 |
1/X = (1/X)^W = \dfrac{1}{X^W}
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30,093 |
1^2 \cdot 1 + 5^3 + 3 \cdot 3 \cdot 3 = 153
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6,021 |
f^{\frac{1}{h}} = f^{1/h}
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-19,068 |
\frac{7}{20} = A_q/(16 \pi)\cdot 16 \pi = A_q
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12,690 |
h = x\cdot 3 \Rightarrow h^2 = 9\cdot x^2 = 3\cdot 3\cdot x^2
|
19,045 |
z^2 + z*2 + 1 = (1 + z)^2
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-20,285 |
\frac{1}{8(-1) + z} (z + 8(-1))/1 = \frac{z + 8(-1)}{8(-1) + z}
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18,368 |
6 = 6 \cdot (-1) + 23 + 11 \cdot \left(-1\right)
|
14,944 |
\frac{0}{0} = \frac{1}{0}\left(0 + 0(-1)\right) = 0/0 - \frac100
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7,456 |
\left(1 + u\right)^{1/6} = (1 + u)^{1/6}
|
138 |
\cos(d + a) = \cos{a} \cdot \cos{d} - \sin{d} \cdot \sin{a}
|
27,453 |
0.6 = (148 + 59 \left(-1\right))/148 = 0.6
|
14,350 |
|v_{l + 1} - v_l| = 1 > \tfrac{v_l v_{l + 1}}{(l + 1)^2}
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-20,557 |
\frac{2}{2} \cdot \frac{1}{(-5) \cdot x} \cdot ((-1) - 9 \cdot x) = \frac{1}{\left(-10\right) \cdot x} \cdot \left(-x \cdot 18 + 2 \cdot (-1)\right)
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-9,486 |
15 \cdot e + 30 \cdot (-1) = 3 \cdot 5 \cdot e - 2 \cdot 3 \cdot 5
|
27,005 |
z_1 \cdot s - u \cdot z_1 - s \cdot z_2 + u \cdot z_2 = (s - u) \cdot (z_1 - z_2)
|
25,744 |
a^2 + a\cdot b + b \cdot b = \left(a \cdot a + b^2 + (a + b)^2\right)/2
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-23,081 |
-\frac{1}{16} \cdot 27 \cdot \frac34 = -81/64
|
-19,647 |
\dfrac43 = \dfrac23 \cdot 2
|
36,589 |
63016 = 4^8 - \frac{1}{2!*2!*2!*2!}*8!
|
36,230 |
(d + f)^2 = 2\times f\times d + f^2 + d^2
|
18,888 |
(d \cdot g \cdot h \cdot x)^2 = h \cdot x \cdot g \cdot d \cdot g \cdot d \cdot x \cdot h
|
33,949 |
1 - q^2 = (-q + 1)*(1 + q)
|
50,479 |
e^{\pi} = (e^{\frac{\pi}{2}})^2 = (\dfrac{1}{e^{\frac{1}{2} \cdot ((-1) \cdot \pi)}})^2 = (\left(i^i\right)^{-1})^2 = \left(i^{-i}\right)^2 = (-1)^{-i}
|
-22,800 |
\frac{24}{32} = \tfrac{8\cdot 3}{4\cdot 8}
|
22,314 |
1 = \sqrt{2} - (-1) + \sqrt{2}
|
13,262 |
0\cdot {m \choose 0} + {m \choose 1} + 6\cdot {m \choose 2} + {m \choose 3}\cdot 6 = m^3
|
2,579 |
a^3 - b^3 = \left(a - b\right) \cdot \left(b \cdot b + a^2 + b \cdot a\right)
|
1,074 |
2520 = \dfrac{6!}{2! \cdot 2! \cdot 2!} \cdot 4 \cdot 7
|
41,663 |
2/64 = \tfrac{1}{32}
|
21,921 |
\frac{1}{7 + 10\cdot n}\cdot x = d \Rightarrow x = 10\cdot n\cdot d + 7\cdot d
|
23,571 |
2 \cdot \sin{0} + \cos{0} = 1
|
12,921 |
\cos\left(z\times 2\right) = \cos^2(z)\times 2 + (-1)
|
12,771 |
1 - a - b + b\cdot a = (1 - a)\cdot (1 - b)
|
11,057 |
\frac{1}{c * c + x * x - c*x}*\left(x^2 * x + c * c * c\right) = x + c
|
24,595 |
(\frac{1}{3}2)^4 = \frac{16}{81}
|
-2,006 |
\frac{23}{12} \cdot \pi + \pi \cdot \frac{5}{3} = 43/12 \cdot \pi
|
-6,640 |
\frac{1}{(q + 10*(-1))*2}*4 = \frac{4}{q*2 + 20*(-1)}
|
-5,827 |
\frac{5}{s\cdot 4 + 20} = \frac{5}{4\cdot (5 + s)}
|
21,307 |
x^2 + 1 - 2 \cdot x = (-x + 1)^2
|
26,069 |
n + (-1) \geq 1 + n \cdot n + n\Longrightarrow n^2 \leq -2
|
16,053 |
100 = (333 + 33\cdot (-1))/3
|
34,364 |
1 + x \lt 0\Longrightarrow x \lt -1
|
52,328 |
\log_e(\frac32) = \log(\frac{3}{2})
|
33,733 |
6 = 18 + 12\cdot (-1)
|
-4,269 |
\frac{10}{r^2} = \frac{1}{r^2} 10
|
21,121 |
x * x + 5 = x^2 + 4*(-1) + 9 = (x + 2)*(x + 2*(-1)) + 9
|
25,238 |
\tan(\tfrac{1}{4} \pi + x) = \cot(\pi/4 - x)
|
23,821 |
1 + \dfrac12 + \frac{1}{4} + 1/8 + \frac{1}{16} + \ldots = 2
|
4,177 |
1 = \cosh^2{z} - \sinh^2{z}\Longrightarrow \sinh^2{z} = \cosh^2{z} + (-1)
|
-20,268 |
8*r/(r*72) = \frac{\frac{1}{r*8}*8*r}{9}
|
-4,842 |
0.16 \cdot 10^{(-5) \cdot (-1) - 3} = 10 \cdot 10 \cdot 0.16
|
-19,020 |
\dfrac{1}{40}\cdot 29 = \frac{x_t}{25\cdot \pi}\cdot 25\cdot \pi = x_t
|
-20,837 |
\frac{1}{9 + x}*\left(9 + x\right)*(-\dfrac{3}{4}) = \dfrac{-x*3 + 27*(-1)}{4*x + 36}
|
-5,572 |
\tfrac{z \cdot 3}{z^2 + 7z + 6} = \frac{3z}{\left(z + 1\right) (z + 6)}
|
12,262 |
i^2=0 \Rightarrow -1=0
|
20,684 |
y^3 + y^2 + 2\cdot (-1) = (y + (-1))\cdot \left(y^2 + 2\cdot y + 2\right) = (y + (-1))\cdot ((y + 1)^2 + 1)
|
33,342 |
2 = y\Longrightarrow 4 = y^2
|
10,931 |
\sin\left(-\frac{2}{2} π + π*21/2\right) = \sin{\dfrac{19}{2} π}
|
21,783 |
-z^6 + 1 = (1 - z)*(1 + z^2 + z)*(z^2 - z + 1)*(1 + z)
|
11 |
\sin\left(\rho \cdot 2\right) = 2 \cdot \sin(\rho) \cdot \cos(\rho)
|
30,955 |
\sqrt{1 - \sin(2 \cdot y)} = \sqrt{(\sin(y) - \cos(y)) \cdot (\sin(y) - \cos(y))} = \sqrt{(\cos(y) - \sin(y))^2}
|
-4,526 |
-\frac{2}{2 + x} - \frac{4}{(-1) + x} = \frac{1}{2\cdot (-1) + x \cdot x + x}\cdot \left(-x\cdot 6 + 6\cdot (-1)\right)
|
16,071 |
1/4 + 1/4 \cdot 2 = \frac143 \lt 1
|
30,125 |
73 = -8 + 3\cdot 27
|
28,951 |
x = 2 \Rightarrow x \in \left(2,3\right]
|
14,256 |
(t^2 + 1 + 2 \cdot t) \cdot 2 - \left(3 - 9 \cdot t^2\right)/3 = 1 + 4 \cdot t + t \cdot t \cdot 5
|
2,181 |
B_2 \times a = a \times B_2
|
15,745 |
Z\cdot B = I \Rightarrow Z\cdot B = I
|
-2,754 |
(3 + 4) \cdot 5^{1/2} = 7 \cdot 5^{1/2}
|
14,975 |
(h + d)\cdot (h + d) = d\cdot d + 2\cdot d\cdot h + h\cdot h
|
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