id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-4,977 |
0.9*10^0 = 0.9*10^{\left(-3\right)*(-1) - 3}
|
23,385 |
A^3 = A \cdot A\cdot A = 2\cdot A \cdot A - I\cdot A = 2\cdot (2\cdot A - I) - A = 3\cdot A - 2\cdot I
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-2,174 |
5/14 - 3/14 = \frac{2}{14}
|
22,931 |
1/2 + (y + 5/2)*(1 + 2*y) = 2*y^2 + 6*y + 3
|
4,774 |
6 \cdot l + 3 = (2 \cdot l + 1) \cdot 3
|
-3,212 |
\sqrt{2}*\left(5 + 3 + 4\right) = 12*\sqrt{2}
|
23,303 |
z \cdot x^3 = f + \int x \cdot x^3\,\mathrm{d}x \Rightarrow f + \frac{x^5}{5} = x^2 \cdot x \cdot z
|
-29,369 |
(5 \cdot y + 1) \cdot (5 \cdot y + \left(-1\right)) = (5 \cdot y)^2 - 1 \cdot 1 = 25 \cdot y^2 + \left(-1\right)
|
20,075 |
z + (-1) = 1 + z + 2\cdot (-1)
|
-9,881 |
\left((-7) \cdot 10^{-1}\right)/4 = \frac{(-7)}{10 \cdot 4} = -\dfrac{1}{40}7
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5,837 |
x^j*j! = \frac{1}{\frac{1}{j!}*x^{-j}}
|
4,470 |
29 = 6\times 7 + 6\times (-1) + 7\times (-1)
|
4,841 |
{k + p + (-1) \choose k} = {k + p + \left(-1\right) \choose (-1) + p}
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26,464 |
{4 \cdot 2 \choose 3} = \frac{1}{(8 + 3 \cdot (-1))! \cdot 3!} \cdot 8! = \frac{6}{3 \cdot 2} \cdot 8 \cdot 7 = 56
|
9,067 |
\left(-1\right) + 2 \cdot l = l^2 - (l + (-1))^2
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48,092 |
14826240 = 15 \times 988416
|
-10,295 |
\frac{5 x + 5}{x*20 + 40 (-1)} = \frac{1}{8 \left(-1\right) + x*4} (1 + x)*5/5
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-30,288 |
(0 + 80)/2 = \frac12 80 = 40
|
-4,942 |
\frac{1}{10^6} \cdot 37.8 = \frac{1}{10^6} \cdot 37.8
|
29,058 |
\sin^2(x) = \sin(x)\cdot \sin(x)
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31,136 |
(x + 5*(-1))^2 - \sqrt{5} * \sqrt{5} = 5*(-1) + x * x - 10*x + 25
|
2,933 |
(X + 3) \cdot (X + 3) \cdot (X + 3) = X^3 + 9\cdot X \cdot X + 27\cdot X + 27 = (X \cdot X + 5\cdot X + 7)\cdot (X + 4) + (-1)
|
12,796 |
\tfrac1n \cdot (n + (-1)) \cdot \pi = (n + (-1)) \cdot \pi/n
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-2,217 |
\frac{9}{19} - \frac{3}{19} = \frac{1}{19}\cdot 6
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-23,302 |
8/21 = 6/7\cdot \frac{4}{9}
|
10,987 |
-(\frac12)^2 + \frac{1}{10}\cdot 3 = \frac{1}{20}
|
21,127 |
(2 + z) (z + 3) = z z + z*6 + 6 - z
|
4,767 |
n + 4 \cdot (-1) = 1 \Rightarrow n = 5
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3,006 |
-y^3 + z^3 = (z^2 + zy + y * y) (-y + z)
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49,101 |
{13 \choose 2} = {2 + 11 \choose 2}
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17,046 |
\cos(2 y) = 1 - 2 \sin^2(y)
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26,698 |
\frac22 \cdot I \cdot 2^{1 / 2} = I \cdot 2^{1 / 2} \gt I
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50,890 |
\infty + \infty = 0
|
20,373 |
\frac{1}{(-y + 1)^5} = (1 + y + y y + y^3 + ...)^5
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-24,039 |
1 + \frac{6}{6} = 1 + 1 = 2
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-7,652 |
\tfrac{1}{-2i - 1}(5i + 5) = \frac{1}{-1 - i \cdot 2}\left(5 + i \cdot 5\right) \frac{1}{i \cdot 2 - 1}(-1 + 2i)
|
15,964 |
1/50 = \frac{1}{500} \cdot 10
|
32,637 |
0 = a^7 + 1 = (a + 1) (a^6 - a^5 + a^4 - a * a * a + a * a - a + 1)
|
-4,366 |
7/6 \cdot b = 7 \cdot b/6
|
17,559 |
2^{m + 4} = 2^{m + 3} + 2^{2 + m} + 2^{m + 1} + 2^m + 2^m
|
4,402 |
( \rho(x), y) = \left( \rho(x), \rho(\rho^{-1}(y))\right) = \left( x, \rho^{-1}(y)\right)
|
46,957 |
{11 \choose 4} {4 \choose 2} = \frac{1}{7! \cdot 4!}11! \frac{1}{2! \cdot 2!}4! = \frac{11!}{7! \cdot 2! \cdot 2!}
|
-2,544 |
\sqrt{10} + \sqrt{10}*4 = \sqrt{10} + \sqrt{10}*\sqrt{16}
|
-7,594 |
\frac{i*20 - 25}{5 - i*4}*\frac{5 + 4*i}{5 + 4*i} = \frac{20*i - 25}{5 - 4*i}
|
15,893 |
2 + 2*(n + 2*(-1)) = 2*\left((-1) + n\right)
|
29,915 |
\sin{x\cdot 3} = \sin(8\cdot x - 5\cdot x)
|
2,649 |
\left(Y \cdot Y^q\right) \cdot \left(Y \cdot Y^q\right) \cdot \left(Y \cdot Y^q\right) = Y \cdot Y^q \cdot Y \cdot Y^q \cdot Y \cdot Y^q = Y^q \cdot Y \cdot Y^q \cdot Y \cdot Y^q \cdot Y = \left(Y^q \cdot Y\right)^3
|
28,793 |
p - r - p = 2\cdot p - r
|
8,347 |
\dfrac{1}{z - b_m} \cdot (z - d_m) + \left(-1\right) = \frac{1}{z - b_m} \cdot \left(z - d_m - z + b_m\right) = \frac{1}{z - b_m} \cdot (b_m - d_m)
|
38,318 |
(1-\frac{1}{\epsilon})^{2} - 4 = (1 - \frac{1}{\epsilon} - 2)(1 - \frac{1}{\epsilon} + 2) = -(1 + \frac{1}{\epsilon})(1-\frac{1}{\epsilon}) = \frac{1}{\epsilon^{2}} - 1
|
-23,821 |
\tfrac{1}{2 + 8}20 = 20/10 = \frac{1}{10}20 = 2
|
43,365 |
10 10 + 5^2 = 100 + 25 = 125 = 121 + 4 = 11 11 + 2 2
|
19,751 |
\frac{\pi}{2^{1/2}} = \frac{\pi}{2} \cdot 2^{1/2}
|
10,295 |
4 + 27*2 + x*81 = x*81 + 58
|
13,276 |
e^{\ln(c^{\epsilon})} = c^{\epsilon}
|
7,151 |
(1 + y + \dots + y^5)^8 = \left(\frac{1}{1 - y}*(1 - y^6)\right)^8 = \dfrac{(1 - y^6)^8}{(1 - y)^8}
|
43,209 |
12/50 \cdot 13/51 \cdot \tfrac{39}{52} + \dfrac{39}{50} \cdot 12/51 \cdot \frac{13}{52} + 39/51 \cdot \frac{1}{52} \cdot 13 \cdot 12/50 = \frac{1}{{52 \choose 3}} \cdot {39 \choose 1} \cdot {13 \choose 2}
|
20,034 |
a \cdot 2 - 2 \cdot b = (a - b) \cdot 2
|
-20,572 |
-7/4 \cdot \frac{1}{3 \cdot (-1) + k} \cdot (3 \cdot (-1) + k) = \frac{1}{12 \cdot (-1) + 4 \cdot k} \cdot (21 - 7 \cdot k)
|
25,381 |
\frac{1}{A \cdot D} = \frac{1}{D \cdot A}
|
9,180 |
\sin^4(z) + \cos^4\left(z\right) = (\sin^2(z) + \cos^2(z))^2 - 2\sin^2(z) \cos^2(z) = 1 - \frac12\sin^{22}(z)
|
2,349 |
x^2 + \left(-1\right) = (x + (-1))\cdot (x + 1) = \sqrt{x^2 + (-1)}\cdot \sqrt{x^2 + (-1)}
|
-4,770 |
\frac{3}{x + (-1)} + \frac{1}{x + 4\cdot (-1)}\cdot 3 = \frac{x\cdot 6 + 15\cdot \left(-1\right)}{x^2 - x\cdot 5 + 4}
|
-19,468 |
5*1/2/(1/7*5) = \frac52*\dfrac{1}{5}*7
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38,576 |
21 = 26 + 5*(-1)
|
-619 |
(e^{\pi \cdot i \cdot 5/3})^5 = e^{5 \cdot \frac{1}{3} \cdot i \cdot \pi \cdot 5}
|
30,726 |
z^2 \cdot 2 + z \cdot 3 + 1 = \left(1 + z \cdot 2\right) \cdot (z + 1)
|
7,973 |
(m + 1)^2 - m^2 = m\cdot 2 + 1
|
-19,167 |
11/30 = \frac{A_s}{9 \cdot π} \cdot 9 \cdot π = A_s
|
4,571 |
(A' \cap R) \cup (R \cap (A' \cap x)) = A' \cap ((A' \cap R) \cup (R \cap x))
|
-16,572 |
117^{1 / 2} \cdot 2 = 2 \cdot (9 \cdot 13)^{\frac{1}{2}}
|
24,763 |
-\sin{d}*\sin{b} + \cos{b}*\cos{d} = \cos(d + b)
|
11,461 |
\frac{1}{20} \cdot (1 + 2 + 3 + \dots + 20) = 21/2 = 10.5
|
1,652 |
0 \cdot (-1) + 3 = 1 + 2 + \left(-1\right) \Rightarrow 2 = 3
|
21,127 |
(z + 2)*\left(z + 3\right) = z^2 + 6*z + 6 - z
|
19,453 |
-i\cdot \sin{\theta} + \cos{\theta} = \cos{-\theta} + i\cdot \sin{-\theta}
|
19,964 |
z^2 + z^2 + 1 = z \cdot z + z + z + z \cdot z = z^2 + z + z + z \cdot z + 1
|
6,901 |
\sin^2(y) = \frac{1}{-4} \times (e^{i \times y} - e^{-i \times y}) \times (e^{i \times y} - e^{-i \times y}) = -(e^{2 \times i \times y} + 2 \times (-1) + e^{-2 \times i \times y})/4
|
-4,324 |
\dfrac{x^4}{10\cdot x^2} = \frac{x^4\cdot \frac{1}{x^2}}{10}\cdot 1
|
-9,319 |
-2 \cdot 2 \cdot 2 \cdot 5 a + 2 \cdot 2 \cdot 2 \cdot 5 = 40 - 40 a
|
-24,658 |
1\cdot 2/(9\cdot 2) = 2/18
|
8,827 |
1 - 27/216 - 111/216 = \dfrac{1}{216} 78 \approx 0.3611
|
4,312 |
\sin(x + d) = \cos\left(x\right)\cdot \sin(d) + \sin(x)\cdot \cos\left(d\right)
|
1,845 |
-D\times 4 = 1 \Rightarrow D = -1/4
|
-18,111 |
79 + 9\cdot (-1) = 70
|
22,623 |
0 = y^2 + 2 \cdot i \cdot y + 2 \cdot (-1) = \left(y + i\right)^2 + (-1) = (y + (-1) + i) \cdot (y + 1 + i)
|
4,870 |
-\frac{1}{4} \cdot r + \dfrac{n}{2} = \frac12 \cdot (n - \frac{r}{2})
|
13,717 |
-z^d + z^f = -(-z^f + 1) + 1 - z^d
|
-2,575 |
5^{1 / 2} = 5^{\frac{1}{2}}*(3 + 2 (-1))
|
-6,634 |
\frac{1}{36 (-1) + q^2 - q \cdot 5}4 = \dfrac{4}{(q + 9\left(-1\right)) \left(q + 4\right)}
|
-20,871 |
\dfrac{1}{7 \cdot (-1) + 7 \cdot z} \cdot (2 \cdot z + 2 \cdot (-1)) = \frac{2}{7} \cdot \frac{z + \left(-1\right)}{(-1) + z}
|
-18,416 |
\frac{r\cdot (r + (-1))}{(r + (-1))\cdot (2 + r)} = \frac{-r + r^2}{2\cdot (-1) + r^2 + r}
|
28,869 |
\sum_{m=1}^\infty \sin{m} = \sin{1} + \sin{2} + \sin{3} + \ldots + \sin{m}
|
-18,610 |
46 = \frac12 \times 92
|
1,797 |
(1 + h)^k \geq k \cdot h + 1 \Rightarrow (1 + h) \cdot (1 + k \cdot h) \leq (1 + h)^k \cdot (1 + h) = (1 + h)^{k + 1}
|
6,143 |
-d^3 + a^3 = \left(-d + a\right)\cdot (d \cdot d + a^2 + a\cdot d)
|
32,625 |
\frac{1}{2}\cdot (1 + (2\cdot 178 + 1)^2)\cdot π = 63725\cdot π \approx 200197.991850009574121
|
21,736 |
\gamma_2 \cdot n + \gamma_1 \cdot q \cdot n = \gamma \implies \frac1n \cdot \gamma = \gamma_2 + q \cdot \gamma_1
|
-19,661 |
4 \cdot 7/\left(8\right) = \frac{28}{8}
|
7,034 |
\sin\left(2 \pi\right) = \sin(10 \pi)
|
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