id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
48,420 |
5\cdot 1/6/6 + \frac{1/6}{6}\cdot 4 + \dfrac{\frac{1}{6}\cdot 3}{6} + \frac{\frac{1}{6}}{6}\cdot 2 + \dfrac{1}{6\cdot 6} + 0\cdot \frac{1}{6}/6 = \frac{1}{6}\cdot \left(\frac06 + \frac{5}{6} + 4/6 + 3/6 + 2/6 + \frac{1}{6}\right)
|
2,267 |
\cos{a\cdot 2} = -\sin^2{a} + \cos^2{a}
|
417 |
|c|\cdot |a| = |a\cdot c|
|
-4,322 |
\frac{y}{y^3} = \dfrac{1}{yy y}y = \frac{1}{y^2}
|
2,024 |
1 + m * m * m + m^2 + 2m = m^3 + (1 + m)^2
|
50,470 |
\cot{z} - \cot{y} = \cos{z}/\sin{z} - \cos{y}/\sin{y} = \dfrac{1}{\sin{z} \cdot \sin{y}} \cdot (\cos{z} \cdot \sin{y} - \sin{z} \cdot \cos{y}) = \frac{\sin(y - z)}{\sin{z} \cdot \sin{y}}
|
29,813 |
((k + 1)\cdot 5 + \left(k + 1\right)^3)/3 = (k^3 + k^2\cdot 3 + k\cdot 8 + 6)/3
|
7,086 |
\left(3 \cdot (-1) + x\right) \cdot (x + 1) = 3 \cdot (-1) + x^2 - 2 \cdot x
|
25,859 |
(x^2)^a = (\frac{1}{x})^a = x^{a + \left(-1\right)}
|
21,063 |
\frac{16}{3} = 1/2*6 + \frac{1}{3}*5 + 1/6*4
|
37,562 |
i\binom{F}{i} = \binom{(-1) + F}{i + (-1)} F
|
21,621 |
c_m = \dfrac{c_m m}{m}1
|
-2,771 |
\sqrt{5}\cdot (4 + 1) = 5\cdot \sqrt{5}
|
5,023 |
\left(n + 2 \cdot (-1)\right) \cdot (n + 2) = 4 \cdot (-1) + n^2
|
28,517 |
\dfrac{1}{5 + 7 \cdot (-1)} \cdot (-2 + 4 \cdot (-1)) = -\frac{1}{-2} \cdot 6 = 3
|
-20,513 |
-\frac{1}{1}*2*j*5/(j*5) = (j*(-10))/(j*5)
|
12,049 |
-c \neq c \Rightarrow 0*(-1) + c \neq -c + 0
|
26,729 |
(1 + s)\cdot (s + (-1)) + 1 = s^2
|
46,929 |
5 * 5 * 5 = 5^2*5
|
48,883 |
\frac{\sin b}{\cos b}=\frac{3}{4} \Rightarrow \frac{9}{16}\cos^2 b+\cos^2b=1 \Rightarrow \cos b=\frac{4}{5} \Rightarrow \sin b=\frac{3}{5}
|
-10,528 |
\dfrac{9}{3\left(-1\right) + k}*4/4 = \frac{1}{4k + 12 \left(-1\right)}36
|
11,506 |
\sqrt{2}\times 2/3 = \tfrac{\sqrt{2}\times 2}{3}
|
1,712 |
2 \cdot (-1) + m - e + m - w = m \cdot 2 + 2 \cdot (-1) - e - w
|
33,707 |
\sin(x*2) = \cos(x) \sin(x)*2
|
10,206 |
u^2 = x^2 \Rightarrow u = x
|
20,806 |
c + b = ( c, b)*( 1, 1) \leq (c * c + b^2)^{1/2}
|
11,292 |
(-1) + 3 + 1 + m + (-1) + m = 2*m + 2
|
15,438 |
\frac{1}{n! \left(n + 2\right)} = \frac{1}{(n + 2)!}(n + 2 + \left(-1\right)) = \frac{1}{\left(n + 1\right)!} - \frac{1}{(n + 2)!}
|
-5,863 |
\dfrac{4}{(k + 7 \cdot (-1)) \cdot (k + 10 \cdot (-1))} \cdot k = \dfrac{4 \cdot k}{k^2 - k \cdot 17 + 70}
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18,353 |
-\left(2 + z\right)\cdot ((-1) + z)^2 = 2\cdot (-1) + 3\cdot z - z^3
|
-10,802 |
\dfrac{144}{12} = 12
|
6,135 |
8 + x^2 + x \cdot 6 = \left(x + 4\right) \cdot (x + 2)
|
-15,100 |
\tfrac{1}{\frac{1}{i^{16} \cdot \frac{1}{\xi^4}}} \cdot i^4 = \frac{i^4}{\frac{1}{i^{16}} \cdot \xi^4}
|
14,084 |
\sin{x} = \sin((2\cdot n + 1)\cdot \pi - x) = \sin(x + 2\cdot n\cdot \pi)
|
33,118 |
\left. \frac{\partial}{\partial i} (\Im{(Z \cdot Z)} \cdot x) \right|_{\substack{ i=i }} = \left. \frac{\partial}{\partial i} (\Im{(Z)} \cdot x) \right|_{\substack{ i=i }}
|
11,882 |
8/11 = 1/2 + 1/4 - \frac{1}{44}
|
31,090 |
b \cdot 2 + h - b = h + b
|
15,780 |
\sigma*A = \sigma*A
|
49,425 |
148894375444481 = 1 + 2^{15} \times 4543895735
|
13,132 |
(x\cdot z + w\cdot y)^2 + \left(w\cdot x - z\cdot y\right) \cdot \left(w\cdot x - z\cdot y\right) = (z^2 + w^2)\cdot \left(y^2 + x \cdot x\right)
|
1,516 |
(x + 2)^{\frac{1}{2}} = (4 + x + 2\times (-1))^{\frac12} = 2\times (1 + (x + 2\times (-1))/4)^{\frac{1}{2}}
|
24,987 |
z + 0 \cdot (-1) = z + 0 \cdot \left(-1\right) + 0
|
-5,207 |
1.56 \cdot 10 = \tfrac{10}{1000} \cdot 1.56 = 1.56/100
|
14,674 |
y^f*y^a = y^{f + a}
|
10,623 |
(1/2 - i)^2 + 2i = (1/2 + i)^2
|
14,305 |
1 - \tfrac{1}{1 - B}\cdot \left(1 - A\right) = \frac{1}{1 - B}\cdot (1 - B - 1 - A) = \dfrac{A - B}{1 - B}
|
10,960 |
(1 - \sqrt{x})\cdot (1 + \sqrt{x}) = -x + 1
|
22,695 |
z = \dfrac1z*z^2
|
-2,257 |
-3/18 + \frac{5}{18} = 2/18
|
18,787 |
0 \leq 3\left(-1\right) + x \cdot 3 \Rightarrow x \geq 1
|
-15,468 |
\dfrac{(\frac{1}{x^3})^2}{\frac{1}{1/x \frac{1}{k^2}}} = \dfrac{1}{k^2 x x^6}
|
32,079 |
... ... = ... \cdot ...
|
10,714 |
F^{24} = F^{16}\cdot F^8
|
4,519 |
\sin\left(90\cdot (-1) + \alpha\right) = -\sin(90)\cdot \cos\left(\alpha\right) + \sin(\alpha)\cdot \cos(90)
|
8,279 |
\sin(b\times F) = \sin(b\times F)
|
8,220 |
\frac{26}{50} \cdot \dfrac{1}{51} \cdot 39 = \frac{169}{425}
|
17,402 |
1601 \cdot 1601 - 79\cdot 1601 + 1601 = 1601\cdot \left(1601 + 79\cdot \left(-1\right) + 1\right) = 1601\cdot 1523
|
10,695 |
\tan^2{w} = (-s + 1)/s \Rightarrow s = \cos^2{w}
|
34,341 |
1 - \frac{1}{(y^{22})!} + \frac{1}{(y^{44})!} - \dotsm = \cos\left(1/y\right)
|
28,076 |
2*|z| = d/dz (z*|z|)
|
11,037 |
(-1) \cdot h \cdot 0 + h \cdot 0 = h \cdot 0 + h \cdot 0 - h \cdot 0
|
45,635 |
\sqrt{6 - \sqrt{20}} = \sqrt{1} - \sqrt{5} \lt 0
|
-29,369 |
(5 \cdot z + 1) \cdot (5 \cdot z + (-1)) = (5 \cdot z)^2 - 1^2 = 25 \cdot z^2 + (-1)
|
-3,245 |
\left(5 + 3*(-1) + (-1)\right)*\sqrt{11} = \sqrt{11}
|
38,843 |
7*14 \dotsm*7l = 7*7*2 \dotsm*7l = 7^l*1*2 \dotsm l = 7^l l!
|
30,834 |
\tan^{-1}(-\infty) = -\frac{\pi}{2}
|
-18,942 |
\dfrac13 = \frac{C_t}{16\cdot \pi}\cdot 16\cdot \pi = C_t
|
13,281 |
3 + (6 + \frac{1}{6 + \frac{5^2}{6 + \dots}} \cdot 3^2)^{-1} = π
|
15,721 |
x^4 = (x \times x)^2
|
5,498 |
2/3 t = t - t/3
|
20,735 |
(a - b) \times (b^2 + a^2 + a \times b) = a^3 - b^3
|
6,123 |
1 + \frac{1}{1 - \delta} \cdot \delta = \frac{1}{-\delta + 1}
|
20,050 |
\cos\left(3 \cdot \left(x + \pi/3\right)\right) = \cos(2 \cdot \pi + 3 \cdot x) = \cos(3 \cdot x)
|
18,522 |
\left(x^2\right)^2 = x \cdot x \cdot x^2 = x \cdot x \cdot x \cdot x = x^4 = x^{2 \cdot 2}
|
-13,941 |
\frac{35}{1 + 6} = \frac{35}{7} = \tfrac{35}{7} = 5
|
21,552 |
1 + 2 + 3 + \dots + r = \left(r + 1\right) \cdot r/2
|
-20,224 |
-\dfrac{7}{2} \frac{1}{1 + y} (y + 1) = \frac{-7 y + 7 \left(-1\right)}{2 + y*2}
|
-6,133 |
\frac{12}{4*(k + 5*(-1))*(k + 9*(-1))} = \frac44*\frac{1}{(k + 9*(-1))*(k + 5*\left(-1\right))}*3
|
17,781 |
\dfrac43 = -8/3 + 4
|
8,583 |
\dfrac{1}{(-1)^k} = \dfrac{1}{(-1)^{k*2}}*(-1)^k
|
33,352 |
\binom{6}{2}*4! = \dfrac{6!}{2!*4!}*4! = \frac{6!}{2!} = 360
|
49,769 |
1 - \left(1 - 1/365\right)^{80000} = 1 - (\frac{1}{365} \cdot 364)^{80000} \approx 1 - 4.8/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
|
38,374 |
0 = 162\cdot (-1) + 48 + 24 + 72\cdot (-1) + 162
|
26,434 |
{4!\over2!}=12
|
4,730 |
\frac{1}{b \cdot d} \cdot (-b \cdot c + f \cdot d) = -\frac{c}{d} + f/b
|
17,900 |
\left(a^T \cdot U \cdot b\right)^T = b^T \cdot U^T \cdot a = b^T \cdot U \cdot a
|
-5,307 |
60.0 \cdot 10^3 = 10^{2 + 1} \cdot 60
|
18,672 |
x'*y + y*x' = x'*y
|
-1,140 |
\frac{1}{3 \cdot 1/4} \cdot (\dfrac19 \cdot (-1)) = -1/9 \cdot \dfrac43
|
6,909 |
2 \cdot h \cdot y \cdot z + 1 = h \cdot y \cdot z + h \cdot y + y \cdot z + z \cdot h + h + y + z + 1 = (h + 1) \cdot (y + 1) \cdot (z + 1)
|
14,483 |
\cot{H} = \dfrac{\cos{H}}{\sin{H}}
|
24,583 |
1 - \frac14 = (\frac12 + 1)\cdot (1 - \frac{1}{2})
|
28,656 |
1 + z^2 + z = \frac{3}{4} + \left(1/2 + z\right) \cdot \left(1/2 + z\right)
|
9,823 |
1 + 4*3^{\frac{1}{8}*9}*\lambda - 4*3^{1/8}*\lambda = 0 \implies 8*3^{\frac18}*\lambda = -1
|
-6,440 |
\frac{(8 + q)\cdot 4 + 6\cdot (4 + q) + 16\cdot \left(-1\right)}{(4 + q)\cdot (8 + q)\cdot 8} = \frac{4}{8\cdot (8 + q)\cdot \left(q + 4\right)}\cdot \left(8 + q\right) + \frac{6\cdot (q + 4)}{8\cdot (q + 4)\cdot (q + 8)} - \tfrac{16}{8\cdot (4 + q)\cdot (8 + q)}
|
8,005 |
(-c + a) \cdot \left(b - c\right) = b \cdot a + c \cdot c - \left(a + b\right) \cdot c
|
6,043 |
-(1 + m^2 + 3\cdot m) + d^2 + d\cdot 3 + 1 = \left(d + m + 3\right)\cdot \left(d - m\right)
|
-1,612 |
-\pi\cdot \frac{11}{12} + \pi\cdot 4/3 = \pi\cdot 5/12
|
-11,628 |
i - 4 + 3 \cdot \left(-1\right) = -7 + i
|
31,549 |
y^3 + y^2 - 10 y + 8 = (4 + y) (\left(-1\right) + y) (2 (-1) + y)
|
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