id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
32,972 |
\sqrt{(6 + 5 \cdot \left(-1\right))^2 + \left(0 + 3\right)^2} = \sqrt{1 + 9} = \sqrt{10} \leq 4
|
1,198 |
L\cdot y = L\cdot y
|
27,340 |
k + \left(3 - k\right)\cdot 0 = k
|
10,604 |
\sin(\cos^{-1}\left(z\right)) = (1 - z^2)^{1 / 2}
|
-22,203 |
r^2 - 15\cdot r + 54 = (r + 6\cdot \left(-1\right))\cdot (r + 9\cdot \left(-1\right))
|
14,217 |
nk + n = (k + 1) n
|
-11,553 |
-3 + 5 - i \cdot 16 = -16 \cdot i + 2
|
36,991 |
h^3*d^3 = (d*h) * (d*h) * (d*h)
|
9,511 |
e^{j + 1} = e^j*e > e^j*2 = e^j + e^j > e^j + 1
|
-1,209 |
-\frac{6}{21} = ((-6)\cdot 1/3)/(21\cdot \frac{1}{3}) = -2/7
|
19,065 |
\frac{\text{d}}{\text{d}y} (1 + y^2 + y) = 1 + 2*y
|
24,682 |
(1 + r) \cdot r = r + r^2
|
-108 |
4\times \left(-1\right) - 17 = -21
|
23,820 |
1 + y + y \cdot y/2! + \dfrac{y^3}{3!} + \frac{1}{4!} \cdot y^4 + \ldots = e^y
|
-20,580 |
5/5 \dfrac{m + 3 (-1)}{m*2 + 2 (-1)} = \frac{5 m + 15 (-1)}{10 \left(-1\right) + 10 m}
|
20,637 |
-2*x^2 + 16*x = -2*(x^2 + 8*\left(-1\right)) = -2*(x + 4*(-1))^2 + 32
|
19,788 |
-0\cdot m + m\cdot \left(x - y\right) = m\cdot x - m\cdot y
|
-18,357 |
\frac{(7 \cdot \left(-1\right) + n) \cdot n}{(n + 7 \cdot (-1)) \cdot (n + 10)} = \frac{n^2 - 7 \cdot n}{70 \cdot (-1) + n^2 + 3 \cdot n}
|
21,433 |
1224 = 6^3 + 10^3 + 2 \cdot 2^2
|
-4,828 |
10^4\cdot 45.0 = 45\cdot 10^{5 - 1}
|
11,682 |
yz_0 - z_0 y_0 + zy - z_0 y = yz - y_0 z_0
|
27,488 |
A*g = A*g
|
23,882 |
\dfrac12\cdot (\dfrac{1}{2} - 2) = -\dfrac34
|
32,837 |
2 \lt 3 \Rightarrow 1/3 \lt 1/2
|
16,033 |
-\cos(\frac{\pi}{2} + x) = \sin{x}
|
-10,898 |
57 = \dfrac{1}{2}*114
|
50,630 |
24 + 24 + 6\cdot (-1) = 42
|
26,005 |
v \cdot u \cdot (t + s) = v \cdot u \cdot t + u \cdot s \cdot v
|
42,664 |
156 = \binom{2}{1} \cdot \binom{13}{2}
|
3,427 |
|C\cdot x - B\cdot A| = |C\cdot x - A\cdot B|
|
24,158 |
x \cdot x^2 = x \cdot x\cdot x = x^2 = x
|
-7,741 |
\tfrac{2 + 26 \cdot i}{-3 \cdot i + 5} = \dfrac{2 + i \cdot 26}{5 - 3 \cdot i} \cdot \dfrac{i \cdot 3 + 5}{5 + 3 \cdot i}
|
9,445 |
4^m + m^4 = (2^m)^2 + (m^2)^2 = (m^2 + 2^m)^2 - 2\cdot 2^m m \cdot m
|
28,214 |
3/20 = \frac12 \cdot \frac{3}{10}
|
17,015 |
\tfrac{1}{\sqrt{3}}\times 2 = 2\times \sqrt{3}/3
|
-5,210 |
7.1 \cdot 10^{(-4) \cdot (-1) + 1} = 10^5 \cdot 7.1
|
-7,064 |
\dfrac36\cdot \frac{1}{7}2 = \frac{1}{7}
|
511 |
0.81\cdot 0.72\cdot x = x\cdot 0.5832
|
10,127 |
\cos{t \cdot 2} = \left(-1\right) + \cos^2{t} \cdot 2
|
9,230 |
p^m\cdot b_m = p^m\cdot b_{m + 1}\cdot p \Rightarrow b_{1 + m}\cdot p = b_m
|
508 |
x \cdot x\cdot 4 + 3\cdot (-1) = (-3^{1 / 2} + 2\cdot x)\cdot (2\cdot x + 3^{1 / 2})
|
-25,483 |
\frac{\mathrm{d}}{\mathrm{d}y} (4\cdot y \cdot y + \cos{y}\cdot 3) = 8\cdot y - \sin{y}\cdot 3
|
-20,393 |
\dfrac{1}{70 q + 35}(-14 q + 56 (-1)) = 7/7 \frac{1}{q\cdot 10 + 5}(8(-1) - q\cdot 2)
|
35,969 |
\sqrt{-k} \sqrt{-l} = \sqrt{-k \cdot (-l)} = \sqrt{kl}
|
-5,082 |
10^{2 + 1} \cdot 18.0 = 18.0 \cdot 10^3
|
25,069 |
(x + 2*(-1))^6 = (x + 2*(-1)) * (x + 2*(-1))*(x + 2*(-1))^4
|
-24,365 |
\left(2 + 6\right)^2 = 8 * 8 = 8^2 = 64
|
17,404 |
\dfrac{2 \cdot a + 2 \cdot a + 3}{2 \cdot a + 2 \cdot b + 1} = 1 + \dfrac{1}{2 \cdot a + 2 \cdot b + 1} \cdot 2 = 1 + \frac{1}{a + b + 1/2}
|
-2,519 |
6 \cdot 2^{1/2} = 2^{1/2} \cdot (5 + 1)
|
392 |
1/4 = 3 \cdot 5/16 - 11/16
|
-20,866 |
\frac{1}{9}*9*\frac{8 + p}{p + 10} = \frac{9*p + 72}{9*p + 90}
|
15,022 |
10^4 \times (1.0 + 0.0001) = 1.0 + 10^4 \times 1
|
3,710 |
(1 + y \cdot y) \left(y + 1\right) (y + (-1)) = \left(-1\right) + y^4
|
-26,015 |
(-b + g)*(g + b) = g^2 - b^2
|
-17,808 |
15*(-1) + 56 = 41
|
-20,411 |
\dfrac{(-8)\times i}{-72\times i + 72\times \left(-1\right)} = \frac18\times 8\times \frac{(-1)\times i}{9\times (-1) - 9\times i}
|
3,831 |
\cos(-\vartheta + x) = \cos(-(-x + \vartheta))
|
21,791 |
\cos(\frac{x}{2})/2 = d/dx \sin\left(\frac{x}{2}\right)
|
23,192 |
\phi^2 + 2 \phi + 2 = (1 + \phi)^2 + 1
|
17,765 |
8\cdot 2^{4\cdot (-1) + n} = 2^3\cdot 2^{n + 4\cdot (-1)}
|
18,879 |
3.75 = \dfrac{1}{100}(1 + 74) + 1 + \frac{1}{100}(1 + 74) + 1/4 + 1
|
26,380 |
\frac{13^2}{5^2} + 2 \cdot \left(-1\right) = \frac{1}{5^2} \cdot (-5^2 + 12^2)
|
-3,145 |
\sqrt{16 \cdot 13} + \sqrt{13} = \sqrt{208} + \sqrt{13}
|
13,396 |
2^{k + 1} = 2.2^k \gt 2\cdot (k + 1) + 1
|
-21,058 |
\frac12*2*2/4 = 4/8
|
-20,480 |
\dfrac{10}{-40} = -1/4*\left(-\frac{1}{-10}*10\right)
|
-26,242 |
5 = D*e^{(-2)*0} = D
|
19,044 |
4 \cdot \pi = 3 \cdot \frac{4}{9^{\frac{1}{2}}} \cdot \pi
|
-4,337 |
\frac{1}{n \cdot n}\cdot n = \dfrac{1}{n\cdot n}\cdot n = 1/n
|
8,953 |
\left(5 + 17*4k\right)*17 = 85 + k*1156
|
9,610 |
(a + b i) (a - b i) = a^2 - b^2 i^2 = a a + b^2
|
-22,298 |
7(-1) + r^2 - r*6 = (7(-1) + r) \left(r + 1\right)
|
15,812 |
x^6 + 1 = \left(x^2\right)^3 + 1 = \left(x^2 + 1\right) \cdot \left(x^4 - x^2 + 1\right)
|
-6,733 |
\frac{1}{100}\cdot 0 + \frac{6}{100} = \dfrac{1}{10}\cdot 0 + \dfrac{6}{100}
|
32,846 |
9^2 + 44 \cdot 44 = 2017
|
19,567 |
(5^2 + 3 \times 3 + 2^2)^{1/2} = 38^{1/2}
|
-9,486 |
-5*2*3 + a*3*5 = 30 \left(-1\right) + 15 a
|
34,006 |
p^2 - t \cdot p \cdot 2 + t^2 \cdot 2 = \left(-t + p\right)^2 + t^2
|
-29,575 |
3\cdot x^2/x = x\cdot 3
|
-30,861 |
\frac{1}{x + 2} \cdot (x^3 + 3 \cdot x \cdot x + 2 \cdot x) = x \cdot x + x
|
13,924 |
4 \cdot \left(l + 1\right)^2 + 1 = 4 \cdot l^2 + 8 \cdot l + 4 + 1 = 4 \cdot l^2 + 1 + 8 \cdot l + 4 \lt 3 \cdot 2^l + 8 \cdot l + 4
|
-23,908 |
\frac{16}{10 + 6} = \dfrac{16}{16} = 16/16 = 1
|
20,726 |
y \cdot A + A \cdot x = (y + x) \cdot A
|
6,474 |
f + e + c + g = f + e + c + g
|
9,513 |
36^2 = 4^2 \cdot 9 \cdot 9
|
2,676 |
\left(1/k\right)^2 = \dfrac{1}{k^2}
|
-2,452 |
5^{1/2}\cdot 25^{1/2} - 9^{1/2}\cdot 5^{1/2} = -3\cdot 5^{1/2} + 5^{1/2}\cdot 5
|
-18,989 |
\frac58 = \frac{1}{36\cdot \pi}\cdot A_q\cdot 36\cdot \pi = A_q
|
25,997 |
(-1) + x = ((-1) + x^{1 / 2})\cdot \left(1 + x^{1 / 2}\right)
|
7,350 |
x^3 - 5 \cdot x^2 + 7 \cdot x + 13 = (1 + x) \cdot (13 + x^2 - 6 \cdot x)
|
957 |
n^{-\dfrac{1}{3}} = \frac{1}{n^{\frac{1}{3}}}
|
10,744 |
n/2 + n/3 + n/4 = \dfrac{1}{12}13 n \gt n
|
12,388 |
\left(65 = 3 \cdot c_1 \cdot t + 20 \Rightarrow c_1 \cdot t = 15\right) \Rightarrow t = 15/(c_1)
|
31,750 |
5^2\times 13 \times 13\times 17\times 29\times 37\times 41 = 3159797225
|
36,707 |
\left(\left(3 \gt z_n\Longrightarrow 27 \gt 9 \cdot z_n\right)\Longrightarrow 12 + 12 \cdot z_n \lt 39 + 3 \cdot z_n\right)\Longrightarrow (z_n + 13) \cdot 3 > 12 \cdot (z_n + 1)
|
29,778 |
\sin{\pi/6}\cdot i + \cos{\frac{\pi}{6}} = \frac{i}{2} + \sqrt{3}/2
|
-4,662 |
x \cdot x + 4\cdot \left(-1\right) = \left(x + 2\right)\cdot (x + 2\cdot \left(-1\right))
|
25,662 |
81 + z^2 + z\cdot (3\cdot d + 1) = 0 \Rightarrow z = (-(1 + d\cdot 3) ± \sqrt{-81\cdot 4 + (1 + d\cdot 3)^2})/2
|
27,283 |
(-1)^z = e^{i\times z\times π} = \cos(z\times π) + i\times \sin(z\times π)
|
27,561 |
3 \cdot 3 + 3 \cdot 9 + 9 \cdot 9 = 9 \cdot \left(1^2 + 3 + 3^2\right) = 9 \cdot 13
|
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