id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
5,662 |
\dfrac{1}{y^{1/2}}((-3) y) = -3y^{1/2}
|
1,474 |
4n^2 + (-1) = (2n + (-1)) (2n + 1)
|
-564 |
\left(e^{\pi\cdot i}\right)^{15} = e^{15\cdot i\cdot \pi}
|
8,715 |
g \cdot g \cdot e = e = g \cdot g \cdot e
|
-4,142 |
\frac{1}{l^3} \cdot l \cdot l \cdot l \cdot \dfrac{1}{40} \cdot 8 = \frac{1}{40 \cdot l^3} \cdot 8 \cdot l^3
|
-29,007 |
4 = \left(4\cdot (-1) + 12\right)/2
|
-20,859 |
\frac{1}{25\times p + 5\times (-1)}\times (-30\times p + 6) = \frac{1}{5\times p + (-1)}\times \left(5\times p + (-1)\right)\times (-\frac{6}{5})
|
-12,347 |
2^{1 / 2}\cdot 6 = 72^{\dfrac{1}{2}}
|
27,695 |
\dfrac{1}{x \cdot d} = \dfrac{1}{x \cdot d}
|
-12,541 |
31 = 90 + 59\cdot (-1)
|
17,337 |
b = h \cdot b = b \cdot h
|
29,511 |
\left\lfloor{\frac15(7 + (-1))}\right\rfloor + 1 = 2
|
6,976 |
\frac{1}{Y\cdot \dfrac{1}{X}} = X/Y
|
22,012 |
2^{1 + k} + 2\cdot \left(-1\right) = 2\cdot ((-1) + 2^k)
|
36,419 |
-x + x \coloneqq -x + x
|
35,082 |
\dfrac{1}{-y^2 + 1} = \tfrac12 \cdot (\dfrac{1}{1 - y} + \frac{1}{1 + y})
|
10,331 |
(-\sqrt{x} + \sqrt{a_m})\cdot (\sqrt{a_m} + \sqrt{x}) = -x + a_m
|
-2,626 |
-\sqrt{6} + \sqrt{24} = \sqrt{4\cdot 6} - \sqrt{6}
|
32,919 |
1/L + 1/M + 1/x = \frac{1}{L*M*x}*(L*M + x*M + x*L)
|
16,860 |
\int\limits_{-\infty}^\infty ...\,\mathrm{d}z = 2 \cdot \int_0^\infty ...\,\mathrm{d}z
|
30,546 |
-4 \cdot x + 12 = 4 \cdot x \cdot x - (x^2 + x + 3 \cdot (-1)) \cdot 4
|
-1,260 |
-20/18 = \frac{1}{18 \cdot 1/2}((-20) \cdot 1/2) = -10/9
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36,245 |
-(8 \cdot 9^5 + 9^6) + 9 \cdot 10^5 = -103833
|
-28,798 |
150 = \pi*2/(\pi*2*\frac{1}{150})
|
38,983 |
x + x = x \cdot 2
|
-15,966 |
-10 \cdot \frac{3}{10} + 7 \cdot 7/10 = 19/10
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-4,233 |
k^2 \cdot 7/6 = 7 \cdot k^2/6
|
19,541 |
-9 = 4 + 2 * 2 + (-1)^2*9 - 4*2 + 18*\left(-1\right)
|
13,277 |
|(-c_k\cdot t + h_k\cdot M)/\left(M\cdot c_k\right)| = |\frac{h_k}{c_k} - \frac{1}{M}\cdot t|
|
-2,429 |
12 \cdot 6^{1/2} = (3 + 4 + 5) \cdot 6^{1/2}
|
-9,286 |
-x*7*7 + 3*7 = -x*49 + 21
|
-26,552 |
2\times y^2 - 40\times y + 200 = 2\times \left(y \times y - 20\times y + 100\right) = 2\times \left(y + 10\times (-1)\right)^2
|
14,971 |
8 \cdot x = 4 \cdot x + 2 \cdot x \cdot 2
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-27,734 |
\frac{\mathrm{d}}{\mathrm{d}x} \csc{x} = -\csc{x} \cot{x}
|
-11,955 |
13/15 = \tfrac{1}{12*\pi}*s*12*\pi = s
|
-20,653 |
-7/8 \frac{1}{-5\varepsilon + 2(-1)}\left(-5\varepsilon + 2(-1)\right) = \frac{14 + 35 \varepsilon}{-40 \varepsilon + 16 \left(-1\right)}
|
-22,805 |
\frac{60}{4 \cdot 12} \cdot 1 = \frac{1}{48} \cdot 60
|
10,420 |
5^{2n} + (-1) = \left(5^n + 1\right) \left(5^n + (-1)\right)
|
-20,339 |
-\frac{36}{-8} = 9/2 \cdot (-\frac{4}{-4})
|
8,821 |
a*\sin{\pi/2} + \cos{\pi/2} = a
|
-11,009 |
112/8 = 14
|
27,041 |
(b + a) \times (b + a) - b \times a \times 2 = a \times a + b^2
|
12,189 |
\left(-5\right)^2 + (-3) * (-3) + 1^2 = 35 = 5*((-5)*(-3) - 5 - 3)
|
7,423 |
11 = (z + \sigma + y) \cdot 6\Longrightarrow z + \sigma + y = \dfrac{11}{6}
|
29,030 |
\csc{\theta} = \frac{1}{\sin{\theta}} = \dfrac{1}{(1 - \cos^2{\theta})^{\tfrac{1}{2}}}
|
15,310 |
-A_1*B_1 + (A_0 + A_1)*\left(B_0 + B_1\right) - B_0*A_0 = A_1*B_0 + B_1*A_0
|
-20,018 |
\frac{s\cdot 5 + 30}{45\cdot (-1) + 5\cdot s} = \frac55\cdot \frac{s + 6}{s + 9\cdot \left(-1\right)}
|
22,130 |
\binom{1}{1}\times \binom{19}{2}/\left(\binom{20}{3}\right) = \frac{1}{20}\times 3
|
4,601 |
-2 \cdot x \cdot e^{-x^2} = (-2 + 4 \cdot x^2) \cdot e^{-x^2}
|
33,017 |
\frac{1}{2^{1 / 2}} = \dfrac{2^{\frac{1}{2}}}{2}
|
-5,036 |
18.0\cdot 10^{5 + 2} = 18\cdot 10^7
|
25,998 |
5 + \left(z + (-1)\right)^4 + z^2\cdot 3 - z\cdot 6 = (z + (-1))^4 + 3\cdot (z + (-1))^2 + 2
|
41,682 |
2^{23} + (-1) = 47 \cdot 178481
|
-20,293 |
\frac{9 - 6 \cdot \delta}{\delta + 5 \cdot (-1)} \cdot 5/5 = \frac{45 - 30 \cdot \delta}{\delta \cdot 5 + 25 \cdot (-1)}
|
20,760 |
\sin(2\cdot \theta) = \cos(\dfrac{\pi}{2} - 2\cdot \theta)
|
52,112 |
770 = {5 \choose 4} \cdot {7 \choose 1} + {7 \choose 2} \cdot {5 \choose 3} + {7 \choose 3} \cdot {5 \choose 2} + {7 \choose 4} \cdot {5 \choose 1}
|
37,155 |
(2k)^2 = (2n+25)^2-549\Rightarrow (2n+25)^2-(2k)^2 = 549 = 3^3\cdot 61
|
1,662 |
-2\cdot \frac{x}{d^3} = 2\cdot x/d\cdot \frac{1}{d}\cdot x
|
14,616 |
0 = t rightarrow 0 = t
|
34,516 |
y^2 \cdot 2 - y \cdot 6 = (-y \cdot 3 + y^2) \cdot 2
|
18,704 |
-(1 + i)*2 = \left(-2\right) (-1) - (2 + i)*2
|
17,020 |
-\frac{1}{e^y + 1} + 1 = \frac{e^y}{1 + e^y}
|
9,556 |
\mathbb{E}[|X| + |Y|] = \mathbb{E}[|X|] + \mathbb{E}[|Y|]
|
26,739 |
273/999 = \frac{91}{333}
|
-19,518 |
\dfrac{1}{5} \cdot 7 \cdot \frac19 \cdot 4 = \frac{\frac{7}{5}}{1/4 \cdot 9} \cdot 1
|
-23,113 |
-\frac{1}{27} \cdot 4 = \frac13 \cdot (\frac{1}{9} \cdot (-4))
|
6,359 |
\frac{48}{50} \cdot \dfrac{3}{51} = 144/2550
|
-1,650 |
\frac94\cdot \pi = 4/3\cdot \pi + \frac{11}{12}\cdot \pi
|
-20,344 |
\dfrac{1}{5}\cdot 5\cdot \frac{1}{4\cdot z}\cdot ((-1) + 5\cdot z) = \left(5\cdot (-1) + 25\cdot z\right)/(20\cdot z)
|
14,872 |
19 = 3^3 - 2 2 2
|
19,156 |
1/\left((-1)\cdot b\right) = \frac{1}{(-1)\cdot b} = \frac{\frac{1}{-1}}{b} = -1/b = -\frac1b
|
729 |
27 + |Y\cdot E| = 27 + |E\cdot Y|
|
37 |
4\cdot a\cdot d + \left(a - d\right)^2 = (d + a)^2
|
17,481 |
(b + f)^2 = b^2 + f^2 + 2*b*f
|
24,603 |
\frac{1}{-(-1) \cdot x^2 + 1} = \frac{1}{1 + x^2}
|
12,492 |
\dfrac1y\cdot 2 = \dfrac{2}{y^2}\cdot y
|
19,043 |
\int (y + 2\cdot (-1))\cdot e^y\,\mathrm{d}y = (y + 2\cdot (-1))\cdot e^y - \int e^y\,\mathrm{d}y = \left(y + 2\cdot (-1)\right)\cdot e^y - e^y = y\cdot e^y - 3\cdot e^y
|
2,719 |
5 = 0 \implies 1 = 0
|
26,608 |
10 \cdot z \cdot z + z \cdot 20 + 10 = 10 \cdot (z + 1)^2
|
29,700 |
-y^2 + x^2 = (-y + x)*(x + y)
|
13,028 |
q^2 - yq*2 + 1 = 0 \Rightarrow q = y ± \sqrt{y^2 + (-1)}
|
9,457 |
(x \cdot 2 + 5) (2 + x \cdot 5) = 10 x^2 + 29 x + 10
|
30,866 |
1/3 = \dfrac{1}{6}\cdot 2
|
-13,952 |
3 + 8 \cdot 6 - 5 = 3 + 48 - 5 = 51 - 5 = 51 + 5 \cdot (-1) = 46
|
785 |
\dfrac23\cdot \tfrac{1}{5}/4 = \frac{1}{30}
|
-1,868 |
\pi \cdot \frac{19}{12} - \dfrac{1}{12} \cdot 19 \cdot \pi = 0
|
-18,639 |
-\frac{7}{22} = -\frac{7}{22}
|
-4,046 |
\frac{1}{2} \cdot 9 = \frac{1}{2} \cdot 9
|
-21,039 |
\frac17 \cdot 7 \cdot (x + 5 \cdot (-1))/8 = (7 \cdot x + 35 \cdot (-1))/56
|
13,610 |
2^{\frac{5}{12}} = 1.334839 \ldots \approx 4/3
|
-4,262 |
\frac{11*1/12}{a^2} = \frac{11}{12*a * a}
|
5,431 |
t^5 + t^3 + t^2 + 1 = (t^2 + 1) \cdot (1 + t^2 - t) \cdot (t + 1)
|
151 |
0 \lt (\sqrt{h_1} - \sqrt{h_2})^2 = h_1 - 2*\sqrt{h_1*h_2} + h_2 = h_1 + 2*(-1) + h_2
|
20,527 |
72/625 = \frac{5*\binom{6}{2}*4!}{5^6}*1
|
-19,388 |
4/5 \cdot \frac{1}{1} \cdot 8 = \dfrac{1}{5} \cdot 4/\left(1/8\right)
|
-19,010 |
\tfrac78 = \frac{A_r}{9*\pi}*9*\pi = A_r
|
11,798 |
L = L \cdot 2 \implies L = 0
|
-2,384 |
\left(-6\right)^3 = \left(-6\right) \times (-6) \times \left(-6\right) = 36 \times (-6) = -216
|
2,088 |
1 + y^3 = (1 + y^2 - y) \cdot (1 + y)
|
-22,189 |
\left(p + 8\right)\cdot \left(p + 7\cdot (-1)\right) = p^2 + p + 56\cdot \left(-1\right)
|
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