id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
6,679 |
((1 + l) \cdot (1 + l) + l \cdot l + l^2 + l) \cdot (-(l + 1) + l) = -(3 \cdot l^2 + l \cdot 3 + 1)
|
12,122 |
\frac{1}{y^n} + \frac{1}{x^n} = \dfrac{1}{y^n x^n}(x^n + y^n)
|
14,874 |
\frac{\partial}{\partial z} (z^4*b^2) = b * b*z^3*4
|
23,547 |
\frac12 ((-1) + \sqrt{5}) = \cos(\frac{2 \pi}{5})\cdot 2
|
22,468 |
(-4) \cdot (-4) \cdot (-4) = (-1) \cdot (-1)^2\cdot 4^3 = -64
|
9,358 |
\max{n,y} = n \implies n \geq y
|
25,211 |
(fb)^2 = (bf)^2
|
17,183 |
\dfrac{(2\cdot l)!}{l!\cdot 2^l} = 3\cdot 5\cdot \dotsm\cdot (2\cdot l + (-1))
|
-1,600 |
-5/12*\pi + \pi*2 = \frac{1}{12}*19*\pi
|
-3,060 |
11^{\frac{1}{2}} + 4^{\dfrac{1}{2}}\cdot 11^{\frac{1}{2}} = 11^{1 / 2} + 11^{\frac{1}{2}}\cdot 2
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32,569 |
9 = 1/2\times 3\times 6
|
12,212 |
p\cdot y/y = y\cdot p/y
|
3,087 |
(-4 + 4 \cdot \left(-1\right))/2 = -4
|
16,921 |
10 \cdot x = \frac{1}{-2} \cdot ((-20) \cdot x) = -0.5 \cdot (-20 \cdot x)
|
19,674 |
\left(a - b\right)^2 = a^2 - b*a*2 + b^2
|
28,408 |
17^5 + 17^5 + 34^5 = 2*4913 * 4913
|
-1,201 |
-21/24 = ((-21)\cdot \frac{1}{3})/(24\cdot \frac13) = -\dfrac{1}{8}\cdot 7
|
31,801 |
\frac12 = 1*2/\left(2*2\right) = \dfrac24
|
-29,651 |
\frac{\text{d}}{\text{d}x} (x*3 + x^3 - 4x^2) = 3x^2 - 8x + 3
|
42,063 |
\operatorname{atan}(\frac13) + \operatorname{atan}(1/7) + \dotsm + \operatorname{atan}(\frac{1}{1 + n^2 + n}) = \operatorname{atan}(\frac{1}{n + 2}n)
|
-4,547 |
15 \cdot (-1) + x^2 - x \cdot 2 = (x + 5 \cdot (-1)) \cdot (3 + x)
|
1,532 |
1 + \frac14 + 1/9 + \dotsm = \dfrac{\pi^2}{6}
|
34,846 |
{20 \choose 5} = \frac{20!}{5! \cdot (20 + 5 \cdot \left(-1\right))!} = 15504
|
30,062 |
4 = 8^{1 / 2}*2^{1 / 2}
|
4,990 |
(-i + l)! = (\left(-1\right) + l - i)! (l - i)
|
8,736 |
\dfrac{1}{x^2 + 2}\cdot (x \cdot x + 1) = 1 - \frac{1}{x^2 + 2}
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-21,058 |
4/8 = \dfrac22\cdot 2/4
|
8,518 |
\frac{1}{2^{2x}}2^{4x - x^2 + (-1)} = 2^{4x - x^2 + \left(-1\right) - 2x} = 2^{2x - x^2 + \left(-1\right)} = 2^{-(x + (-1))^2}
|
29,863 |
\sin^{-1}(\sin{y}) = \sin^{-1}(\sin(\pi - y)) = \pi - y
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-22,940 |
60/96 = 12*5/\left(8*12\right)
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26,517 |
4 = \frac12\cdot ((-1)\cdot (-1) + 7)
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16,994 |
e^{i \cdot y} \cdot e^z = e^{y \cdot i + z}
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27,537 |
1/(f c) = \frac{1}{f c}
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14,689 |
(-\frac{1}{2})^{\frac{1}{\frac12}} = (-1/2) \times (-1/2) = \dfrac{1}{4}
|
28,065 |
(U \cap x) \cap U_j = \left(U \cap U_j\right) \cap (x \cap U_j)
|
7,874 |
1 + 2 \cos{2 y_k} = 1 + 2*(1 - 2 \sin^2{y_k}) = \frac{1}{\sin{y_k}} \sin{3 y_k}
|
12,590 |
\sin^5{z} = \sin^4\left(z\cdot \sin{z}\right) = \left(1 - \cos^2{z}\right) \cdot \left(1 - \cos^2{z}\right)\cdot \sin{z}
|
-15,747 |
\frac{p}{\frac{1}{\frac{1}{p^{25}}\cdot n^{15}}} = \tfrac{p}{p^{25}\cdot \frac{1}{n^{15}}}
|
26,520 |
(y + z) \cdot (-y + z) \cdot (y \cdot y + z^2) = z^4 - y^4
|
30,662 |
0 = G E - G - E + 1 = (G + (-1)) \left(E + (-1)\right)
|
14,229 |
\left(C\cdot x - b\right)^W\cdot (C\cdot x - b) = \left(x^W\cdot C^W - b^W\right)\cdot (C\cdot x - b) = x^W\cdot C^W\cdot C\cdot x - x^W\cdot C^W\cdot b - b^W\cdot C\cdot x + b^W\cdot b
|
15,605 |
(-1) + 2\cdot m = 2\cdot (1 + m) + 3\cdot \left(-1\right)
|
-2,434 |
\sqrt{2}*(2 + 5 + 3*(-1)) = \sqrt{2}*4
|
13,858 |
12 = \left(1 + 1\right)*(1 + 2)*(1 + 1)
|
22,763 |
4 = \rho^2 - y^2 = (\rho - y)\cdot \left(\rho + y\right)
|
-7,014 |
\frac{1}{21} = 1/7 \cdot 2/6
|
11,027 |
\sin(d + g) = \sin\left(d\right)\cdot \cos(g) + \sin(g)\cdot \cos(d)
|
-26,536 |
(4 - x)\times \left(x + 4\right) = -x^2 + 4^2
|
27,146 |
\operatorname{im}{(x)} = \sin{\pi\cdot l/k} \Rightarrow x = e^{\frac{l}{k}\cdot \pi\cdot i}
|
23,395 |
42 = \frac{1}{5!*1!*1!}*7!
|
1,121 |
t^3 - 10\cdot t^2 + t\cdot 33 + 36\cdot \left(-1\right) = (t + 4\cdot (-1))\cdot \left(3\cdot (-1) + t\right)^2
|
17,744 |
y_1*g_1 = z_2*g_2 \Rightarrow z_2 = \dfrac{g_1*y_1}{g_2}*1
|
14,328 |
f^z = e^{\ln(f^z)} = e^{z\ln(f)}
|
18,123 |
z^4 + 4 = (2 + z * z - 2*z)*(2 + z^2 + 2*z)
|
42,326 |
649\cdot 9 + 6 = 5847
|
22,884 |
\left(C_2 + C_1\right)^3 = C_1^3 + 3*C_2*C_1^2 + 3*C_1*C_2^2 + C_2^3
|
2,606 |
1/36 + (1 - 1/36) \frac{216}{1111} = \frac{8671}{39996} \approx 0.2168
|
-28,920 |
5*\dfrac19/9 = \dfrac{5}{9*9} = 5/81
|
13,498 |
1 = y/y \Rightarrow 1/y = \dfrac{1}{y}
|
-22,837 |
60/72 = \frac{12}{12\cdot 6}\cdot 5
|
24,941 |
\sin(19\pi/12)=-(1+\sqrt{3})/2\sqrt{2}
|
7,503 |
\frac{\frac1d}{h} \cdot a = a \cdot \frac{1}{d}/h = \frac{a}{d \cdot h}
|
-20,135 |
\frac{45\cdot k}{k\cdot 81} = 5/9\cdot \frac{9\cdot k}{9\cdot k}\cdot 1
|
42,882 |
\dfrac{1}{1 + \frac{1}{a + \left(-1\right)}} = 1 - 1/a
|
-9,312 |
x^2*27 = x*3*3*3 x
|
883 |
2^{n + (-1)}\cdot 2 + 1 = 3\cdot 2^{n + (-1)} - 2^{(-1) + n} + 3 + 2\cdot (-1)
|
-10,446 |
10 = -32 - 80 \cdot t + 20 = -80 \cdot t + 12 \cdot (-1)
|
-4,715 |
\frac{15 + 7\cdot y}{y^2 + y\cdot 6 + 5} = \frac{1}{1 + y}\cdot 2 + \frac{5}{y + 5}
|
22,930 |
\tan{x}\cdot \sin{x} + \cos{x} = 0 \Rightarrow \dfrac{1}{\cos{x}}\cdot (\sin^2{x} + \cos^2{x}) = 0
|
3,878 |
-b^2 + h^2 = (h + b) \cdot (h - b)
|
21,272 |
b^2 + a^2 + ba*2 = (a + b) * (a + b)
|
-6,554 |
\dfrac{4 \cdot x}{x^2 + 7 \cdot x + 6} = \frac{4 \cdot x}{(1 + x) \cdot (6 + x)}
|
11,267 |
2\cdot \sqrt{x\cdot y} \lt x^2 + 2\cdot x\cdot y + y^2 - x - y = (x + y) \cdot (x + y) - x + y = (x + y)\cdot (x + y + (-1))
|
-5,886 |
\frac{1}{x^2 - 17*x + 72}*3 = \tfrac{1}{(8*(-1) + x)*(9*(-1) + x)}*3
|
16,351 |
\dfrac{1}{h_1}a + h_2/\left(h_1\right) = \frac{1}{h_1}(h_2 + a)
|
19,454 |
(0 \cdot (-1) + y)^x = y^x
|
-7,543 |
\frac{1}{-1 + i\cdot 5}\cdot (-1 + i\cdot 5)\cdot \frac{1}{-i\cdot 5 - 1}\cdot (9\cdot i + 7) = \dfrac{7 + 9\cdot i}{-1 - i\cdot 5}
|
-14,214 |
\frac{4}{6 + 5 (-1)} = \tfrac41 = \dfrac41 = 4
|
39,579 |
\frac{3}{4} = \frac12 + 1/4
|
-22,868 |
\dfrac{110}{66} = \dfrac{5 \cdot 22}{ 3\cdot 22}
|
37,793 |
393 = 38 \times \left(-1\right) + 431
|
1,501 |
1 + d + d^2 + d * d * d + \dotsm + d^m = \frac{1 - d^{1 + m}}{1 - d}
|
9,844 |
\left\{v\right\} = ( v + x, x + v) \implies \left[x,v\right] = 0
|
8,833 |
\left(-1\right) + \cos^2{u}*2 = \cos{u*2}
|
-11,763 |
\frac{1}{49}100 = (10/7)^2
|
3,343 |
n = -(n^2 - n) + n n
|
-13,356 |
\dfrac{7}{6 + 5 \times \left(-1\right)} = 7/1 = \dfrac71 = 7
|
-12,239 |
41/45 = \frac{t}{10\cdot \pi}\cdot 10\cdot \pi = t
|
26,409 |
\frac{6}{7} = \dfrac{1}{3 - 1 + 1/2 + 1/3}
|
19,926 |
h^U = h^{-\left\lfloor{U}\right\rfloor + U} h^{\left\lfloor{U}\right\rfloor}
|
-23,088 |
-\frac{1}{27}\cdot 128 = -\frac{32}{9}\cdot \frac43
|
-23,021 |
24/84 = \frac{12 \cdot 2}{12 \cdot 7}
|
10,007 |
((T_{d + 2\times (-1)} + 0.25)\times 1.01 + 0.25)\times 1.01 = \left(1.01\times T_{d + 2\times (-1)} + 0.25\times 1.01 + 0.25\right)\times 1.01
|
10,472 |
\frac{1}{4} = 3/8\cdot 2/3
|
-22,003 |
\dfrac{4}{8} + \dfrac{8}{5} = {\dfrac{4 \times 5}{8 \times 5}} + {\dfrac{8 \times 8}{5 \times 8}} = {\dfrac{20}{40}} + {\dfrac{64}{40}} = \dfrac{{20} + {64}}{40} = \dfrac{84}{40}
|
12,848 |
\left(b b - 4 c\right)^{1 / 2} = i \cdot (4 c - b^2)^{1 / 2} = i \|b^2 - 4 c\|^{\dfrac{1}{2}}
|
18,901 |
3 - 3*(-1) + 5 = 1
|
1,032 |
\dfrac{4}{3}\cdot (3/2)^2 = 3
|
-3,248 |
7*6^{1/2} = (4 + 3)*6^{1/2}
|
26,996 |
9^1 = 9^{\frac12} \cdot 9^{1/2}
|
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