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18,098 | \frac{\partial}{\partial x} x^a = ax^{a + (-1)} |
28,425 | g_1 g_1^{g_2} = g_1^{g_2 + 1} |
39,590 | \sin(2 \pi + y) = \sin\left(y\right) |
23,937 | \dfrac{15}{36} = 1 - 1/36 - 20/36 |
-25,830 | z^2 + z \cdot 3 + 5 = \dfrac{z^3 - z \cdot 4 + 15 \cdot \left(-1\right)}{z + 3 \cdot (-1)} |
-2,660 | \sqrt{16} \cdot \sqrt{11} + \sqrt{11} = \sqrt{11} \cdot 4 + \sqrt{11} |
8,198 | E(e^Y) = e^{E(Y)} |
8,540 | \frac{\sin{z}}{z^2} = \frac{\sin{z}*\frac1z}{z} |
26,517 | 4 = \frac12(7 - -1) |
23,386 | \dfrac{-1 + 5 \cdot (-1)}{-2 + 4 \cdot (-1)} = -6/(-6) = 1 |
23,007 | \frac{F/M\cdot M}{M} = \frac{F}{M} |
7,638 | \frac{4}{t \cdot 4} = \dfrac{1}{t} |
-26,456 | 128 - 32 \cdot x + 2 \cdot x^2 = (x^2 + 64 - x \cdot 16) \cdot 2 |
17,276 | x*(cW + Ud) = Wx c + dxU |
-23,125 | -\frac12\cdot \tfrac18\cdot 5 = -5/16 |
38,287 | 105 = 10\cdot (1 + 2 + 3 + 4) + 5 |
18,693 | ( x', y') + ( \psi, y'') + ( x, y) = \left( \psi + x', y' + y''\right) + \left( x, y\right) |
5,031 | {\left(-1\right) + i \choose 2} = \frac12 \cdot \left(\left(-1\right) + i\right) \cdot (i + 2 \cdot \left(-1\right)) |
31,936 | 2\cdot \pi\cdot \sigma^2 = \left(\pi\cdot 2\right)^{1/2}\cdot \sigma\cdot \left(\pi\cdot 2\right)^{1/2}\cdot \sigma |
32,833 | x^{R*y} = x^{y*R} |
44,894 | N \geq 8 \cdot 9 \cdot 5 \cdot 7 \cdot 11 \cdot 13 = 360360 \gt \overline{N} |
22,507 | det\left(-G \cdot F + x\right) = det\left(-F \cdot G + x\right) |
34,017 | 2*(0*(-1) + 1) = 2 |
-10,149 | 0.01 \cdot \left(-64\right) = -\tfrac{64}{100} = -\frac{16}{25} |
4,857 | \frac17 \cdot 40 = -2/7 + 6 |
-22,711 | 110/77 = 11\cdot 10/(7\cdot 11) |
-12,345 | 144^{\frac{1}{2}} = 12 |
12,122 | \frac{1}{x^l \cdot z^l} \cdot (x^l + z^l) = \frac{1}{x^l} + \frac{1}{z^l} |
-18,726 | \left(-1\right) \cdot 0.0359 + 0.0446 = 0.0087 |
21,471 | \frac{T*k*3}{x} = v * v \Rightarrow \sqrt{3*k*T/x} = v |
36,277 | c^2 + z * z + 2*c*z = (c + z)^2 |
23,159 | 1000 = 2^3 \cdot 5^2 \cdot 5 |
1,609 | 35.7/4.4 = \frac{35.7}{4.4}*\dfrac{10}{10} = \tfrac{357}{44} |
40,551 | 0 = (-1)^3 - 3 \cdot (-1) + 2 \cdot (-1) |
4,442 | 12 \cdot x^3 + 8 \cdot x^2 - x + (-1) = \left(x + \frac{1}{2}\right) \cdot \left(12 \cdot x^2 + 2 \cdot x + 2 \cdot (-1)\right) = 2 \cdot (x - 1/2) \cdot (6 \cdot x^2 + x + (-1)) |
-10,283 | \frac{1}{8\times n}\times 6\times \frac33 = \tfrac{1}{n\times 24}\times 18 |
-1,208 | (1/3*(-4))/7 = 1/(7*(-\dfrac14*3)) |
-5,166 | \tfrac{1}{100} \cdot 1.1 = 1.1/100 |
38,286 | \cos(2*x) = 2*\cos^2\left(x\right) + (-1) = 1 - 2*\sin^2(x) |
-9,269 | y^3\cdot 4 + 4\cdot y^2 = 2\cdot 2\cdot y\cdot y + y\cdot 2\cdot 2\cdot y\cdot y |
-2,892 | 50^{1/2} + 32^{1/2} = (25*2)^{1/2} + (16*2)^{1/2} |
-2,582 | 2 \cdot \sqrt{11} = \sqrt{11} \cdot (5 + 3 \cdot (-1)) |
24,274 | 3 x + 1 = 3 (x + 3 (-1)) + 10 = 3 (x + 3 \left(-1\right)) + 5\cdot 2 |
2,538 | E^2 = E_\phi^2 + E_z^2 \Rightarrow \sqrt{E_\phi^2 + E_z^2} = E |
-20,038 | -5/8*\frac{1}{7*p + 9}*\left(9 + 7*p\right) = \tfrac{1}{72 + p*56}*(-35*p + 45*(-1)) |
-20,551 | \frac{24 \cdot c}{-8 \cdot c + 16 \cdot (-1)} = \dfrac{3 \cdot c}{2 \cdot (-1) - c} \cdot 8/8 |
-11,505 | -8 + 0\cdot (-1) - 20\cdot i = -8 - i\cdot 20 |
-1,287 | 8\cdot \frac13/(\frac12\cdot (-7)) = -\tfrac{1}{7}\cdot 2\cdot \frac13\cdot 8 |
-1,644 | \frac{29}{12}\cdot \pi - 2\cdot \pi = 5/12\cdot \pi |
11,579 | (21 + 30 + 10 + 12 + 3)/14 = \frac{1}{14}*76 |
1,880 | \int x^3 \cdot \sqrt{\left(-x + 2\right) \cdot (2 + x)}\,dx = \int \sqrt{2 \cdot 2 - x^2} \cdot x^3\,dx |
32,032 | x^2 - x \cdot 4 + 5(-1) = (x + 2\left(-1\right))^2 + 9\left(-1\right) |
-20,019 | \dfrac{p - 10}{7p + 9} \times \dfrac{8}{8} = \dfrac{8p - 80}{56p + 72} |
24,396 | -2 \cdot x^2 - 4 \cdot x + 8 \cdot \left(-1\right) + x^3 + 2 \cdot x^2 + 4 \cdot x = 8 \cdot \left(-1\right) + x^3 |
-26,462 | b^2 + g^2 - 2\cdot g\cdot b = (-b + g)^2 |
16,859 | n^2\cdot 2 + 3\cdot n + 1 = 1 + n\cdot (3 + n\cdot 2) |
48,811 | \dfrac{36}{60}\cdot 30 = 18 |
7,684 | Z^2 \cdot H^2 = \left(Z \cdot H\right)^2 |
27,301 | x^a\cdot x^d = x^{a + d} |
8,586 | -a \cdot (-\frac1b) = (0 - a) \cdot (0 - 1/b) |
27,884 | x^4\cdot 4 = (2\cdot x^2)^2 |
12,170 | \sqrt{4 + \sqrt{3}\cdot 2} = \sqrt{\left(\sqrt{3} + 1\right)^2} |
53,625 | \int \frac{1}{y * y + 4}*y^2\,dy = \int \frac{1}{y^2 + 4}*(y^2 + 4 + 4*(-1))\,dy = \int 1\,dy - 4*\int \frac{1}{y * y + 4}\,dy |
11,151 | 59 \cdot \left(93 \cdot 31 - 31 \cdot 29\right) = 59 \cdot 31 \cdot 2^6 |
27,478 | 1 = \frac{1}{0!^2} \cdot (2 \cdot 0)! |
-2,225 | \frac{1}{17}\cdot 3 = 9/17 - \frac{1}{17}\cdot 6 |
50,889 | 2^{2 k + 1} = \sum_{l=0}^{2 k + 1} \binom{2 k + 1}{l} = \sum_{l=0}^k \binom{2 k + 1}{l} + \sum_{l=k + 1}^{2 k + 1} \binom{2 k + 1}{l} |
-5,233 | 65.1 \cdot 10^{5 - 2} = 10^3 \cdot 65.1 |
4,462 | \left(-1\right) + n^2 = ((-1) + n) \cdot (1 + n) |
27,130 | 1/(f\cdot h) = 1/(h\cdot f) = 1/\left(f\cdot h\right) |
-3,404 | \sqrt{7}*\left(1 + 5 + 4\left(-1\right)\right) = \sqrt{7}*2 |
1,529 | \sin(q + \frac{1}{2} \times \pi) = \cos(\pi/2) \times \sin(q) + \sin(\pi/2) \times \cos(q) |
27,285 | \binom{4 + 2}{2} = \binom{4 + 2}{4} = \dfrac{1}{4!\cdot 2!}6! = 15 |
25,029 | \sum_{i=0}^l g^i = \sum_{i=0}^{l + 1 + (-1)} g^i |
37,219 | 60 = 5!/2 |
16,609 | \dfrac{1}{1! \cdot 1! \cdot 1!} \cdot \left(1 + 1 + 1\right)! = 3! = 6 |
3,526 | -(9 + y)^2\cdot 3 + 12 = 0 \Rightarrow 4 = (9 + y) \cdot (9 + y) |
32,914 | (l + 1)! = (l + 1) l! < (l + 1) \frac{1}{2^l}l^l |
27,957 | \frac1FF = \frac{F}{F} |
-10,418 | -\frac{5}{4 \cdot l} \cdot \frac55 = -\dfrac{1}{l \cdot 20} \cdot 25 |
11,705 | |x * x| = |x|^2 = (\Re{(x)})^2 + (\Im{(x)})^2 |
12,308 | (2*j + 1) * (2*j + 1) = 4*j^2 + 4*j + 1 = 4*(j^2 + j) + 1 |
2,728 | 1 + n^3 = (n + 1)*(n^2 - n + 1) |
48,440 | 377 = 13*29 |
11,479 | \frac{1}{676} = \frac{1}{52} \cdot 2 \cdot \frac{1}{52} \cdot 2 |
10,027 | 0 = -2 \cdot \gamma + x \implies x = \gamma \cdot 2 |
-1,409 | 7/2\cdot \frac{7}{2} = 7\cdot \frac{1}{2}/\left(2\cdot 1/7\right) |
33,904 | e^{i\cdot x\cdot \pi} = \left(e^{i\cdot \pi}\right)^x = \left(-1\right)^x |
21,136 | 25^{2 + k} = 5^{4 + k \cdot 2} |
200 | n*2 + 1 = -n^2 + (1 + n)^2 |
-19,102 | \frac{1}{15} = A_s/(36 \pi)\cdot 36 \pi = A_s |
-656 | (e^{\pi i/12})^{20} = e^{20 \frac{i\pi}{12}} |
15,087 | x\cdot e_1 + e_2\cdot y + e_3\cdot z = e_3\cdot z + x\cdot e_1 + y\cdot e_2 |
37,050 | 2 = 9/16\cdot \left(-\frac23\right) + \frac{19}{8} |
17,939 | 2 + e^{2 \times r} + e^{-2 \times r} = (e^r)^2 + 2 \times e^r \times e^{-r} + (e^{-r})^2 = (e^r + e^{-r})^2 |
-1,727 | -\pi \frac{1}{6}5 = \frac{\pi}{3} - \dfrac{7}{6} \pi |
6,732 | s^4 + 256\times \left(-1\right) = \left(s \times s - 4^2\right)\times \left(s \times s + 4^2\right) = (s + 4\times (-1))\times (s + 4)\times (s^2 + 16) |
15,190 | \tfrac{1}{(1 - x^2)^{1/2}} = \frac{d}{dx} \sin^{-1}\left(x\right) |
4,712 | \left(y + y^2/2! + \dfrac{1}{3!}*y^2 * y + \dotsm\right)^{-1} = \frac{1}{\left(-1\right) + e^y} |
-8,405 | \left(-4\right)*5 = -20 |
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