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23,505 | \tan(2 x) = \frac{\sin(x \cdot 2)}{\cos(x \cdot 2)} |
15,286 | (-1) + x * x = (x + (-1))*(x + 1) |
3,684 | ((-1)\cdot (-1))^{1 / 2} = \left((-1) \cdot (-1)\right)^{\frac{1}{2}} = |-1| = 1 |
3,242 | s\cdot i\cdot x\cdot 2\cdot \frac12\cdot r = s\cdot r\cdot i\cdot x |
31,592 | 0 = n^2 + 5 \cdot n + 12 \cdot (-1) \Rightarrow n^3 = 60 \cdot (-1) + n \cdot 37 |
37,242 | 8*6*5 = 240 |
13,058 | 8 + 2 \cdot y = 104 \Rightarrow y = \frac12 \cdot (104 + 8 \cdot \left(-1\right)) = 48 |
3,267 | \left(y + 2\right) \cdot (y + 3) = 6 + y^2 + 5 \cdot y |
14,823 | t_i \cdot t_i = t_i^2\cdot \frac33 |
4,378 | 5 + z*2 = 2z + 2 + 3 |
13,564 | Q - z = j \cdot s \Rightarrow j = \frac1s \cdot (-z + Q) |
22,471 | \frac{1}{x + 2} \cdot \left(2 \cdot x^4 + 1\right) = 0 + \tfrac{2 \cdot x^4 + 1}{x + 2} |
17,348 | \left(1 + m\right)! = \left(m + 1\right) \cdot m \cdot (m + (-1)) \cdot \left(2 \cdot (-1) + m\right) \cdot ... \cdot 2 |
26,531 | d^g = \frac{1}{d^{-g}} |
-3,561 | \dfrac{6q}{12q^2} = \dfrac{6}{12} \cdot \dfrac{q}{q^2} |
20,760 | \cos(-\theta\times 2 + \frac{\pi}{2}) = \sin(2\times \theta) |
4,973 | (2 \cdot (-1) + y) \cdot (y + 2) = 4 \cdot \left(-1\right) + y^2 |
8,283 | a*g = 1/(\dfrac{1}{a*g}) = \frac{1}{1/a*1/g} = 1/(\frac{1}{g}*1/a) = g*a |
27,985 | |y + (-1)| = |1 - y| \geq |1| - |y| = 1 - |y| rightarrow 3/4 \leq |y| |
17,570 | -\frac{1}{k + 1}\cdot \frac{1}{2} + \dfrac{1}{k + (-1)}\cdot 1/2 = \frac{1}{((-1) + k)\cdot (1 + k)} |
-17,282 | \frac{76.7}{100} = 0.767 |
32,920 | \frac{1}{5}\cdot 300\cdot 3 = 180 |
22,756 | |y_1|/|y_2| = |\frac{1}{y_2}\cdot y_1| |
-1,700 | \pi/2 + \pi/4 = \pi \cdot 3/4 |
27,066 | (z - y)\cdot (z^{\left(-1\right) + n} + \dots + y^{n + (-1)}) = z^n - y^n |
31,502 | 1 + x = \frac{1}{x}\left(x + x^2\right) |
28,870 | A\cdot D = B\cdot D rightarrow A\cdot B = 2\cdot A\cdot D |
12,466 | \tfrac{z_n}{1 + z_n} = 1 - \tfrac{1}{1 + z_n} |
-1,975 | \frac{1}{3}\pi + \frac{7}{4}\pi = \frac{25}{12}\pi |
-20,904 | \frac{90*(-1) + n*9}{9 - 63*n} = 9/9*\frac{10*(-1) + n}{-n*7 + 1} |
-10,539 | -\frac{10}{15 + q \cdot 9} \cdot 4/4 = -\frac{40}{60 + 36 \cdot q} |
16,197 | a \times a - b^2 = (a + b)\times \left(a - b\right) |
3,341 | 2 \cdot 999 = 1998 |
-23,492 | \frac18\cdot 3\cdot \frac{4}{9} = \frac16 |
30,562 | 2\sqrt{3}/3 = 2/(\sqrt{3}) |
37,625 | 52\cdot 144 + 144^2 = 168^2 |
8,062 | \sin{6*x}/2 = \sin{x*3}*\cos{x*3} |
28,662 | \frac1w = (M\cdot x + l\cdot w)/w = M\cdot x/w + l |
13,221 | |a_n - a_{n + k} + b_n - b_{k + n}| = |a_n + b_n - b_{k + n} + a_{n + k}| |
28,946 | 1/B = Z \cdot C \implies \frac{1}{Z \cdot B} = C |
-5,372 | 2.03 \cdot 10 = \frac{2.03}{1000} \cdot 10 = \frac{1}{100} \cdot 2.03 |
-27,521 | 2\cdot 3\cdot 5\cdot 7 = 210 |
31,163 | 4 \cdot x^2 = (2 \cdot x)^2 = 2 \cdot 2 \cdot x \cdot x |
10,604 | \sqrt{-x^2 + 1} = \sin(\arccos{x}) |
13,610 | 2^{5/12} = 1.334839\cdot \dots \approx 4/3 |
6,441 | 3\tan^2(x) = -3 + 3\sec^2(x) |
11,164 | \mathbb{E}[W_1] + \mathbb{E}[W_2] + \dots + \mathbb{E}[W_f] = \mathbb{E}[W_1 + W_2 + \dots + W_f] |
14,279 | \operatorname{acos}\left(\cos{0}\right) = \operatorname{acos}(\cos{\pi*2}) |
9,744 | 16/3 = -\dfrac23*((1 + (-1))^3 - \left(1 + 1\right) * (1 + 1)^2) |
-9,122 | -s*2*2*5 = -s*20 |
7,064 | 4 \times (k + 1) \times (k + 1) + (-1) = (2 \times k + 1) \times \left(2 \times k + 3\right) = \left(2 \times k + 1\right) \times (2 \times (k + 1) + 1) |
20,466 | \frac{1}{\frac{1}{\frac{1}{\frac{1}{25}}}} = 5^{-2(-(-1) (-1))} = 5^2 = 25 |
39,055 | j \cdot j^2 + 3 \cdot j^2 + 3 \cdot j + 1 = (j + 1)^3 |
3,684 | ((-1) \cdot (-1))^{\frac{1}{2}} = ((-1)^2)^{\dfrac{1}{2}} = |-1| = 1 |
21,642 | S \cdot X = S \cdot X |
4,014 | 24/23 = 1 + \frac{1}{23} |
-1,650 | \pi\cdot 9/4 = \pi \tfrac{1}{12}11 + \pi \frac{1}{3}4 |
10,838 | 4 = 2 t t\cdot (1 - 1/7) = 12/7 t^2 |
26,483 | 2*x - x^2 = 1 - ((-1) + x)^2 \Rightarrow \sqrt{1 - (x + (-1))^2} = \sqrt{2*x - x^2} |
3,949 | \tfrac{1}{-x + (x^2 + 1)^{1/2}} = (x \cdot x + 1)^{1/2} + x |
27,399 | (h - (g \times h \times 2)^{1/2} + g) \times (h + (g \times h \times 2)^{1/2} + g) = g \times g + h^2 |
7,816 | x + z = -1 \implies z \cdot x = -2004 |
-20,605 | \frac{q \cdot 28 + 4}{28 \cdot \left(-1\right) - 12 \cdot q} = \frac{1 + 7 \cdot q}{7 \cdot \left(-1\right) - q \cdot 3} \cdot 4/4 |
-3,346 | 176^{1 / 2} + 44^{\frac{1}{2}} = (16*11)^{1 / 2} + \left(4*11\right)^{1 / 2} |
21,670 | \mathbb{E}(X) = 0 \Rightarrow \mathbb{E}(X^2) = 0 |
35,525 | 1 + 2^{10500} + 2^{5251} = (1 + 2^{5250}) \cdot (1 + 2^{5250}) |
9,029 | (z_2 + z_1)^2 = z_2^2 + 2z_2 z_1 + z_1^2 |
-22,863 | 21\times 2/(21\times 3) = \tfrac{1}{63}\times 42 |
-7,042 | 2/12 \cdot \dfrac{4}{11} = 2/33 |
-17,752 | 8 = 50*(-1) + 58 |
29,234 | \tfrac{z^2}{2*(-1) + z} = z + 2 + \frac{1}{z + 2*(-1)}*4 |
26,924 | 39 = \left(-1\right) + 10\times 4 |
25,658 | \frac{E \cdot L}{A \cdot E} = \tan(A \cdot E \cdot L) rightarrow \arctan(\frac{E \cdot L}{E \cdot A}) = L \cdot A \cdot E |
-1,382 | -20/54 = \frac{(-20)*1/2}{54*\frac12} = -10/27 |
12,109 | (1 + k)^3 - k^3 = 3 \cdot k^2 + k \cdot 3 + 1 |
-485 | e^{10*\frac{11*i*\pi}{12}} = (e^{\frac{11*\pi*i}{12}})^{10} |
-10,609 | \frac144*\frac{3}{3z + 2} = \frac{1}{12 z + 8}12 |
34,509 | 2\cdot 1+2\cdot 4+2\cdot 9=28 |
-1,669 | -\pi\cdot \frac34 = -\tfrac{19}{12}\cdot \pi + \frac56\cdot \pi |
1,453 | 1638 = 2*3^2*7*13 = (1^2 + 1^2)*3^2 (2^2 + 1^2 + 1^2 + 1^2) \left(3^2 + 2^2\right) |
38,386 | |z^2 + 1| = z \cdot z + 1 = |z|^2 + 1 |
530 | w_2 F = -iw_1 F \Rightarrow Fw_2 = Fw_1 = 0 |
36,574 | \binom{r + 3}{r} = \binom{r + 3}{3} = (r + 1)*\left(r + 2\right)*(r + 3)/3! |
41,120 | \left(\binom{21}{4} + \binom{20}{4}\right)*60 = 5*4*3*\binom{21}{4} + \binom{20}{4}*\binom{3}{2}*5*4 |
27,031 | c^{x + 1} \coloneqq c\cdot c^x |
10,271 | {2\cdot x \choose x + (-1)} = \frac{(2\cdot x)!}{(x + (-1))!\cdot (x + 1)!} = \frac{1}{x + 1}\cdot x\cdot {2\cdot x \choose x} |
30,864 | (\psi + (-1)) \cdot (\psi + (-1)) + 1 \cdot 1 = \psi^2 - 2\psi + 2 |
36,127 | (6^{\frac{1}{2}} + 3)/6 = \frac{1}{6} \cdot 6^{1 / 2} + 1/2 |
12,680 | \frac{1}{(x + 1)*2} + \frac{1}{2*(-x + 1)} = \tfrac{1}{1 - x^2} |
13,132 | (z^2 + v^2) \cdot (x^2 + y^2) = (z \cdot x + v \cdot y) \cdot (z \cdot x + v \cdot y) + (-z \cdot y + v \cdot x) \cdot (-z \cdot y + v \cdot x) |
41,820 | 7^2 + 7\cdot 11 + 11 \cdot 11 = 13\cdot \left(2^2 + 2\cdot 3 + 3^2\right) = 13\cdot 19 |
17,775 | (y + 3\cdot (-1))\cdot (4\cdot (-1) + y)\cdot (y + 5\cdot (-1)) = 60\cdot \left(-1\right) + y^3 - 12\cdot y \cdot y + 47\cdot y |
27,678 | \frac{4}{10} = \dfrac{2}{5} |
30,551 | {-1/2 \choose 2} = \frac{1}{8}\cdot 3 |
13,458 | -{31 \choose 2}\cdot {3 \choose 1} + {82 \choose 2} = 1926 |
174 | \left(1 + y\right) (y + \left(-1\right)) = \left(-1\right) + y * y |
-4,295 | \frac{40}{36} \cdot \frac{x^2}{x^3} = \dfrac{40 \cdot x^2}{36 \cdot x^3} |
38,326 | \tan^2(\pi/6) = \dfrac{1}{3} |
-19,510 | 5\cdot 1/3/(\frac13\cdot 2) = \dfrac{1}{3}\cdot 5\cdot \frac{3}{2} |
24,004 | \theta^2 \theta^2 = \theta \theta^3 = 3\theta^2 - \theta |
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