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34,582 | \cos(x) = 2 \cos^2(x/2) + \left(-1\right) = 1 - 2 \sin^2(x/2) |
24,800 | \frac{1/3}{\dfrac{1}{3} \cdot (1 + x)} = \frac{1}{x + 1} |
30,226 | y = y/\|y\| \|y\| |
28,812 | x^\zeta x^z = x^{z + \zeta} |
26,198 | 12130303122=2*3^3*7*59*543911 |
380 | \|\int a\,dz\|^2 = \|I\|^2 = I \cdot I = I \cdot \int a\,dz |
2,750 | -g \cdot (-f) = f \cdot g |
-29,431 | \frac{3*12}{5} = \frac{36}{5} |
8,604 | z * z + 3*z + 2*(-1) = \dfrac{1}{z + 1}*(z^3 + z^2*4 + z + 2*\left(-1\right)) |
-1,380 | -\dfrac19\cdot 7\cdot (-9/7) = \left(1/7\cdot \left(-9\right)\right)/((-9)\cdot \dfrac{1}{7}) |
-25,665 | \frac{\text{d}}{\text{d}r} (4*r^3 + r) = 3*4*r * r + 1 = 12*r^2 + 1 |
47,364 | \frac{1}{0.25}*0.5 = 2 |
-4,553 | \frac{\epsilon \cdot 7 + 20 \cdot (-1)}{\epsilon^2 - \epsilon \cdot 6 + 8} = \frac{3}{2 \cdot (-1) + \epsilon} + \dfrac{4}{\epsilon + 4 \cdot (-1)} |
22,973 | 12 = \frac{1}{3} 36 |
-19,485 | \frac{7}{3}\cdot 7/9 = \dfrac{7\cdot 7}{3\cdot 9} = \frac{49}{27} |
-18,322 | \frac{1}{-6*t + t^2}*\left(t^2 + t*3 + 54*(-1)\right) = \frac{1}{t*(t + 6*(-1))}*(6*(-1) + t)*\left(t + 9\right) |
-11,798 | \frac{4}{81} = \left(\frac{1}{9}\cdot 2\right) \cdot \left(\frac{1}{9}\cdot 2\right) |
27,566 | 2/3 \times 2/3 = 4/9 |
23,976 | \left(AB = C \Rightarrow \dfrac1AC = AB/A\right) \Rightarrow B = C/A |
16,755 | pq = (-(q \cdot q + p^2) + (p + q)^2)/2 |
20,199 | e^{X + Y} = e^X e^Y\Longrightarrow (X,Y) = 0 |
37,623 | 1 + 2 + 3 + \cdots + m = m + 2 |
5,227 | (\lambda - \sigma) \times (\lambda - \sigma) = \lambda \times \lambda - 2 \times \sigma \times \lambda + \sigma^2 |
1,936 | z + 1 = \dfrac{\pi}{2} \cdot 3 + \cos(\pi \cdot 3/2) \Rightarrow \pi \cdot 3/2 + 2 \cdot (-1) = z |
14,452 | K\times N\times g = N\times g\times K |
-9,178 | -z \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times z = -96 \times z^2 |
9,352 | 2*x_i + \left(-1\right) = x_i |
1,873 | (a*c)^2 = c^2*a * a |
13,314 | \sin(h) = x rightarrow h = \operatorname{asin}(x) |
37,810 | \log_e(z) + \log_e\left(y\right) = 0\Longrightarrow 0 = \log_e(z*y) |
-18,258 | \frac{z}{(6\cdot (-1) + z)\cdot (6\cdot \left(-1\right) + z)}\cdot (z + 6\cdot \left(-1\right)) = \frac{z^2 - z\cdot 6}{36 + z \cdot z - 12\cdot z} |
10,964 | 2\cdot \frac34 = \frac{3}{2} |
-9,345 | 2 \cdot 3 \cdot 5 \cdot m + 2 \cdot 5 = 10 + m \cdot 30 |
-20,718 | 4/4 \cdot (-3 \cdot z + 9 \cdot \left(-1\right))/6 = (36 \cdot (-1) - 12 \cdot z)/24 |
6,561 | \tfrac{1}{8} = \frac{\frac12}{2} \cdot 1/2 |
-30,899 | 4 = 8\cdot (-1) + 3\cdot 4 |
10,253 | \frac{r_n - 1/(r_n)}{r_n + (-1)} = 1 + \frac{1 - 1/(r_n)}{r_n + \left(-1\right)} \geq 1 + \frac{1}{2 \cdot (r_n + \left(-1\right))} |
3,065 | 2 - \dfrac{2}{3 - x} = \frac{1}{3 - x} \cdot (4 - 2 \cdot x) = \dfrac{2}{3 - x} \cdot (2 - x) |
47,953 | (-1) + 2^{11} = 23\cdot 89 |
22,219 | 3/8 + 1/8 = \frac{1}{8} \cdot 4 = \frac{1}{2} |
26,329 | 0 = \left|{(M - x)^R}\right| = \left|{M^R - x}\right| |
29,070 | B\cdot X\cdot x = x\cdot B\cdot X |
14,582 | (-\alpha + 1)^{i/2} \cdot (1 - \alpha)^{\dfrac{i}{2}} = \left(1 - \alpha\right)^i |
30,665 | \frac{1}{18}*2 = 1/(3*6) + \frac{1}{3*6} |
16,834 | a + f = 16\Longrightarrow -f + a = 1 |
19,353 | x^{\frac{1}{2}}*V = x^{\frac{1}{2}}*V |
24,732 | \dfrac{1}{l + 2*(-1)} - \dfrac{1}{l + 2} = \frac{1}{l^2 + 4*(-1)}*4 |
-6,098 | \frac{1}{36 + z*4} 5 = \frac{1}{4 \left(z + 9\right)} 5 |
27,807 | \frac{1}{x + (-1)}(x^2 + (-1)) = \frac{1}{x + (-1)}\left(x + 1\right) (x + (-1)) = x + 1 |
-10,613 | 4/4\cdot (-\frac{4\cdot z + 3}{3\cdot z + 2}) = -\dfrac{16\cdot z + 12}{8 + z\cdot 12} |
2,366 | (2 + x)/(\left(-1\right)*x) = \frac{y}{\left(-1\right)*(y + 4*(-1))}\Longrightarrow y = 2*x + 4 |
31,191 | -b\cdot (-e) = b\cdot e |
44,880 | \frac{(1 - y) \cdot e^y}{y + e^y} = \frac{1 - y}{1 + y \cdot e^{-y}} = (1 - y) \cdot \left(1 - y \cdot e^{-y} + y^2 \cdot e^{-2 \cdot y} - \dotsm\right) |
13,470 | (-1) + \tan{\frac12 π} = 1 + \tan{\frac12 π} |
6,882 | z^2 = \sqrt{z}\cdot \sqrt{z}\cdot \sqrt{z}\cdot \sqrt{z} |
-11,646 | 22 i - 15 + 8 = -7 + i*22 |
5,714 | B = y \cdot k \Rightarrow y = B/k |
26,416 | a^{\dfrac1d} = a^{1/d} |
-14,249 | (8 + 4 \times 10) - 5 \times 9 = (8 + 40) - 5 \times 9 = 48 - 5 \times 9 = 48 - 45 = 3 |
-25,510 | \frac{\mathrm{d}}{\mathrm{d}t} (\frac{1}{t + 2} \times 4) = -\dfrac{4}{(t + 2)^2} |
2,943 | e^l = e^{1/(\frac1l)} |
6,767 | b\times (-a) = -b\times a |
-522 | -30 \times \pi + \pi \times 361/12 = \pi/12 |
33,378 | \sum_{x=1}^n (x + 1) = \sum_{x=1}^n x + \sum_{x=1}^n 1 |
30,624 | \frac{1}{(3(-1) + 4)!*3!}4! + \frac{1}{2! (6 + 2\left(-1\right))!}6! = 19 |
-605 | e^{17 \frac{7\pi i}{6}} = \left(e^{\frac{\pi i*7}{6}}\right)^{17} |
21,554 | 1 + \cdots + t^{1 + n} = \frac{1}{-t + 1}\cdot \left(1 - t^{1 + n} + t^{1 + n}\cdot (-t + 1)\right) |
-6,201 | \frac{6}{(t + 2)\cdot (2 + t)}\cdot (t + 2) - \frac{(2 + t)\cdot 2}{(t + 2)\cdot (2 + t)} + \frac{6\cdot t}{(t + 2)\cdot (t + 2)} = \dfrac{6\cdot (2 + t) - 2\cdot \left(2 + t\right) + 6\cdot t}{\left(t + 2\right)\cdot \left(2 + t\right)} |
5,338 | \sum_{n=0}^\infty \left(n + 1\right) \cdot x^n = \frac{\partial}{\partial x} \sum_{n=0}^\infty x^n |
29,870 | (g_2 + (-1))/2 = \dfrac{1}{-1} \cdot (b + 3 \cdot (-1)) = (g_1 + 4 \cdot (-1))/1 = j \implies 1 + 2 \cdot j = g_2\wedge b = -j + 3\wedge g_1 = j + 4 |
44,045 | \tan^{-1}\left(0\right) = 0 |
30,440 | 1 - \dfrac194 = 5/9 |
-1,988 | 5/4 \pi - \pi \tfrac{1}{12}19 = -\frac{\pi}{3} |
-4,700 | -\frac{1}{y + 2} - \dfrac{1}{5 + y}\cdot 3 = \frac{11\cdot (-1) - y\cdot 4}{y^2 + y\cdot 7 + 10} |
21,775 | \left(l + (-1)\right)! \times (l + 1)! = \frac{l + 1}{l + (-1)} \times l! \times l! > l! \times l! |
-3,562 | \frac{1}{k^2}*k*110/33 = \dfrac{k}{33*k^2}*110 |
17,690 | (-1) + d \cdot x = 0\Longrightarrow 1 = d \cdot x |
-3,690 | 4/3\cdot p^2 = p^2\cdot 4/3 |
15,283 | \int 1*2 \pi s\,\mathrm{d}s = 2 s s/2 \pi = \pi s^2 |
8,609 | \binom{l}{k} = \tfrac{1}{\left(l - k\right)!\cdot k!}\cdot l! |
36,427 | (1 - p)^4 \cdot p + (1 - p)^5 = (1 - p)^4 \cdot (p + 1 - p) = (1 - p)^4 |
6,830 | e^{v + u} = e^v \cdot e^u |
2,810 | z^r - b^r = (-b + z) (z^{r + (-1)} + z^{r + 2\left(-1\right)} b + ... + b^{r + 2\left(-1\right)} z + b^{(-1) + r}) |
12,995 | (-f + x)^2 = x^2 - 2\cdot f\cdot x + f^2 |
21,012 | (d\cdot y)^2 = (d\cdot y)^2 |
9,764 | \theta^3 + (-1) = (1 + \theta^2 + \theta) ((-1) + \theta) |
771 | -d + p = -p*(-\frac1d + 1/p)*d |
28,116 | |\frac{5x^2 + 7}{2x^2 - x} - \frac{1}{2}5| = |\frac{1}{2x * x - x}(5x^2 - 5x^2 + \dfrac52 x + 7)| = |\tfrac{1}{2x^2 - x}(\frac{5}{2} x + 7)| |
-20,724 | \frac66 \times \dfrac{n + 9 \times (-1)}{4 - 9 \times n} = \frac{1}{-n \times 54 + 24} \times (6 \times n + 54 \times (-1)) |
-26,408 | \dfrac{1}{z^4}\cdot z^3 = z^{-4 + 3} = 1/z |
-19,309 | 7/1\cdot \frac{9}{2} = \frac{1}{2}\cdot 9/\left(\frac{1}{7}\right) |
2,147 | (1 + 1)^x = \binom{x}{0} + \binom{x}{1} + \binom{x}{2} + ... |
12,675 | \left[a_x,b_x\right] \approx [a_y, b_y]\Longrightarrow \left[a_x, b_x\right] \approx [a_y,b_y] |
1,275 | \sin(z) = \sin(z + 2 \times \pi) |
23,344 | z - x + 1 = z - \left(-1\right) + x |
-22,264 | (8 + r) \cdot (r + 6) = r \cdot r + 14 \cdot r + 48 |
27,749 | 31 + (x^2 + 4\cdot x + 9)\cdot (4\cdot (-1) + x) = x^3 - x\cdot 7 + 5\cdot (-1) |
-30,343 | 0 = \left(r \cdot w_0\right)^2 + 3 \cdot r \cdot w_0 + 18 \cdot (-1) = (r \cdot w_0 + 6) \cdot (r \cdot w_0 + 3 \cdot (-1)) |
17,141 | -h + f - x = -h + f - x |
18,392 | 6 \cdot x^2 + \varepsilon \cdot x \cdot 11 - \varepsilon^2 \cdot 35 = (7 \cdot \varepsilon + x \cdot 2) \cdot \left(-5 \cdot \varepsilon + x \cdot 3\right) |
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