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2,219 | D_J \cdot N_J = N_J \cdot D_J |
28,608 | \dfrac{2}{36} = \frac{1}{18} |
-2,743 | \left(1 + 2 + 4\right)*3^{1/2} = 7*3^{1/2} |
-19,676 | \dfrac{2\cdot 4}{7} = \frac{8}{7} |
12,861 | -s*s*x = -1 \implies 1/s = x*s |
3,525 | (23\cdot (-1) + g)^2 + g \cdot g = 289 rightarrow 0 = 240 + g \cdot g\cdot 2 - g\cdot 46 |
27,447 | \tfrac{\frac{1}{19^{20}}}{\frac{1}{20^{20}}} = \dfrac{20^{20}}{19^{20}} \approx 2.79 |
10,988 | 2 \cdot (-1) + x = 3 \implies 5 = x |
38,294 | 1 + 2*m^2 + 3*m = (m + 1)*\left(2*m + 1\right) |
-18,949 | 23/40 = H_x/(16\times π)\times 16\times π = H_x |
36,114 | \frac{1}{4 + 1}*(9 + 2) = \frac{1}{5}*11 |
26,193 | (y + f/2) \cdot (y + f/2) + c - \dfrac{1}{4} \cdot f \cdot f = y \cdot y + f \cdot y + c |
-1,060 | \frac{1}{5}*2/\left(\tfrac{1}{4}*\left(-5\right)\right) = -4/5*\frac25 |
26,806 | (-4)^k/(-4) = (-4)^{k + (-1)} = (-1)^{k + (-1)}*4^{k + (-1)} |
-15,711 | \dfrac{(s^5)^2}{\frac{1}{s^{12}*\frac{1}{r^{12}}}} = \frac{s^{10}}{\dfrac{1}{s^{12}}*r^{12}} |
5,576 | 2/3 \cdot \frac{1}{10} \cdot 4 \cdot \frac36 = 2/15 |
-20,107 | \frac{20 \cdot q + 28}{20 \cdot \left(-1\right) + 4 \cdot q} = \frac14 \cdot 4 \cdot \dfrac{5 \cdot q + 7}{5 \cdot (-1) + q} |
17,738 | \cos(\theta) = \sin(-\theta + \pi/2) |
-3,696 | \frac{p}{p \cdot p} \cdot 45/99 = \frac{9 \cdot 5}{11 \cdot 9} \cdot \frac{p}{p \cdot p} |
-26,572 | 9^2 - (x \cdot 2)^2 = (9 - 2 \cdot x) \cdot (9 + x \cdot 2) |
-9,460 | -2 \cdot 2 \cdot 5 \cdot p + 5 \cdot (-1) = 5 \cdot (-1) - p \cdot 20 |
13,921 | 4 + (x + 2 \cdot (-1)) \cdot (x + 2) = x^2 |
51,013 | z^9 + (-1) = \left(z - e^{i\frac{2\pi}{9}}\right) \left(-e^{-\pi \cdot 2/9 i} + z\right) \dots \cdot (z - e^{i \cdot 8\pi/9}) (z - e^{-\frac{\pi \cdot 8}{9}1 i}) (\left(-1\right) + z) |
16,990 | m = \left\{..., m, 1, 2\right\} |
-10,688 | \tfrac{5}{g\cdot 12 + 8\cdot (-1)}\cdot \frac13\cdot 3 = \frac{1}{36\cdot g + 24\cdot (-1)}\cdot 15 |
5,944 | (2\cdot k + X) \cdot (2\cdot k + X) = k^2\cdot 4 + k\cdot X\cdot 4 + X^2 |
23,645 | (1 + k)!/k! = k + 1 |
28,289 | \sin(y*2) = 2 \cos(y) \sin(y) |
-3,182 | \sqrt{7} \times \left(4 + 3 \times (-1)\right) = \sqrt{7} |
-2,814 | 10 \cdot \sqrt{13} = \sqrt{13} \cdot (1 + 4 + 5) |
38,445 | \tfrac{65}{288} = \frac{5}{2^5\cdot 3^2}\cdot 13 |
39,196 | 100*102 + 2 = \left(101 + (-1)\right)*(101 + 1) + 2 = 101^2 + (-1) + 2 = 101^2 + 1 |
-22,053 | 9/10 = \frac{1}{30}\cdot 27 |
-6,347 | \frac{2}{r^2 + r\cdot 14 + 48} = \frac{1}{(6 + r) (r + 8)}2 |
-2,233 | -\frac{1}{19} \cdot 8 + \frac{1}{19} \cdot 10 = 2/19 |
18,307 | x \cdot x = 0\Longrightarrow x = 0 |
30,381 | \left(p + (-1)\right)*(x + (-1))*\left(s + (-1)\right) = p*x*s - p*x + x*s + s*p + p + x + s + (-1) = p*x*s + \left(-1\right) + 357*(-1) |
-9,347 | -3*3*3*3 - 2*3*3*3*s = 81*(-1) - 54*s |
6,840 | 0.9025 = \tanh{x}/x \approx 1 - \frac{x^2}{3} + 2 \cdot x^4/15 |
28,422 | 1867 (-10000) + 10000 \cdot 1867 = 0 |
-20,557 | \frac{1}{(-10) x} (-18 x + 2 (-1)) = 2/2 \frac{1}{\left(-5\right) x} (-9 x + (-1)) |
32,683 | \frac{6 - 9 \cdot 0}{1 + 0 \cdot (-1)} = \frac11 \cdot 6 = 6 |
42,474 | 21\times 6 + 16\times 6 + 11\times 6 + 6\times 6 = 324 |
3,739 | \frac{19}{100} = \frac{1}{10} + \frac{1}{10} - 1/100 |
-7,164 | \frac{7}{24} = 5/8\cdot \frac{1}{9}\cdot 6\cdot 7/10 |
38,327 | V^T \cdot V = V \cdot V^T |
-26,361 | -5/3\cdot (-\frac{5}{3}) = 25/9 |
22,857 | \left(m + 1\right)^2 - 31 m + 257 = m^2 + 2m + 1 - 31 m + 257 = m^2 - 29 m + 258 |
10,120 | 3^{\frac{z}{2}} = 2^z + (-1) = 4^{\frac{1}{2}z} + (-1) |
-17,479 | 24 = 44 + 20 \cdot (-1) |
-16,884 | 4 = -2 \cdot k^2 - 5 \cdot k + 4 \cdot (-2 \cdot k) + 4 \cdot (-5) = -2 \cdot k \cdot k - 5 \cdot k - 8 \cdot k + 20 \cdot (-1) |
10,968 | x^k\cdot x^M = x^{M + k} |
-8,060 | (-52 - 14*i + 130*i + 35*(-1))/29 = \frac{1}{29}*(-87 + 116*i) = -3 + 4*i |
-28,795 | 3 = \frac{1}{1/3\times 2\times \pi}\times 2\times \pi |
4,517 | \left(77 = \left(l \cdot 3 + 1\right) \cdot 2 + 6 h + (1 + 2 k) \cdot 3 rightarrow 72 = 6 \left(h + k + l\right)\right) rightarrow h = 12 - l - k |
10,756 | n/b - n/g' = -\frac{1}{g'}*b*\dfrac{n}{b} + n/b |
32,485 | 5\cdot q\cdot 7\cdot q\cdot 3\cdot q + -3\cdot q\cdot 3\cdot q\cdot (-3\cdot q) = 105\cdot q^3 + 27\cdot q^3 = 66\cdot q |
-18,539 | t + 9\cdot \left(-1\right) = 6\cdot (3\cdot t + 2) = 18\cdot t + 12 |
7,655 | 2^{2^n}\times 2^{2^m} = 2^{2^m + 2^n} |
16,743 | \frac13 \cdot \pi = \operatorname{atan}(\sqrt{3}) |
-2,030 | \pi \cdot 23/12 = \pi + 11/12 \cdot \pi |
-2,608 | \sqrt{16\times 2} + \sqrt{9\times 2} = \sqrt{18} + \sqrt{32} |
21,505 | \frac{4}{2} + 1/2 - 2/2 = \frac{3}{2} |
12,970 | \frac{2*1/3}{3}*\frac{2}{3} = \frac{4}{27} |
29,348 | 4^5 + 45^5 + 57^5 + 90^5 + 91^5 + 98^5 = (4 + 45 + 57 + 90 + 91 + 98)^4 |
54,545 | \frac{1}{U_1}\cdot (U_2 - U_0) = \dfrac{1}{U_1}\cdot (U_2 - U_0)\cdot \frac{U_2 + U_2}{U_2 + U_0} = -\frac{U_1}{U_2 + U_0} |
-10,731 | \frac{15}{36 \cdot m + 12 \cdot (-1)} = \frac{3}{3} \cdot \frac{5}{4 \cdot (-1) + m \cdot 12} |
4,011 | x = (z^2 + (-1)) e^{(-1) + 2012 z} \implies \frac{x}{z * z + \left(-1\right)} = e^{2012 z + (-1)} |
29,999 | \sqrt {-1}\cdot \sqrt{-1}=-1 |
17,224 | \frac{\left(-2\right)\cdot x}{x^2} = -\frac2x |
32,424 | \frac{8 + (-1)}{4 + 8 + (-1)}*0.4*\frac{8}{4 + 8}*0.4 = 56/825 |
856 | a h^4 a = h^6 \Rightarrow h^4 = a h^6 a = h^9 |
11,623 | 4 - (4 + y^2 - y*4)*7 = 24*\left(-1\right) - y^2*7 + 28*y |
-1,632 | \dfrac12\cdot 3\cdot π = \frac{π}{2} + π |
-20,026 | \dfrac{56 (-1) + 56 s}{s*48 + 48 (-1)} = 7/6 \tfrac{1}{8(-1) + 8s}(s*8 + 8(-1)) |
4,874 | 2^{\frac13(n + 1)} = 2^{\frac{1}{3}}*2^{n/3} > n*2^{\frac13} |
35,111 | 1/(B\cdot Z) = \frac{1}{Z\cdot B} |
23,107 | \sqrt{1 - x \cdot x} = \cos\left(\sin^{-1}(x)\right) |
1,451 | \sin\left(Y_1 + Y_2\right) = \cos(Y_1) \cdot \sin\left(Y_2\right) + \cos(Y_2) \cdot \sin(Y_1) |
-27,491 | 8 \cdot f \cdot f = 2 \cdot 2 \cdot f \cdot f \cdot 2 |
25,174 | \sqrt{5} \cdot 6^{1/4}/50 = (\tfrac{24}{10^6})^{1/4} |
25,736 | \frac{1}{x^9} + \frac{1}{z^9} = \dfrac{1}{x^9*z^9}*(x^9 + z^9) |
18,467 | 0 = 2/3 \cdot (-6 \cdot x^2 + 1) \Rightarrow x = 1/\left(\sqrt{6}\right) |
16,391 | \frac{1}{4 + x}x = \frac{x}{4 + i + x - i} |
38,411 | G^x G^l = G^{x + l} |
30,165 | 2\cdot \cos{a}\cdot \sin{a} = \sin{a\cdot 2} |
2,574 | (e + g) \cdot f = e \cdot f + f \cdot g |
34,118 | vx^1 = vx |
8,529 | \tan\left(\operatorname{arccot}\left(t\right)\right) = 1/\cot\left(\operatorname{arccot}(t)\right) = 1/t |
20,898 | S^2 = \left(\sqrt{n + \sqrt{n + \sqrt{n + ...}}}\right)^2 = n + S |
16,035 | \frac{1}{15}*2 = 4/3 - \dfrac{6}{5} |
-719 | (e^{\dfrac{5}{6}\cdot \pi\cdot i})^4 = e^{\dfrac56\cdot i\cdot \pi\cdot 4} |
14,672 | \left((-1) + n\right)\cdot \left(2\cdot (-1) + n\right) + 4 = 6 + n^2 - n\cdot 3 |
26,116 | \sin{\frac{1}{2} \cdot C} \cdot \cos{\frac12 \cdot C} \cdot 2 = \sin{C} |
-3,062 | \sqrt{5} \cdot 7 = (1 + 2 + 4) \sqrt{5} |
19,591 | -w \times -x \times (w + x) \times 3 = \left(x + w\right)^3 - w^3 - x^3 |
-10,696 | \frac{18 (-1) + y*4}{30 y + 18} = \frac{2}{2} \frac{2y + 9\left(-1\right)}{15 y + 9} |
35,181 | (x^b)^a = (x^b)^a |
6,330 | 12 = -3 \cdot \left(3 + 2 \cdot (-1)\right) + (2 + 3) \cdot 3 |
8,360 | -\frac{1}{4} \cdot p^2 + (x + p/2)^2 + q = x^2 + p \cdot x + q |
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