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15,451 | \tan^{-1}{u} = \int \frac{1}{u \cdot u + 1}\,\mathrm{d}u |
13,753 | (-f + g\cdot 4)^2 = g \cdot g\cdot 16 - f\cdot g\cdot 8 + f^2 |
-2,494 | \sqrt{16}\cdot \sqrt{6} + \sqrt{6} + \sqrt{6}\cdot \sqrt{4} = 4\cdot \sqrt{6} + \sqrt{6} + \sqrt{6}\cdot 2 |
43,347 | 0 = 2 \times 0 + 0^2 |
-2,877 | -\sqrt{117} + \sqrt{325} = -\sqrt{9 \cdot 13} + \sqrt{25 \cdot 13} |
11,826 | 9 + x^2 - 6x = (3(-1) + x)^2 |
-18,695 | 0.8833 = (-1)\cdot 0.0359 + 0.9192 |
35,503 | x^4 - x^2 + 1 = \frac{1}{x \cdot x + 1} \cdot (1 + x^6) |
5,662 | -\sqrt{z}*3 = (z*(-3))/(\sqrt{z}) |
-4,427 | -\frac{2}{2 + x} - \frac{1}{1 + x}\times 3 = \frac{-5\times x + 8\times \left(-1\right)}{2 + x \times x + 3\times x} |
13,515 | x^2 - z^2 = (x - z)\cdot (z + x) |
21,531 | \dfrac{1}{z^2 + 1} \cdot z^2 = \frac{z^2 + 1 + (-1)}{z^2 + 1} = 1 - \frac{1}{z^2 + 1} |
-21,043 | \frac{1}{4}2*\frac{3}{3} = 6/12 |
13,896 | \left(\lambda + h\right)^2 = \lambda^2 + \lambda\cdot h\cdot 2 + h^2 |
-20,074 | \frac{1}{r + 3*(-1)}*6*r*8/8 = \tfrac{48}{24*(-1) + 8*r}*r |
-20,221 | 8/9*\frac19*9 = \frac{72}{81} |
36,733 | \frac{1}{b^n}\cdot b^x = b^{-n + x} |
19,575 | j + x = j + 1 + x + \left(-1\right) |
3,399 | 63\%\cdot x + x\cdot 24\% = 87\%\cdot x |
-21,657 | -\frac{4}{11} = -\frac{1}{11}\times 4 |
27,474 | 1 = c\cdot k\cdot 2 \implies c = \frac{1}{2\cdot k} |
-23,631 | 2*\frac{1}{3}/3 = 2/9 |
17,584 | f \cdot d^x = f \cdot d^x |
18,431 | \left(6\cdot x + 3\cdot (2\cdot l + 1) = 9 = 6\cdot \left(x + l\right) + 3 \implies l + x = 1\right) \implies 1 - l = x |
-20,478 | \frac{1}{7}\cdot 1 = \frac{1}{35\cdot q + 35\cdot (-1)}\cdot \left(5\cdot (-1) + q\cdot 5\right) |
35,619 | \dfrac{1}{2} = \frac{1}{12321} + 12319/24642 |
23,018 | \cos(x + z) = \cos{z}\times \cos{x} - \sin{z}\times \sin{x} |
32,032 | z * z - 4*z + 5*(-1) = (2*(-1) + z)^2 + 9*(-1) |
10,123 | \tfrac{2^1 \binom{2}{1}}{4^2} = 4/16 |
-8,039 | \dfrac{-7i - 9}{i - 3} = \dfrac{1}{-3 + i}(-9 - 7i) \dfrac{-3 - i}{-i - 3} |
7,071 | 100 f + 10 b + 1 + 100 f + 10 b + 2 + \cdots + 100 f + 10 b + 5 = 15 + f*100*5 + 10 b*5 |
-11,112 | \left(x + (-1)\right)^2 + b = (x + \left(-1\right)) (x + (-1)) + b = x^2 - 2x + 1 + b |
-10,337 | \tfrac{12}{p \cdot 50} = \frac{1}{p \cdot 25} 6 \cdot 2/2 |
-22,961 | 80/70 = \dfrac{8 \times 10}{10 \times 7} |
31,892 | (1 - u^{1/2})/1 + \frac{1}{u^{1/2}}*(u^{1/2} - u) = 2*(-u^{1/2} + 1) |
6,081 | z^2 + y^2 \alpha^2 + 2 \alpha y z = (z + y \alpha)^2 |
34,225 | 1 * 1 + 8^2 = 65 |
25,547 | -\dfrac{5^{\frac13}}{2} + 1 = 1 - (\dfrac15\times 8)^{-\frac{1}{3}} |
29,009 | \binom{a + g}{a} = \binom{a + g}{g} = \frac{(a + g)!}{a! \cdot g!} |
27,505 | e^{xz} = 1 + zx + x * x z^2/2! + \cdots |
-11,922 | 9.752 \times 0.1 = \dfrac{9.752}{10} |
3,799 | 18\cdot x\cdot y + 18\cdot x\cdot z + 18\cdot y\cdot z = 49 + 91\cdot (-1) = -42 \implies y\cdot x + z\cdot x + y\cdot z = -7/3 |
-19,823 | -\tfrac14 \cdot 7 = -1.75 |
-20,342 | \frac{k\cdot (-2)}{3\cdot (-1) - 3\cdot k}\cdot \frac{3}{3} = \frac{1}{-9\cdot k + 9\cdot (-1)}\cdot (k\cdot (-6)) |
6,964 | 1 + \frac{1}{n}2 = \tfrac{1}{n}(n + 2) |
-13,533 | \dfrac{1}{4 + 9}\cdot 39 = 39/13 = \frac{1}{13}\cdot 39 = 3 |
28,756 | \cos^2{R} = 1 - \sin^2{R} |
12,241 | det\left(-A\cdot B + I\cdot \lambda\right) = det\left(I\cdot \lambda - A\cdot B\right) |
25,063 | x = \frac{1}{2}\cdot x + x/2 |
13,175 | \mathbb{E}\left[R\right] = \mathbb{E}\left[-R\right] = -\mathbb{E}\left[R\right] |
5,001 | \tfrac{4\cdot \frac{1}{9}}{2} = 2/9 |
-3,342 | \sqrt{11} + \sqrt{9}\cdot \sqrt{11} = \sqrt{11}\cdot 3 + \sqrt{11} |
13,600 | 1/3 + \frac{2}{9} = 3/9 + \frac29 = \frac59 |
6,529 | m^{1 / 2} + (2 + m)^{1 / 2} - 2(m + 1)^{\frac{1}{2}} = (2 + m)^{1 / 2} - (1 + m)^{1 / 2} - (m + 1)^{1 / 2} + m^{1 / 2} |
5,131 | y/s = \cos{\theta} \Rightarrow y = s \cdot \cos{\theta} |
3,113 | d D_0 = D_0 d |
3,874 | \mathbb{E}(W + Q) = \mathbb{E}(Q) + \mathbb{E}(W) |
24,625 | P(x) := 27\cdot (-1) + x^6 + 10\cdot x^3 := 27\cdot (-1) + \left(x^3\right)^2 + x \cdot x \cdot x\cdot 10 |
-24,735 | -\frac{1}{100}\cdot 60 = -\frac{160}{100} = -1.6 |
23,639 | x = (x + T \cdot x)/2 = \frac{x}{2} + T \cdot x/2 |
33,386 | y \cdot g \cdot E = E \cdot y \cdot g |
-6,717 | \frac{7}{100} + \frac{6}{10} = \frac{7}{100} + 60/100 |
27,831 | 1.96 \times \sqrt{\tfrac{1}{4 \times n}} = \frac{1.96}{2 \times \sqrt{n}} \approx 1/(\sqrt{n}) |
-10,539 | \frac14 \cdot 4 \cdot (-\frac{10}{15 + q \cdot 9}) = -\dfrac{40}{36 \cdot q + 60} |
7,296 | 1 + t^6 = (1 + t^4 - t^2)\cdot (t^2 + 1) |
32,548 | (-\frac13 - 1)^2\cdot \frac59 + (2 - 1/3)^2\cdot \dfrac{1}{9}\cdot 4 = \frac{20}{9} |
17,611 | 4*x^2 = 2*x*2*x |
5,415 | \sqrt{2} = \alpha\Longrightarrow -\sqrt{2} + \alpha = 0 |
42,196 | 2^k = \left(1 + 1\right)^k |
24,782 | -y/x = \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{1}{10 \cdot y - 6 \cdot x} \cdot (6 \cdot y - 10 \cdot x) |
6,846 | \frac12*1/2 + \frac12*1/2 = 1/2 |
29,453 | y^2 + x^2 = r^2 \Rightarrow r = \sqrt{x^2 + y^2} |
20,266 | \frac{1^q}{1^q} = 1^q |
-5,466 | \frac{1}{4\cdot q + 40} = \frac{1}{4\cdot (q + 10)} |
28,540 | \binom{j + (-1) + 1 + (-1)}{j + (-1)} = \binom{j + (-1)}{(-1) + j} |
23,976 | \left(H_1 = H_2\cdot B \Rightarrow H_1/(H_2) = H_2\cdot B/\left(H_2\right)\right) \Rightarrow B = H_1/(H_2) |
3,056 | x \cdot f \cdot z \cdot f = x \cdot z \cdot f^2 |
-8,802 | 5 \times 6 \times 4 = 120 |
-10,248 | -\dfrac{1}{50}\cdot 38 = -0.76 |
-23,316 | 5/9*\frac{1}{4} 3 = \frac{5}{12} |
-9,107 | 56.1\% = \frac{1}{100}56.1 |
27,584 | \frac{1}{20}9 = \frac15 + \frac{1}{4} |
-21,093 | \dfrac{1}{3}*2*2/2 = 4/6 |
8,335 | \sin(x)\cdot \cos(x)\cdot 2 = \sin(2\cdot x)\Longrightarrow 4\cdot \sin^2(x)\cdot \cos^2(x) = \sin^{22}(x) |
-6,392 | \frac{k}{k^2 + 15*k + 54} = \frac{1}{(k + 6)*(k + 9)}*k |
19,222 | d - c = \frac{-c^3 + d^3}{c^2 + d d + d c} |
47,464 | 0! + 3 \cdot 1! = 4 = 2 \cdot 2! |
-3,038 | \sqrt{6}\cdot 4 + 5\cdot \sqrt{6} = \sqrt{25}\cdot \sqrt{6} + \sqrt{16}\cdot \sqrt{6} |
-20,336 | \frac{2}{-y \cdot 7 + 5 \cdot (-1)} \cdot 2/2 = \frac{1}{-14 \cdot y + 10 \cdot \left(-1\right)} \cdot 4 |
51,082 | a + (x - \alpha) \cdot (x - \gamma) \cdot (-\beta + x) = a + x^3 - (\alpha + \beta + \gamma) \cdot x^2 + (\alpha \cdot \gamma + \beta \cdot \alpha + \beta \cdot \gamma) \cdot x - \alpha \cdot \beta \cdot \gamma |
18,935 | 15 + t = t \cdot \dfrac14 \cdot 5 rightarrow 60 = t |
-4,797 | 1\times 10^{3 - -1} = 10^4\times 1 |
23,104 | 1 + 4\cdot t = -7 + 4\cdot (2 + t) |
32,823 | \|y\| = \|y\| = |y| \|1\| |
19,116 | \frac{2}{z + 2} = \frac{2}{z + (-1) + 3} = \frac{2}{3} \cdot \frac{2}{(z + (-1))/3 + 1} |
17,375 | y'*z - x'*y = -y'*z + x'*y |
8,511 | \sin(x) + \sin(y) + \sin\left(\theta\right) = 0 = \cos\left(x\right) + \cos(y) + \cos(\theta) |
30,678 | l \cdot l = l^2 - 2\cdot l + 1 + (-1) + 2\cdot l = (l + (-1))^2 + 2\cdot l + (-1) |
1,878 | 12*34 = (10 + 2)*\left(30 + 4\right) = 3*10 * 10 + \left(2*3 + 4\right)*10^1 + 2*4*10^0 |
13,684 | 1 + n \cdot 4 = 1 + n \cdot 2 \cdot 2 |
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