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22,196 | \mathbb{E}[(2\cdot A + 1) \cdot (2\cdot A + 1)] = \mathbb{E}[4\cdot A^2 + 4\cdot A + 1] = 4\cdot \mathbb{E}[A^2] + 4\cdot \mathbb{E}[A] + 1 |
34,316 | \dfrac{1}{y} = \dfrac{1}{y} |
25,085 | f^3 + b^3 + h^3 + (fb + hb + fh) (f + b + h) = (f + b + h)^3 \Rightarrow 0 = f^3 + b^3 + h * h^2 |
34,843 | \cosh x + \sinh x = e^x |
956 | \sin(90 - \theta) = -\cos{90} \sin{\theta} + \sin{90} \cos{\theta} \Rightarrow \cos{\theta} |
-1,510 | \frac{20}{12} = \frac{20 \cdot 1/4}{12 \cdot 1/4} = 5/3 |
19,814 | 25^{x + 2} - 5^{2 + x*2} = ((-1) + 25)*5^{2 + 2*x} |
34,862 | x^3 = y \cdot y \cdot y = z \cdot z^2 = x\cdot y\cdot z |
30,204 | (-1) + x^4 = (x + 1)\cdot (x \cdot x + 1)\cdot ((-1) + x) |
7,941 | F \times ( i \times x, w) = F \times \left( -x, i \times w\right) = -F \times \left( x, i \times w\right) |
-5,623 | \frac{5}{s*3 + 12*(-1)} = \frac{1}{3*(4*(-1) + s)}*5 |
1,231 | 8/45 = \frac13\cdot \frac{8}{15} |
-17,468 | 64 - 37 = 27 |
1,937 | (-x^2 + 1) \cdot (-x + 1)^2 = -x^4 + 2 \cdot x^3 - x \cdot 2 + 1 |
13,306 | \dfrac{1}{3^{1 / 2}} \cdot 75^{1 / 2} = \left(75/3\right)^{1 / 2} = 25^{\frac{1}{2}} = 5 |
19,580 | 1 + h^2 + 3*h = 0 \Rightarrow h^2 = -h*3 + (-1) |
26,820 | \left((-6) + E \cdot 9 = 3 \Rightarrow 3 + 6 = E \cdot 9\right) \Rightarrow E = 1 |
14,534 | h - a = |h - a| < h - a |
20,728 | (b - c)^2 \geq 4(1 + b + c)^2 - 4(b + c) * (b + c) = 4*(1 + 2b + 2c) > 8(b + c) |
-10,291 | 16 = -10 + 20*m + 40*(-1) = 20*m + 50*(-1) |
-29,627 | \frac{\mathrm{d}}{\mathrm{d}x} (2*x^4 + x^3 + 3*x * x) = x*6 + x^3*8 + 3*x^2 |
10,427 | \left(-1\right) + A^n = (A + (-1))*(1 + A + \ldots + A^{n + (-1)}) |
-20,492 | 3/3 \cdot \frac{1}{r + 6 \cdot \left(-1\right)} \cdot (r + 10 \cdot (-1)) = \frac{r \cdot 3 + 30 \cdot (-1)}{3 \cdot r + 18 \cdot \left(-1\right)} |
10,139 | 75\cdot \dfrac{1}{180}\cdot \pi = \frac{5}{12}\cdot \pi |
27,670 | \cot{Z} - \tan{Z} = (\cos^2{Z} - \sin^2{Z})/\left(\sin{Z}\cdot \cos{Z}\right) = 2\cdot \cot{2\cdot Z} |
26,691 | a^4 + a^2 = (a^2 + a)^2 = (a*\left(a + 1\right))^2 = (a*a^4)^2 = a^{10} |
-6,393 | \frac{4}{(6 + x)*3} = \dfrac{1}{18 + 3*x}*4 |
21,051 | \frac{dp}{ds} = \frac{4p^2}{4ps} = \dfrac1sp |
35,669 | x_0\cdot f = f\cdot x_0 |
-3,246 | 2 \sqrt{5} + \sqrt{5} = \sqrt{5} + \sqrt{4} \sqrt{5} |
-30,565 | -\tfrac{243}{-81} = -81/(-27) = -\frac{1}{-9}27 = 3 |
-16,779 | -5 = 12 \cdot l^2 - 15 \cdot l - 5 \cdot 4 \cdot l - -25 = 12 \cdot l^2 - 15 \cdot l - 20 \cdot l + 25 |
3,138 | e \geq 2 \cdot (2 - l + e) \implies 4 \cdot (-1) + l \cdot 2 \geq e |
20,791 | (x^2*2 + 2y^2) (2yy' + 2x) = 4y * y * y y' + x^3*4 + 4y' y x * x + 4y^2 x |
-15,620 | \dfrac{r^{16}\cdot \frac{1}{z^8}}{\frac{1}{r^5}\cdot \frac{1}{z^5}}\cdot 1 = \tfrac{r^{16}}{\frac{1}{r^5}}\cdot \dfrac{1}{z^8\cdot \frac{1}{z^5}} = \frac{1}{z^3}\cdot r^{16 - -5} = \tfrac{r^{21}}{z^3} |
-7,381 | \dfrac{1}{13}\times 4\times \frac{1}{14}\times 5 = \frac{10}{91} |
-3,919 | \dfrac{5}{6} = \frac{1}{6}5 |
20,155 | (1^2 + 1 \cdot 1 + 2^2)^2 - (1^3 + 1^3 + 2^3)\cdot (1 + 1 + 2) = 36 + 40\cdot (-1) = -4 |
30,287 | (z + \sqrt{1 - z^2})^2 = z^2 + 2 \cdot z \cdot \sqrt{1 - z^2} + 1 - z^2 = 2 \cdot z \cdot \sqrt{1 - z^2} + 1 |
24,690 | \tfrac13 = 1/6 + 1/6 |
11,825 | -x \cdot 2 + x^2 = \left(x + \left(-1\right)\right)^2 + (-1) |
20,262 | \cos{x} = \cos^2{x/2}\times 2 + \left(-1\right) |
6,258 | \frac{5}{16} = 1/8\cdot 20/8 |
19,676 | 2 \cdot x + c_2 \cdot 4 = 0 rightarrow x = -2 \cdot c_2 |
35,378 | \frac{1}{a \cdot 1/b} = \frac{1}{a} \cdot b |
-4,631 | \dfrac{-4x + 19}{x^2 - 9x + 20} = -\frac{1}{x + 5(-1)} - \frac{3}{x + 4(-1)} |
22,389 | 2\cdot \delta\cdot x + \delta^2 = (\delta + x)^2 - x^2 |
30,914 | \cos(\phi) = -2*\sin^2(\phi/2) + 1 |
2,070 | (95 + 12 \cdot \left(-1\right)) \cdot (12 + 95) = 8881 |
4,050 | \operatorname{re}{(e^{i*x} * e^{i*x})} = \operatorname{re}{\left(e^{2*x*i}\right)} \Rightarrow \cos(x*2) = \cos^2(x) - \sin^2(x) |
26,911 | 4 = z\cdot 2 - y \Rightarrow y + 4 = 2\cdot z |
10,723 | 2 \times z \times w + w^2 + 3 = 0 = z^2 + 2 \times z \times w |
9,496 | X^2 + Y^2 = X^2 + Y^2 - 2*X*Y + 2*X*Y = (X - Y) * (X - Y) + 2*X*Y |
22,415 | x^{\dfrac{1}{2}} = x^{\tfrac{1}{2}} |
30,808 | y^3 - y^2 + 2*y + (-1) = y + 2*y^2 + 2*y + 2 = 2*y * y + 2 |
3,411 | \dfrac{\pi}{8} = -\pi/16 + 3 \cdot \pi/16 |
14,692 | \|v\|^2 = (\sqrt{v_1 \cdot v_1 + v_2^2 + v_3^2})^2 = v_1^2 + v_2^2 + v_3^2 |
20,751 | T^{\frac{1}{2}} \cdot x^{1/2} \cdot T^{1/2} \cdot x^{1/2} = T \cdot x |
12,561 | h^3 + d * d * d + x^3 - 3*d*x*h = \left(-h*x + h^2 + d^2 + x^2 - d*h - x*d\right)*(x + h + d) |
31,889 | \tan^{-1}\left(1\right) + \tan^{-1}(2) + \tan^{-1}(3) = \tan^{-1}\left(-3\right) + \tan^{-1}(3) = 0 |
24,119 | \sqrt{z + 2}*(z + 2) = (z + 2)^{3/2} |
1,734 | 2^{1 + k} + (-1) = 2^{k + 1} + (-1) |
4,720 | z^3 + z \cdot z = 2\cdot z - z^2 = 2\cdot z - 2 - 2\cdot z = 4\cdot z + 2\cdot (-1) |
4,293 | \tan(x*g) = \tan(0.5*x*g + 0.5*x*g) = \frac{\tan(0.5*x*g)}{1 - \tan^2(0.5*x*g)}*2 |
27,305 | 10836 = 3^2\cdot 2^2\cdot 7\cdot 43 |
19,496 | (-C + A) \left(C + A\right) = -C * C + A^2 |
21,503 | V \gt 1 - U \implies U \gt 1 - V |
19,929 | \left(0^X\right)^C = 0^C = 1 = 1^X = (0^C)^X |
-5,817 | \frac{1}{(6(-1) + q) (q + 10)}4 = \frac{4}{q^2 + 4q + 60 (-1)} |
27,447 | \frac{\frac{1}{19^{20}}}{\frac{1}{20^{20}}} = \tfrac{1}{19^{20}}20^{20} \approx 2.79 |
-20,066 | \frac13 3 \dfrac{1}{\left(-8\right) z} (-5 z + 2 (-1)) = \dfrac{1}{\left(-24\right) z} (-15 z + 6 (-1)) |
24,743 | x \cdot l + x = \left(l + 1\right) \cdot x |
15,231 | v = \tan^{-1}(z_2/(z_1)) \Rightarrow \tan(v)\cdot z_1 = z_2 |
-20,978 | \frac{-4\cdot t + 5}{4 - t\cdot 7}\cdot 3/3 = \frac{-t\cdot 12 + 15}{12 - 21\cdot t} |
10,596 | \dfrac{1}{x \cdot y} = \tfrac{1}{y \cdot x} |
22,105 | \mathbb{N} \coloneqq \left\{2, \dots, 3, 1\right\} |
28,443 | \left|{x}\right| \left|{-Y + \lambda \nu}\right| \left|{1/x}\right| = \left|{x}\right| \left|{\nu \lambda - Y}\right| \left|{1/x}\right| |
-9,464 | -6 r = -r*2*3 |
15,419 | (n*y + d - \eta)*\left(n*y + d - \eta\right) = (-\eta + y*n + d)^2 |
-5,773 | \frac{1}{3 \times (o + 9)} = \frac{1}{27 + 3 \times o} |
-4,899 | 0.78\times 10^{2 + 0\times \left(-1\right)} = 10^2\times 0.78 |
35,737 | \cot(1) \sin\left(1\right) = \cos(1) |
11,268 | 4\cdot j + 7 = 2\cdot (2\cdot j + 3) + 1 |
8,392 | x^4 + (-1) = (1 - x)\cdot (1 + x)\cdot ((-1) - x^2) |
10,464 | ma xh' = ah' \frac{ax}{a}1 m |
18,397 | 2^{l + 1} = 2\cdot 2^l \geq 2\cdot 4\cdot l \cdot l > 4\cdot l^2 + 8\cdot l + 4 = 4\cdot (l \cdot l + 2\cdot l + 1) = 4\cdot (l + 1)^2 |
-1,715 | \pi*\frac{13}{6} = \pi*\frac43 + \pi*\frac{5}{6} |
-30,859 | \frac{12}{\left(-1\right) + z} = \frac{1}{-z^2 + z^4}(z^3*12 + 12 z^2) |
392 | 1/4 = -\dfrac{11}{16} + \frac{5}{16}\cdot 3 |
15,872 | Z = \frac14X + Z/2 \implies Z = X/2 |
28,335 | \left(d^2 \sinh^2(t) + d \cdot d\right)^{1/2} = d \cdot (\sinh^2(t) + 1)^{1/2} = d\cosh(t) |
18,568 | x^2 + y \cdot y + z^2 + 2\cdot (z\cdot x + y\cdot x + z\cdot y) = 36\Longrightarrow 9 = z\cdot x + y\cdot x + y\cdot z |
35,516 | \frac{1}{13}13 = 1 |
12,174 | \tfrac34 = \frac12 + 1/4 |
4,966 | -\tfrac{1}{(-1) + y_{l + 1}} + 1 = \dfrac{y_{l + 1} + 2\cdot (-1)}{\left(-1\right) + y_{l + 1}} |
24,018 | \cos(3\cdot x) = -\cos(x)\cdot 3 + 4\cdot \cos^3(x) |
7,288 | \frac{1}{\binom{4}{2}} \times (-\binom{2}{2} + \binom{3}{2}) = \frac{1}{3} |
20,657 | \dfrac{c}{4 \cdot a} = \frac{c \cdot c}{4 \cdot a \cdot c} \geq \frac{1}{(c + a)^2} \cdot c^2 |
24,739 | g_1\cdot \dotsm\cdot g_\delta = a\cdot g_1\cdot \dotsm\cdot a\cdot g_\delta = a^\delta\cdot g_1\cdot \dotsm\cdot g_\delta |
27,504 | \tfrac{1}{2}*2*2 = 2 = 1/2*0 = 0 |
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