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int64 -30,985
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32,114 | b \cdot a - a - b = -b + a \cdot (\left(-1\right) + b) |
46,250 | 8 \frac{7!}{x! (7 - x!)} = \frac{1}{x! (8 + (-1) - x)!} 8! = \frac{8!}{x! \left(8 - x + 1\right)!} |
8,710 | 1 + m^5 \cdot 6 + 15 \cdot m^4 + 20 \cdot m^3 + 15 \cdot m^2 + m \cdot 6 = -m^6 + (1 + m)^6 |
11,096 | |gNg^{-1}|=|N|\implies gNg^{-1}=N |
1,458 | 1 + n = 2^n - \left((-1) + n\right)\cdot 2^{2\cdot \left(-1\right) + n} + 2^{4\cdot (-1) + n}\cdot \frac{1}{2!}\cdot (n + 3\cdot (-1))\cdot \left(n + 2\cdot (-1)\right) - \dots |
16,514 | 1 * 1 (1 + 1)^2/4 = \frac{4}{4} = 2 |
-7,503 | \frac{1}{2} \cdot 15 = \frac16 \cdot 45 |
25,690 | \mathbb{E}(h\cdot k) = \mathbb{E}(h)\cdot \mathbb{E}(k) |
17,530 | \frac{3}{2} \dfrac{1/2}{2}3 = \frac{3}{2}*\frac{3}{4} = \frac{1}{8}9 |
-1,869 | -5/6*\pi = -\pi*11/12 + \pi/12 |
-9,272 | -55*x^2 = -5*11*x*x |
27,274 | \xi\cdot x\cdot b = x\cdot \xi\cdot b |
23,289 | 208=256-48 |
29,766 | \frac{\partial}{\partial f} \left(u \cdot x\right) = \frac{\partial}{\partial f} (u \cdot x) |
16,187 | -z + z*2 = z |
-6,341 | \dfrac{1}{30*(-1) + z^2 - 7*z}*4 = \frac{4}{\left(z + 10*(-1)\right)*\left(3 + z\right)} |
-26,170 | \frac64 + \frac{1}{4} \cdot 14 = 1.5 + 3.5 = 5 |
30,260 | z\cdot x + i\cdot y = x\cdot z + i\cdot y + y\cdot z |
-22,289 | p^2 + 4\cdot p + 12\cdot (-1) = (2\cdot (-1) + p)\cdot (6 + p) |
11,497 | (d\cdot f)^{1 - n} = d\cdot f\cdot (d\cdot f)^{-n} = d\cdot f\cdot f^{-n}\cdot d^{-n} = d\cdot f^{1 - n}\cdot d^{-n} |
5,075 | \left(-1\right) + z/2 = \dfrac{100}{2} - z \implies z = 34 |
-22,307 | C^2 + C*3 + 2 = (1 + C)*(C + 2) |
19,729 | -\cos\left(x\right) = \cos(x - \pi) |
1,421 | \dfrac{1}{(-1) \cdot x} = \frac{1}{(-1) \cdot x} + \tfrac{0}{x} = \frac{1}{(-1) \cdot x} + \frac1x \cdot (1 - 1) = \frac{1}{(-1) \cdot x} + 1/x - \frac{1}{x} |
14,890 | 0 = \sin(x)\Longrightarrow 0 = x |
26,074 | 5 \cdot 1109 + 4999 \left(-1\right) = 546 |
19,685 | 4*k + k^2 - 2*k + 1 = 1 + k^2 + k*2 |
22,911 | 2^{1 + n}\cdot (1 + n) = \left(n + 1\right)\cdot 2\cdot 2^n |
-6,137 | \frac{1}{3*(x + 9)}*4 = \frac{4}{27 + 3*x} |
11,771 | -1/(\sqrt{3}) = \tan(5\cdot \pi/6) |
43,245 | 80 \cdot 11 + 1 = 881 |
19,626 | |1/x - \frac{1}{3}| = \frac{1}{3 \cdot x} \cdot |x + 3 \cdot (-1)| \lt \dfrac16 \cdot |x + 3 \cdot (-1)| |
1,431 | -\frac{1}{n + 1} + \tfrac{1}{(-1) + n} = \dfrac{2}{(-1) + n^2} |
34,889 | 3\left(-1\right) + 36 = 33 |
8,223 | \cos^\sin{z}{z} = (\cos^2{z})^{\tfrac{1}{2} \cdot \sin{z}} = \left(1 - \sin^2{z}\right)^{\sin{z/2}} |
980 | \left(\frac1a\cdot a\cdot x\right)^2 = \dfrac{x}{a}\cdot \frac{a\cdot x}{a}\cdot a |
-29,004 | -35.5 = \dfrac{1}{2}(-27 - 44) |
2,764 | 1 = 15*x + 4*\gamma\Longrightarrow x = -1,\gamma = 4 |
29,454 | \tan\left(z + 2 \cdot \pi\right) = \tan(z) |
34,249 | \sin{5/2} - \left(\frac{5}{5 + 1}\right)^{1/2} = -0.314 \dots < 0 |
31,933 | (-1) + 2 + 2 + 2 + (-1) + (-1) = 3 |
5,703 | \bar{z}\cdot (T^2 - \lambda^2) = \bar{z}\cdot (T + \lambda)\cdot (-\lambda + T) |
-9,145 | t*2*3*7*t = 42*t^2 |
-18,420 | \frac{x + x^2}{x^2 - 6x + 7(-1)} = \frac{x*\left(x + 1\right)}{(x + 1) (x + 7(-1))} |
6,250 | \mathbb{E}(D_2*D_1) = \mathbb{E}(D_2)*\mathbb{E}(D_1) |
25,243 | π = π\times 2/2 |
-12,152 | \dfrac15 = \frac{s}{8 \cdot \pi} \cdot 8 \cdot \pi = s |
6,590 | \frac{1}{2} (-1 + 9) = 4 |
16,595 | \sin(x + π*2) = \sin{x} |
30,199 | B = X^2 \Rightarrow B^{\dfrac{1}{2}} = X |
8,802 | a \cdot p \cdot x + d \cdot x \cdot q = x \cdot (d \cdot q + a \cdot p) |
-25,073 | \sec^2{4*x}*\tan{4*x}*8 = d/dx \sec^2{4*x} |
41,584 | 4\cdot 17 + 3\cdot (-1) - 2\cdot 5 = 68 + 3\cdot \left(-1\right) + 10\cdot (-1) = 55 |
30,446 | 1 = x \cdot e^{x \cdot 6} \Rightarrow x \approx 0.2387 |
11,938 | n \cdot 4 + 4 = 4 \cdot (1 + n) |
-20,803 | \dfrac11 10*5/5 = \frac{1}{5} 50 |
-16,424 | 28^{1 / 2}*8 = (4*7)^{1 / 2}*8 |
-679 | e^{12*i*\pi/12} = (e^{\pi*i/12})^{12} |
11,325 | 1/\left(\dfrac56\cdot 6\right) = \dfrac15 |
51,535 | \cos{x} = \cos(\dfrac12\times x + \frac12\times x) = \cos^2{\frac{x}{2}} - \sin^2{\frac{x}{2}} = 1 - 2\times \sin^2{\frac{x}{2}} |
23,483 | r \cdot r^r = r^{r + 1} |
-1,817 | \tfrac{\pi}{12} + \pi = \pi \frac{13}{12} |
-18,617 | 5x + 5 = 7 \cdot (3x + 9) = 21 x + 63 |
27,892 | a\cdot z + d = \dfrac{1}{z} rightarrow z^2\cdot a + d\cdot z + (-1) = 0 |
-20,648 | -\frac{48}{24 - t \cdot 60} = 6/6 \cdot (-\frac{1}{4 - 10 \cdot t} \cdot 8) |
-549 | (e^{\frac{1}{12}\cdot 19\cdot π\cdot i})^6 = e^{6\cdot π\cdot i\cdot 19/12} |
7,151 | (1 + x + \dots + x^5)^8 = (\frac{1 - x^6}{1 - x})^8 = \frac{1}{\left(1 - x\right)^8}\cdot (1 - x^6)^8 |
3,021 | \sin\left(x + z\right) = \cos(z)\cdot \sin(x) + \sin(z)\cdot \cos(x) |
25,371 | \pi*20 = \pi*8 + 8*\pi + \pi*4 |
35,409 | \binom{F}{-k + F} = \binom{F}{k} |
-4,464 | x^2 - x + 20*(-1) = (x + 5*\left(-1\right))*(x + 4) |
-20,080 | -\frac{54}{54 \cdot (-1) + 6 \cdot l} = -\frac{1}{l + 9 \cdot (-1)} \cdot 9 \cdot \frac{6}{6} |
27,160 | 1/52 - \dfrac{1}{52} \cdot 1/51 = \frac{1}{52} \cdot 50/51 |
2,880 | x \cdot 2 + (-1) = (-\dfrac12 + x) \cdot 2 |
17,473 | 2^x + (-1) + 2^x = 2 \cdot 2^x + (-1) = 2^{x + 1} + \left(-1\right) |
-22,347 | (p + 1) \cdot (p + 10 \cdot (-1)) = 10 \cdot \left(-1\right) + p^2 - p \cdot 9 |
-20,969 | \dfrac{1}{z*9 + 18 (-1)} (90 \left(-1\right) + 9 z) = \frac{10 (-1) + z}{2 (-1) + z}*9/9 |
25,094 | b < -2 \Rightarrow 2 \lt -b |
53,102 | \frac{\text{d}y}{\text{d}x} = (y + x) \cdot (y + x) \Rightarrow 1 + \frac{\text{d}y}{\text{d}x} = \frac{\partial}{\partial x} (y + x) = 1 + (y + x)^2 |
-23,404 | \frac{4\cdot 1/5}{6} = \frac{2}{15} |
9,156 | x*f = x * x * x*f^3 = (f*x) * \left(f*x\right)^2 = f*x |
-2,772 | 48^{1 / 2} + 12^{1 / 2} + 3^{1 / 2} = (4*3)^{1 / 2} + 3^{1 / 2} + (16*3)^{\dfrac{1}{2}} |
-7,956 | \frac{i + 8}{-2 + i} = \dfrac{1}{i - 2}\cdot (i + 8)\cdot \dfrac{1}{-2 - i}\cdot \left(-2 - i\right) |
-10,475 | -\frac{21}{2} = -\frac12 \cdot 21 |
14,658 | k*r_0*\pi*2/\left(2*\pi*r_1\right) = k*r_0/r_1 |
27,177 | \dfrac{1}{(2 \cdot l + 2) \cdot (1 + 2 \cdot l)} = \frac{1}{(2 + l \cdot 2)!} \cdot (2 \cdot l)! |
-493 | \dfrac{\pi}{2} = \frac{17}{2}*\pi - 8*\pi |
18,741 | \frac{1}{5 + V^2} \times (20 + V \times V \times 2) = 2 + \frac{10}{V^2 + 5} |
6,103 | px + pz = p \cdot (z + x) |
35,414 | 5 - \frac17 = \frac{1}{7}\times ((-1) + 35) |
-30,803 | 4\times x^2 + 24 = 4\times (x^2 + 6) |
8,636 | b \cdot C \cdot \frac{l}{b \cdot C} \cdot C = l \cdot C = b \cdot \frac{l}{b} \cdot C |
42,433 | \|g + 0*(-1)\| = \|g\| |
7,402 | A^{2n} = 0 \Rightarrow 0 = A^n |
-15,700 | \frac{\dfrac1a \frac{1}{z^4}}{a^3 z^3} = \dfrac{1/a \frac{1}{z^4}}{z^3 a^3}1 |
18,857 | \frac{50}{17 \cdot 16} = \frac{1}{16} \cdot 2 + \tfrac{1}{17} |
-1,378 | \frac45 \cdot \frac13 \cdot 2 = \dfrac{4 \cdot 1/5}{3 \cdot \dfrac{1}{2}} |
-9,351 | -y \cdot y\cdot 121 = -y\cdot 11\cdot 11 y |
31,549 | z^3 + z^2 - 10*z + 8 = (4 + z)*(z + \left(-1\right))*(z + 2*(-1)) |
20,314 | 9 \cdot x^4 \cdot 2 \cdot x + 6 \cdot x^5 + x \cdot x \cdot 5 \cdot 4 \cdot x^3 = 44 \cdot x^5 |
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