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int64 -30,985
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29,006 | (\sqrt{5} + 1)/2 = \tfrac{1}{2} + \dfrac{\sqrt{5}}{2} |
3,301 | \left(z = 1 + z \implies z^2 = 1 + z^2 + 2 \cdot z\right) \implies 2 \cdot z + 1 = 0 |
-1,947 | -7/6\cdot \pi = -17/12\cdot \pi + \pi/4 |
3,869 | \tfrac{(x\cdot m_A)^9}{\left(x\cdot m_A\right)^2} = \left(m_A\cdot x\right)^7 |
35,130 | 2^{-2 + 2\cdot (-1)} = \dfrac{1}{(2 + 2)^2} |
5,297 | a_1/x + \dfrac{a_2}{x} = (a_2 + a_1)/x |
4,771 | \varphi = \dfrac{1}{2} \cdot \left(1 + \sqrt{5}\right) = 1 + 1/\varphi |
-7,598 | \frac{1}{-i*2 + 2}(6 - 14 i) \dfrac{2 + 2i}{2 + i*2} = \frac{-14 i + 6}{2 - i*2} |
19,339 | \frac{2}{2} \cdot 1/6 = 1/6 |
-5,059 | 10^{4 - 3}*16.8 = 16.8*10^1 |
-20,286 | -10/7*\dfrac33 = -30/21 |
4,941 | X = B \cdot X - B \cdot X \Rightarrow X^2 = -X^2 \cdot B + X \cdot X \cdot B |
29,450 | \cos(A)\cdot \cos\left(B\right) + \sin(B)\cdot \sin(A) = \cos(A - B) |
26,299 | M_1 = M_1^{1/2}*M_1^{1/2} |
15,182 | \sqrt{e^{i \cdot x}} = e^{i \cdot x/2} = \cos\left(x/2\right) + i \cdot \sin(\frac{x}{2}) |
12,294 | (a + b)/2 = \frac12*(2*a + b - a) = a + \frac12*(b - a) |
-20,938 | \frac{1}{9}9 (6 + x)/9 = (9x + 54)/81 |
42,735 | 1/2 = 1/(2*2) + \frac{1}{2*2} |
-16,544 | 8\sqrt{175} = 8\sqrt{25\cdot 7} |
37,320 | c+(a+b)=(c+a)+b |
9,194 | v''\cdot x^2 + v'\cdot x = 1 \Rightarrow v''\cdot x + v' = \frac1x |
25,785 | x = 2 + x + 2 \left(-1\right) |
-21,814 | -13/10 = -\frac{1}{10}*13 |
-1,897 | 5/4 \pi = \pi \frac{7}{6} + \pi/12 |
19,274 | 0 = \left\{( 2, 2), ( 0, 0), ( 1, 1), ...\right\} |
-1,170 | \frac{1}{(-9)\cdot 1/8}\cdot (\left(-1\right)\cdot 8\cdot 1/3) = -\dfrac89\cdot (-8/3) |
15,621 | 1386 = \frac{1}{2}\cdot \frac{1}{5!^2\cdot 1!}\cdot 11! |
38,817 | \sum_{k=1}^\infty \frac{1}{k^4} = \sum_{k=1}^\infty \frac{1}{(k \cdot 2)^4} + \sum_{k=0}^\infty \frac{1}{(2 \cdot k + 1)^4} \implies \sum_{k=0}^\infty \frac{...}{(k \cdot 2 + 1)^4} = \tfrac{1}{16} \cdot 15 \cdot \sum_{k=1}^\infty \dfrac{1}{k^4} |
-4,857 | 10^{12 + 5(-1)}*0.81 = 10^7*0.81 |
36,635 | m + n \leq z + y < m + n + 2 \Rightarrow \left\lfloor{y + z}\right\rfloor = m + n |
-5,732 | \dfrac{1}{5\cdot (-1) + 5\cdot t}\cdot 4 = \dfrac{4}{5\cdot (t + (-1))} |
21,956 | 2 \times \cos(0)/\cos(0) = 2 |
-6,699 | 0/10 + 9/100 = 9/100 + \tfrac{1}{100} 0 |
-26,654 | (3\cdot x + 1)\cdot (7\cdot \left(-1\right) + x) = 7\cdot (-1) + 3\cdot x^2 - 20\cdot x |
18,672 | x \cdot z + z \cdot x = z \cdot x |
15,027 | \frac{1}{x^2 + x + 1} \cdot \left(0.5 \cdot x \cdot x + x + 1\right) = 1 - \frac{0.5 \cdot x \cdot x}{x^2 + x + 1} \cdot 1 = 1 - \frac{1}{1 + 1/x + \frac{1}{x^2}} \cdot 0.5 |
-20,014 | -6/5*\frac{x + 9*(-1)}{x + 9*(-1)} = \frac{1}{x*5 + 45*(-1)}*(-6*x + 54) |
1,266 | 3^2*3^{x + 2} = 3^{4 + x} |
-11,788 | 9^{-\frac{1}{2}} = (\dfrac19)^{\dfrac{1}{2}} |
9,309 | z^2 + 2z + 1 = (z + 1) \cdot (z + 1) |
13,061 | \dfrac{1}{2}*b^2 + \dfrac{f^2}{2} = \frac12*\left(f^2 + b^2\right) |
27,614 | (1 + 0.5 + 0.5^2)\cdot 305 = 305\cdot (1 + 0.5)\cdot 0.5 + 305 |
-9,175 | 60 \cdot (-1) + z \cdot 6 = -5 \cdot 2 \cdot 2 \cdot 3 + 2 \cdot 3 \cdot z |
15,111 | \left( x, \Phi\left(f\right) \cdot B \cdot y\right) = ( x, \Phi(f) \cdot y \cdot B) |
-27,696 | d/dy (16*\sin{y}) = \cos{y}*16 |
35,074 | -4 \cdot (3 + p) + 9 \cdot p^2 = (p \cdot 3 + (-1))^2 + 2 \cdot p + 13 \cdot (-1) |
22,321 | 111\cdot \dotsm = 1 |
15,318 | 3 = 4 \cdot \csc(y + 2) - 3 \cdot \cot^2(y + 2) = 4 \cdot \csc(y + 2) - 3 \cdot (\csc^2\left(y + 2\right) + (-1)) |
3,964 | x x - 4 (x + 1) = 8 (-1) + (x + 2 (-1)) (x + 2 (-1)) |
35,670 | 1 = \sin{-\frac12 \cdot \pi \cdot 3} |
9,789 | (1 + y) (1 + y * y) (1 + y^4) \dotsm*(1 + y^{2^n}) = \frac{1}{-y + 1}\left(1 - y^{2^{n + 1}}\right) |
30,290 | 9 = (2 + 1) (2 + 1) |
5,679 | b\cdot \frac{a}{a}\cdot b\cdot a/b = \dfrac{b}{b}\cdot \frac{a}{a}\cdot b\cdot a |
7,831 | (n\cdot 2 + 2)! = (n\cdot 2 + 1)!\cdot (2\cdot n + 2) |
957 | \tfrac{1}{n^{\frac13}} = n^{-\tfrac{1}{3}} |
17,599 | X^3 + 1 = (X + 1) (X^2 - X + 1) |
21,198 | x^4 - x x*22 - x + 110 = \left(10 (-1) + x x + x\right) \left(x x - x + 11 \left(-1\right)\right) |
8,271 | 6 = \frac12\cdot \left(4\cdot (-1) + 16\right) |
8,827 | 1 - \frac{1}{216}*27 - \frac{111}{216} = \dfrac{1}{216}*78 \approx 0.3611 |
-1,590 | \pi \times \frac{3}{4} = 0 + 3/4 \times \pi |
17,660 | 6 \cdot \left(2^k + 3^{k + \left(-1\right)}\right) = 6 \cdot 2^k + 6 \cdot 3^{(-1) + k} |
16,061 | \left(x^2 + 2*x + 2\right)*\left(2 + x^2 - x*2\right) = x^4 + 4 |
14,586 | -(1 + \cos{x \cdot 2})/2 + 1 = \sin^2{x} |
5,150 | -\frac{1}{y^2} = \frac{1}{y^4}*(\left(-1\right)*y^2) |
-20,631 | 4/3 \times \dfrac{5 \times x}{x \times 5} \times 1 = \frac{20}{x \times 15} \times x |
26,811 | \frac{t'*a*1^{-1}}{s*t*1^{-1}} = 1/t*a/\left(s*1/t'\right) |
41,299 | 0 = x^{32} + \left(-1\right) = \left(x^{16} + 1\right)\cdot (x^{16} + (-1)) = (x^{16} + 1)\cdot (x^8 + 1)\cdot \left(x^8 + (-1)\right) |
31,474 | \left(-2\cdot y + z\right)\cdot (z - y\cdot 3) = z \cdot z - z\cdot y\cdot 5 + y \cdot y\cdot 6 |
17,120 | \frac{1}{a^2 + ab + b^2} = \frac{a - b}{(a - b) (a^2 + ab + b^2)} = \frac{a - b}{a^3 - b^3} |
26,855 | a \cdot b \cdot w = w \cdot b \cdot a |
5,390 | g \cdot f = g = f \cdot g |
7,534 | k_2 = \sqrt{x} \Rightarrow x = k_2^2 |
16,337 | \frac{1}{R^2} = \frac{4}{R} + \left(-1\right) = 4\cdot (4 - R) + (-1) = 15 - 4\cdot R |
8,818 | \frac{1}{250}\times 203 = \frac{1}{30^4}\times 657720 |
6,047 | f_2 \cdot g_2 - f_1 \cdot g_1 = g_2 \cdot f_2 - g_2 \cdot f_1 + g_2 \cdot f_1 - g_1 \cdot f_1 |
21,230 | x^2\cdot 6 + 5\cdot y\cdot x + y \cdot y + x + 2\cdot y + 15\cdot (-1) = (5 + 3\cdot x + y)\cdot (3\cdot \left(-1\right) + x\cdot 2 + y) |
-26,623 | 28-7x^2=7(4-x^2) =7(2+x)(2-x) |
-9,289 | 10\times z + 14 = z\times 2\times 5 + 2\times 7 |
-6,602 | \frac{4}{(x + 5 \cdot \left(-1\right)) \cdot 5} = \frac{4}{25 \cdot \left(-1\right) + x \cdot 5} |
15,616 | (2^2 + (-1))\cdot ((-1) + 3^2)\cdot \cdots\cdot (300^2 + (-1)) = ((-1) + 2)\cdot (1 + 2)\cdot (3 + (-1))\cdot (3 + 1)\cdot \cdots\cdot (300 + (-1))\cdot \left(1 + 300\right) |
-611 | \frac{143}{12}*\pi - 10*\pi = 23/12*\pi |
5,857 | (d - b) \cdot (d + b) = d^2 - b \cdot d + d \cdot b - b \cdot b = d^2 - b^2 |
9,718 | 0 = (A*Y - I*x)*v \implies Y*v*\left(-I*x + A*Y\right) = 0 |
-1,283 | \tfrac{1}{1/5 \cdot 7} \cdot ((-7) \cdot 1/2) = -\frac72 \cdot \dfrac{1}{7} \cdot 5 |
32,800 | -9 \cdot y \cdot y = -y \cdot y \cdot 9 |
25,722 | 54 = 10 \times (-1) + 2^6 |
5,105 | \gamma\cdot \alpha\cdot \beta = \gamma\cdot \beta\cdot \alpha |
9,146 | h_1\cdot g\cdot h_2/g = \frac{g\cdot h_1}{g}\cdot \frac{h_2\cdot g}{g}\cdot 1 |
-27,476 | 48\cdot 4 = 192 |
6,309 | \dfrac{1}{\left(2 + 0\right)^{\frac{1}{2}} + (2 + 0 \cdot \left(-1\right))^{\frac{1}{2}}} \cdot 2 = \dfrac{2}{2 \cdot 2^{\frac{1}{2}}} = \frac{1}{2^{1 / 2}} |
35,782 | \dfrac{1}{a \cdot b} = \frac{1}{a \cdot b} |
44,809 | 7\cdot \left(2^{21} + (-1)\right) = 14680057 |
24,240 | \left(x + z\right)^2 = z^2 + x^2 + xz \cdot 2 |
6,233 | y_1 = -8\cdot y_1^3 - y_2\cdot y_2 = -4\cdot y_2 - 4\cdot y_1^3 |
16,861 | \left(B e^A\right)^U = (e^A)^U B^U = e^{A^U} B^U |
-1,238 | \frac14*3*(-6/5) = ((-6)*\frac15)/\left(4*\frac{1}{3}\right) |
9,048 | ( 2, 1, -5) + ( x, l, n) = ( 5, 9, 0)\Longrightarrow \left( 5, 9, 0\right) = ( 2 + x, 1 + l, 5 \cdot (-1) + n) |
-10,656 | \frac55\cdot (-4/n) = -\dfrac{1}{n\cdot 5}\cdot 20 |
21,089 | \dfrac{b^2}{g^2} = 3^{\frac{1}{2}}/4 \Rightarrow 3^{1 / 2} = b,2 = g |
26,372 | \tan(x) = \frac{1}{1 - \frac{x * x}{3 - \frac{x * x}{5 - \ldots}}}*x |
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