\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
Test:
Jmat.Real.dawson
Bits:
128 bits
Bits error versus x
Time: 43.1 s
Input Error: 14.4
Output Error: 0.2
Log:
Profile: 🕒
\(\begin{cases} \frac{\left(\left(1 + \frac{0.1049934947}{x \cdot x}\right) + \frac{0.0072644182 \cdot 1}{{\left({x}^3\right)}^2}\right) + \left(\left(\frac{\frac{0.0424060604 \cdot 1}{{x}^3}}{x} + \frac{0.0001789971}{{x}^{10}}\right) + \frac{\frac{1 \cdot 0.0005064034}{{\left({x}^3\right)}^2}}{x \cdot x}\right)}{\left(\left(\left(\left(1 + \frac{\frac{1}{x}}{{x}^3} \cdot 0.2909738639\right) + \frac{0.0694555761 \cdot 1}{{\left({x}^3\right)}^2}\right) + \left(\frac{\frac{1 \cdot 0.0140005442}{{\left({x}^3\right)}^2}}{x \cdot x} + \frac{\frac{1}{{x}^3} \cdot \frac{1}{{x}^3}}{\frac{{x}^{6}}{0.0003579942}}\right)\right) + \left(\frac{0.7715471019}{x \cdot x} + \frac{\frac{1}{{x}^3} \cdot \frac{1}{{x}^3}}{\frac{{x}^{4}}{0.0008327945}}\right)\right) \cdot x} & \text{when } x \le -3272.973f0 \\ \frac{\left(\left(x + {x}^3 \cdot 0.1049934947\right) + \left(x \cdot 0.0424060604\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) + \left(\left(0.0001789971 \cdot {x}^3\right) \cdot {\left({x}^2 \cdot {x}^2\right)}^2 + \left(x \cdot 0.0072644182 + {x}^3 \cdot 0.0005064034\right) \cdot {\left({x}^2\right)}^3\right)}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(e^{\log \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right)} + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)} & \text{when } x \le 22525.45f0 \\ \frac{\left(\left(1 + \frac{0.1049934947}{x \cdot x}\right) + \frac{0.0072644182 \cdot 1}{{\left({x}^3\right)}^2}\right) + \left(\left(\frac{\frac{0.0424060604 \cdot 1}{{x}^3}}{x} + \frac{0.0001789971}{{x}^{10}}\right) + \frac{\frac{1 \cdot 0.0005064034}{{\left({x}^3\right)}^2}}{x \cdot x}\right)}{\left(\left(\left(\left(1 + \frac{\frac{1}{x}}{{x}^3} \cdot 0.2909738639\right) + \frac{0.0694555761 \cdot 1}{{\left({x}^3\right)}^2}\right) + \left(\frac{\frac{1 \cdot 0.0140005442}{{\left({x}^3\right)}^2}}{x \cdot x} + \frac{\frac{1}{{x}^3} \cdot \frac{1}{{x}^3}}{\frac{{x}^{6}}{0.0003579942}}\right)\right) + \left(\frac{0.7715471019}{x \cdot x} + \frac{\frac{1}{{x}^3} \cdot \frac{1}{{x}^3}}{\frac{{x}^{4}}{0.0008327945}}\right)\right) \cdot x} & \text{otherwise} \end{cases}\)

    if x < -3272.973f0 or 22525.45f0 < x

    1. Started with
      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
      30.9
    2. Applied simplify to get
      \[\color{red}{\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x} \leadsto \color{blue}{\frac{x}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right) + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)} \cdot \left(\left(\left(\left(x \cdot 0.0424060604\right) \cdot {x}^3 + \left(\left(x \cdot x\right) \cdot 0.1049934947 + 1\right)\right) + \left(\left(x \cdot x\right) \cdot 0.0001789971\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0072644182 + \left(0.0005064034 \cdot x\right) \cdot x\right)\right)\right)}\]
      30.9
    3. Using strategy rm
      30.9
    4. Applied add-cube-cbrt to get
      \[\color{red}{\frac{x}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right) + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)} \cdot \left(\left(\left(\left(x \cdot 0.0424060604\right) \cdot {x}^3 + \left(\left(x \cdot x\right) \cdot 0.1049934947 + 1\right)\right) + \left(\left(x \cdot x\right) \cdot 0.0001789971\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0072644182 + \left(0.0005064034 \cdot x\right) \cdot x\right)\right)\right)} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{x}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right) + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)} \cdot \left(\left(\left(\left(x \cdot 0.0424060604\right) \cdot {x}^3 + \left(\left(x \cdot x\right) \cdot 0.1049934947 + 1\right)\right) + \left(\left(x \cdot x\right) \cdot 0.0001789971\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0072644182 + \left(0.0005064034 \cdot x\right) \cdot x\right)\right)\right)}\right)}^3}\]
      30.9
    5. Applied simplify to get
      \[{\color{red}{\left(\sqrt[3]{\frac{x}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right) + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)} \cdot \left(\left(\left(\left(x \cdot 0.0424060604\right) \cdot {x}^3 + \left(\left(x \cdot x\right) \cdot 0.1049934947 + 1\right)\right) + \left(\left(x \cdot x\right) \cdot 0.0001789971\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0072644182 + \left(0.0005064034 \cdot x\right) \cdot x\right)\right)\right)}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\frac{\left(\left(x \cdot \left(0.0001789971 \cdot x\right)\right) \cdot \left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) + \left(\left(x \cdot 0.0424060604\right) \cdot {x}^3 + \left(1 + 0.1049934947 \cdot {x}^2\right)\right)\right) + \left(\left(0.0005064034 \cdot x\right) \cdot x + 0.0072644182\right) \cdot \left({x}^3 \cdot {x}^3\right)}{\frac{\left(\left(\left({x}^3 \cdot {x}^3\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) \cdot \left(\left(2 \cdot 0.0001789971\right) \cdot {x}^2 + 0.0008327945\right) + \left(\left(\left(x \cdot 0.7715471019\right) \cdot x + 1\right) + {x}^3 \cdot \left(x \cdot 0.2909738639\right)\right)\right) + \left({x}^3 \cdot {x}^3\right) \cdot \left(0.0694555761 + x \cdot \left(0.0140005442 \cdot x\right)\right)}{x}}}\right)}}^3\]
      30.9
    6. Applied taylor to get
      \[{\left(\sqrt[3]{\frac{\left(\left(x \cdot \left(0.0001789971 \cdot x\right)\right) \cdot \left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) + \left(\left(x \cdot 0.0424060604\right) \cdot {x}^3 + \left(1 + 0.1049934947 \cdot {x}^2\right)\right)\right) + \left(\left(0.0005064034 \cdot x\right) \cdot x + 0.0072644182\right) \cdot \left({x}^3 \cdot {x}^3\right)}{\frac{\left(\left(\left({x}^3 \cdot {x}^3\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) \cdot \left(\left(2 \cdot 0.0001789971\right) \cdot {x}^2 + 0.0008327945\right) + \left(\left(\left(x \cdot 0.7715471019\right) \cdot x + 1\right) + {x}^3 \cdot \left(x \cdot 0.2909738639\right)\right)\right) + \left({x}^3 \cdot {x}^3\right) \cdot \left(0.0694555761 + x \cdot \left(0.0140005442 \cdot x\right)\right)}{x}}}\right)}^3 \leadsto \frac{0.1049934947 \cdot \frac{1}{{x}^2} + \left(1 + \left(0.0072644182 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2 + \left(0.0001789971 \cdot \frac{1}{{x}^{10}} + \left(0.0424060604 \cdot \frac{{\left(\frac{1}{x}\right)}^3}{x} + 0.0005064034 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^2}\right)\right)\right)\right)}{\left(0.0008327945 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{4}} + \left(0.7715471019 \cdot \frac{1}{{x}^2} + \left(0.0003579942 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{6}} + \left(0.0140005442 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^2} + \left(1 + \left(0.0694555761 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2 + 0.2909738639 \cdot \frac{{\left(\frac{1}{x}\right)}^3}{x}\right)\right)\right)\right)\right)\right) \cdot x}\]
      0
    7. Taylor expanded around inf to get
      \[\color{red}{\frac{0.1049934947 \cdot \frac{1}{{x}^2} + \left(1 + \left(0.0072644182 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2 + \left(0.0001789971 \cdot \frac{1}{{x}^{10}} + \left(0.0424060604 \cdot \frac{{\left(\frac{1}{x}\right)}^3}{x} + 0.0005064034 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^2}\right)\right)\right)\right)}{\left(0.0008327945 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{4}} + \left(0.7715471019 \cdot \frac{1}{{x}^2} + \left(0.0003579942 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{6}} + \left(0.0140005442 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^2} + \left(1 + \left(0.0694555761 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2 + 0.2909738639 \cdot \frac{{\left(\frac{1}{x}\right)}^3}{x}\right)\right)\right)\right)\right)\right) \cdot x}} \leadsto \color{blue}{\frac{0.1049934947 \cdot \frac{1}{{x}^2} + \left(1 + \left(0.0072644182 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2 + \left(0.0001789971 \cdot \frac{1}{{x}^{10}} + \left(0.0424060604 \cdot \frac{{\left(\frac{1}{x}\right)}^3}{x} + 0.0005064034 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^2}\right)\right)\right)\right)}{\left(0.0008327945 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{4}} + \left(0.7715471019 \cdot \frac{1}{{x}^2} + \left(0.0003579942 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{6}} + \left(0.0140005442 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^2} + \left(1 + \left(0.0694555761 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2 + 0.2909738639 \cdot \frac{{\left(\frac{1}{x}\right)}^3}{x}\right)\right)\right)\right)\right)\right) \cdot x}}\]
      0
    8. Applied simplify to get
      \[\frac{0.1049934947 \cdot \frac{1}{{x}^2} + \left(1 + \left(0.0072644182 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2 + \left(0.0001789971 \cdot \frac{1}{{x}^{10}} + \left(0.0424060604 \cdot \frac{{\left(\frac{1}{x}\right)}^3}{x} + 0.0005064034 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^2}\right)\right)\right)\right)}{\left(0.0008327945 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{4}} + \left(0.7715471019 \cdot \frac{1}{{x}^2} + \left(0.0003579942 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{6}} + \left(0.0140005442 \cdot \frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^2} + \left(1 + \left(0.0694555761 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2 + 0.2909738639 \cdot \frac{{\left(\frac{1}{x}\right)}^3}{x}\right)\right)\right)\right)\right)\right) \cdot x} \leadsto \frac{\left(\left(1 + \frac{0.1049934947}{x \cdot x}\right) + \frac{0.0072644182 \cdot 1}{{\left({x}^3\right)}^2}\right) + \left(\left(\frac{\frac{0.0424060604 \cdot 1}{{x}^3}}{x} + \frac{0.0001789971}{{x}^{10}}\right) + \frac{\frac{1 \cdot 0.0005064034}{{\left({x}^3\right)}^2}}{x \cdot x}\right)}{\left(\left(\left(\left(1 + \frac{\frac{1}{x}}{{x}^3} \cdot 0.2909738639\right) + \frac{0.0694555761 \cdot 1}{{\left({x}^3\right)}^2}\right) + \left(\frac{\frac{1 \cdot 0.0140005442}{{\left({x}^3\right)}^2}}{x \cdot x} + \frac{\frac{1}{{x}^3} \cdot \frac{1}{{x}^3}}{\frac{{x}^{6}}{0.0003579942}}\right)\right) + \left(\frac{0.7715471019}{x \cdot x} + \frac{\frac{1}{{x}^3} \cdot \frac{1}{{x}^3}}{\frac{{x}^{4}}{0.0008327945}}\right)\right) \cdot x}\]
      0.0

    9. Applied final simplification

    if -3272.973f0 < x < 22525.45f0

    1. Started with
      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
      0.6
    2. Applied simplify to get
      \[\color{red}{\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x} \leadsto \color{blue}{\frac{x}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right) + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)} \cdot \left(\left(\left(\left(x \cdot 0.0424060604\right) \cdot {x}^3 + \left(\left(x \cdot x\right) \cdot 0.1049934947 + 1\right)\right) + \left(\left(x \cdot x\right) \cdot 0.0001789971\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0072644182 + \left(0.0005064034 \cdot x\right) \cdot x\right)\right)\right)}\]
      0.5
    3. Using strategy rm
      0.5
    4. Applied add-exp-log to get
      \[\frac{x}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(\color{red}{\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)} + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)} \cdot \left(\left(\left(\left(x \cdot 0.0424060604\right) \cdot {x}^3 + \left(\left(x \cdot x\right) \cdot 0.1049934947 + 1\right)\right) + \left(\left(x \cdot x\right) \cdot 0.0001789971\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0072644182 + \left(0.0005064034 \cdot x\right) \cdot x\right)\right)\right) \leadsto \frac{x}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(\color{blue}{e^{\log \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right)}} + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)} \cdot \left(\left(\left(\left(x \cdot 0.0424060604\right) \cdot {x}^3 + \left(\left(x \cdot x\right) \cdot 0.1049934947 + 1\right)\right) + \left(\left(x \cdot x\right) \cdot 0.0001789971\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0072644182 + \left(0.0005064034 \cdot x\right) \cdot x\right)\right)\right)\]
      0.4
    5. Using strategy rm
      0.4
    6. Applied associate-*l/ to get
      \[\color{red}{\frac{x}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(e^{\log \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right)} + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)} \cdot \left(\left(\left(\left(x \cdot 0.0424060604\right) \cdot {x}^3 + \left(\left(x \cdot x\right) \cdot 0.1049934947 + 1\right)\right) + \left(\left(x \cdot x\right) \cdot 0.0001789971\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0072644182 + \left(0.0005064034 \cdot x\right) \cdot x\right)\right)\right)} \leadsto \color{blue}{\frac{x \cdot \left(\left(\left(\left(x \cdot 0.0424060604\right) \cdot {x}^3 + \left(\left(x \cdot x\right) \cdot 0.1049934947 + 1\right)\right) + \left(\left(x \cdot x\right) \cdot 0.0001789971\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0072644182 + \left(0.0005064034 \cdot x\right) \cdot x\right)\right)\right)}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(e^{\log \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right)} + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)}}\]
      0.4
    7. Applied simplify to get
      \[\frac{\color{red}{x \cdot \left(\left(\left(\left(x \cdot 0.0424060604\right) \cdot {x}^3 + \left(\left(x \cdot x\right) \cdot 0.1049934947 + 1\right)\right) + \left(\left(x \cdot x\right) \cdot 0.0001789971\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0072644182 + \left(0.0005064034 \cdot x\right) \cdot x\right)\right)\right)}}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(e^{\log \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right)} + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)} \leadsto \frac{\color{blue}{\left(\left(\left({x}^2 \cdot {x}^2\right) \cdot \left(0.0424060604 \cdot x\right) + \left(0.1049934947 \cdot {x}^2\right) \cdot x\right) + x\right) + \left(\left({x}^3 \cdot 0.0005064034 + x \cdot 0.0072644182\right) \cdot \left({x}^3 \cdot {x}^3\right) + \left({x}^2 \cdot \left(0.0001789971 \cdot x\right)\right) \cdot {\left({x}^2 \cdot {x}^2\right)}^2\right)}}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(e^{\log \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right)} + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)}\]
      0.3
    8. Applied simplify to get
      \[\frac{\color{red}{\left(\left(\left({x}^2 \cdot {x}^2\right) \cdot \left(0.0424060604 \cdot x\right) + \left(0.1049934947 \cdot {x}^2\right) \cdot x\right) + x\right)} + \left(\left({x}^3 \cdot 0.0005064034 + x \cdot 0.0072644182\right) \cdot \left({x}^3 \cdot {x}^3\right) + \left({x}^2 \cdot \left(0.0001789971 \cdot x\right)\right) \cdot {\left({x}^2 \cdot {x}^2\right)}^2\right)}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(e^{\log \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right)} + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)} \leadsto \frac{\color{blue}{\left(\left(x + {x}^3 \cdot 0.1049934947\right) + \left(x \cdot 0.0424060604\right) \cdot \left({x}^2 \cdot {x}^2\right)\right)} + \left(\left({x}^3 \cdot 0.0005064034 + x \cdot 0.0072644182\right) \cdot \left({x}^3 \cdot {x}^3\right) + \left({x}^2 \cdot \left(0.0001789971 \cdot x\right)\right) \cdot {\left({x}^2 \cdot {x}^2\right)}^2\right)}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(e^{\log \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right)} + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)}\]
      0.4
    9. Applied simplify to get
      \[\frac{\left(\left(x + {x}^3 \cdot 0.1049934947\right) + \left(x \cdot 0.0424060604\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) + \color{red}{\left(\left({x}^3 \cdot 0.0005064034 + x \cdot 0.0072644182\right) \cdot \left({x}^3 \cdot {x}^3\right) + \left({x}^2 \cdot \left(0.0001789971 \cdot x\right)\right) \cdot {\left({x}^2 \cdot {x}^2\right)}^2\right)}}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(e^{\log \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right)} + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)} \leadsto \frac{\left(\left(x + {x}^3 \cdot 0.1049934947\right) + \left(x \cdot 0.0424060604\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) + \color{blue}{\left(\left(0.0001789971 \cdot {x}^3\right) \cdot {\left({x}^2 \cdot {x}^2\right)}^2 + \left(x \cdot 0.0072644182 + {x}^3 \cdot 0.0005064034\right) \cdot {\left({x}^2\right)}^3\right)}}{\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) \cdot \left(e^{\log \left(\left(2 \cdot 0.0001789971\right) \cdot \left(x \cdot x\right)\right)} + 0.0008327945\right) + \left(\left(1 + \left(x \cdot 0.2909738639\right) \cdot {x}^3\right) + \left(0.7715471019 \cdot x\right) \cdot x\right)\right) + \left(x \cdot x\right) \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(0.0694555761 + 0.0140005442 \cdot \left(x \cdot x\right)\right)\right)}\]
      0.3

  1. Removed slow pow expressions

Original test:


(lambda ((x default))
  #:name "Jmat.Real.dawson"
  (* (/ (+ (+ (+ (+ (+ 1 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x))