\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
Test:
Jmat.Real.dawson
Bits:
128 bits
Bits error versus x
Time: 21.7 s
Input Error: 14.4
Output Error: 0.1
Log:
Profile: 🕒
\(\begin{cases} \frac{\frac{(0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(\frac{0.0072644182}{{\left({x}^3\right)}^2}\right))_* + (0.0001789971 * \left(\frac{\frac{\frac{1}{{x}^3}}{{x}^3}}{{x}^{4}}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*}{x}}{(0.0003579942 * \left({\left(\frac{1}{{x}^3}\right)}^{4}\right) + \left((0.0008327945 * \left(\frac{\frac{\frac{1}{{x}^3}}{{x}^3}}{{x}^{4}}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(\frac{0.0694555761}{{x}^{6}}\right))_*\right))_*} & \text{when } x \le -472.8452f0 \\ \frac{x \cdot \left((0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3\right))_* + (0.0001789971 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{(0.0003579942 * \left({\left({x}^2\right)}^3 \cdot {x}^{6}\right) + \left((\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({x}^2\right)}^3\right))_* + (0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*} & \text{when } x \le 2520.2073f0 \\ \frac{\frac{(0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(\frac{0.0072644182}{{\left({x}^3\right)}^2}\right))_* + (0.0001789971 * \left(\frac{\frac{\frac{1}{{x}^3}}{{x}^3}}{{x}^{4}}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*}{x}}{(0.0003579942 * \left({\left(\frac{1}{{x}^3}\right)}^{4}\right) + \left((0.0008327945 * \left(\frac{\frac{\frac{1}{{x}^3}}{{x}^3}}{{x}^{4}}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(\frac{0.0694555761}{{x}^{6}}\right))_*\right))_*} & \text{otherwise} \end{cases}\)

    if x < -472.8452f0 or 2520.2073f0 < 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 \cdot \left((0.0005064034 * \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) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{(\left(2 \cdot 0.0001789971\right) * \left(\left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(x \cdot x\right)\right) + \left((\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) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_* + (0.0008327945 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.2909738639 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*}}\]
      30.9
    3. Using strategy rm
      30.9
    4. Applied add-cube-cbrt to get
      \[\color{red}{\frac{x \cdot \left((0.0005064034 * \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) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{(\left(2 \cdot 0.0001789971\right) * \left(\left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(x \cdot x\right)\right) + \left((\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) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_* + (0.0008327945 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.2909738639 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*}} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{x \cdot \left((0.0005064034 * \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) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{(\left(2 \cdot 0.0001789971\right) * \left(\left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(x \cdot x\right)\right) + \left((\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) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_* + (0.0008327945 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.2909738639 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*}}\right)}^3}\]
      30.9
    5. Applied simplify to get
      \[{\color{red}{\left(\sqrt[3]{\frac{x \cdot \left((0.0005064034 * \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) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{(\left(2 \cdot 0.0001789971\right) * \left(\left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(x \cdot x\right)\right) + \left((\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) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_* + (0.0008327945 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.2909738639 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*}}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\frac{x \cdot \left((0.0001789971 * \left({\left({x}^3 \cdot {x}^2\right)}^2\right) + \left((0.0424060604 * \left({x}^2 \cdot {x}^2\right) + \left((\left(x \cdot 0.1049934947\right) * x + 1)_*\right))_*\right))_* + (0.0005064034 * \left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) + \left(0.0072644182 \cdot {\left({x}^3\right)}^2\right))_*\right)}{(\left(0.0001789971 \cdot 2\right) * \left({\left({x}^3\right)}^2 \cdot {\left({x}^3\right)}^2\right) + \left((\left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) * 0.0140005442 + \left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^2 \cdot 0.0694555761\right)\right))_* + (0.0008327945 * \left({\left({x}^3 \cdot {x}^2\right)}^2\right) + \left((0.2909738639 * \left({x}^2 \cdot {x}^2\right) + \left((\left(x \cdot 0.7715471019\right) * x + 1)_*\right))_*\right))_*\right))_*}}\right)}}^3\]
      30.9
    6. Applied taylor to get
      \[{\left(\sqrt[3]{\frac{x \cdot \left((0.0001789971 * \left({\left({x}^3 \cdot {x}^2\right)}^2\right) + \left((0.0424060604 * \left({x}^2 \cdot {x}^2\right) + \left((\left(x \cdot 0.1049934947\right) * x + 1)_*\right))_*\right))_* + (0.0005064034 * \left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) + \left(0.0072644182 \cdot {\left({x}^3\right)}^2\right))_*\right)}{(\left(0.0001789971 \cdot 2\right) * \left({\left({x}^3\right)}^2 \cdot {\left({x}^3\right)}^2\right) + \left((\left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) * 0.0140005442 + \left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^2 \cdot 0.0694555761\right)\right))_* + (0.0008327945 * \left({\left({x}^3 \cdot {x}^2\right)}^2\right) + \left((0.2909738639 * \left({x}^2 \cdot {x}^2\right) + \left((\left(x \cdot 0.7715471019\right) * x + 1)_*\right))_*\right))_*\right))_*}}\right)}^3 \leadsto \frac{(0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(0.0072644182 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2\right))_* + (0.0001789971 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{4}}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*}{x \cdot (0.0003579942 * \left({\left({\left(\frac{1}{x}\right)}^3\right)}^{4}\right) + \left((\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(\frac{0.0694555761}{{x}^{6}}\right))_* + (0.0008327945 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{4}}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}\]
      0.0
    7. Taylor expanded around inf to get
      \[\color{red}{\frac{(0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(0.0072644182 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2\right))_* + (0.0001789971 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{4}}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*}{x \cdot (0.0003579942 * \left({\left({\left(\frac{1}{x}\right)}^3\right)}^{4}\right) + \left((\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(\frac{0.0694555761}{{x}^{6}}\right))_* + (0.0008327945 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{4}}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}} \leadsto \color{blue}{\frac{(0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(0.0072644182 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2\right))_* + (0.0001789971 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{4}}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*}{x \cdot (0.0003579942 * \left({\left({\left(\frac{1}{x}\right)}^3\right)}^{4}\right) + \left((\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(\frac{0.0694555761}{{x}^{6}}\right))_* + (0.0008327945 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{4}}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}}\]
      0.0
    8. Applied simplify to get
      \[\frac{(0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(0.0072644182 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2\right))_* + (0.0001789971 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{4}}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*}{x \cdot (0.0003579942 * \left({\left({\left(\frac{1}{x}\right)}^3\right)}^{4}\right) + \left((\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(\frac{0.0694555761}{{x}^{6}}\right))_* + (0.0008327945 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^2}{{x}^{4}}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*} \leadsto \frac{\frac{(0.0001789971 * \left(\frac{{\left(\frac{1}{x}\right)}^3 \cdot {\left(\frac{1}{x}\right)}^3}{{x}^{4}}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(\frac{1 \cdot 0.0072644182}{{\left({x}^3\right)}^2}\right))_*}{x}}{(0.0003579942 * \left({\left({\left(\frac{1}{x}\right)}^3\right)}^{4}\right) + \left((0.0008327945 * \left(\frac{{\left(\frac{1}{x}\right)}^3 \cdot {\left(\frac{1}{x}\right)}^3}{{x}^{4}}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(\frac{0.0694555761}{{x}^{6}}\right))_*\right))_*}\]
      0.0

    9. Applied final simplification
    10. Applied simplify to get
      \[\color{red}{\frac{\frac{(0.0001789971 * \left(\frac{{\left(\frac{1}{x}\right)}^3 \cdot {\left(\frac{1}{x}\right)}^3}{{x}^{4}}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(\frac{1 \cdot 0.0072644182}{{\left({x}^3\right)}^2}\right))_*}{x}}{(0.0003579942 * \left({\left({\left(\frac{1}{x}\right)}^3\right)}^{4}\right) + \left((0.0008327945 * \left(\frac{{\left(\frac{1}{x}\right)}^3 \cdot {\left(\frac{1}{x}\right)}^3}{{x}^{4}}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(\frac{0.0694555761}{{x}^{6}}\right))_*\right))_*}} \leadsto \color{blue}{\frac{\frac{(0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(\frac{0.0072644182}{{\left({x}^3\right)}^2}\right))_* + (0.0001789971 * \left(\frac{\frac{\frac{1}{{x}^3}}{{x}^3}}{{x}^{4}}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*}{x}}{(0.0003579942 * \left({\left(\frac{1}{{x}^3}\right)}^{4}\right) + \left((0.0008327945 * \left(\frac{\frac{\frac{1}{{x}^3}}{{x}^3}}{{x}^{4}}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(\frac{0.0694555761}{{x}^{6}}\right))_*\right))_*}}\]
      0.0

    if -472.8452f0 < x < 2520.2073f0

    1. Started with
      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
      0.2
    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 \cdot \left((0.0005064034 * \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) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{(\left(2 \cdot 0.0001789971\right) * \left(\left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(x \cdot x\right)\right) + \left((\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) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_* + (0.0008327945 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.2909738639 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*}}\]
      0.2
    3. Applied taylor to get
      \[\frac{x \cdot \left((0.0005064034 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{(\left(2 \cdot 0.0001789971\right) * \left(\left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) \cdot \left(x \cdot x\right)\right) + \left((\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_* + (0.0008327945 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.2909738639 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*} \leadsto \frac{x \cdot \left((0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3\right))_* + (0.0001789971 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{(0.0003579942 * \left({\left({x}^2\right)}^3 \cdot {x}^{6}\right) + \left((\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({x}^2\right)}^3\right))_* + (0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*}\]
      0.2
    4. Taylor expanded around 0 to get
      \[\color{red}{\frac{x \cdot \left((0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3\right))_* + (0.0001789971 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{(0.0003579942 * \left({\left({x}^2\right)}^3 \cdot {x}^{6}\right) + \left((\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({x}^2\right)}^3\right))_* + (0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*}} \leadsto \color{blue}{\frac{x \cdot \left((0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3\right))_* + (0.0001789971 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{(0.0003579942 * \left({\left({x}^2\right)}^3 \cdot {x}^{6}\right) + \left((\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({x}^2\right)}^3\right))_* + (0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*}}\]
      0.2

  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))