\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
Test:
Jmat.Real.dawson
Bits:
128 bits
Bits error versus x
Time: 33.5 s
Input Error: 14.1
Output Error: 0.1
Log:
Profile: 🕒
\(\begin{cases} \frac{\frac{(0.0001789971 * \left({\left({\left(\frac{1}{x}\right)}^3\right)}^3 \cdot \frac{1}{x}\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({\left(\frac{1}{x}\right)}^3 \cdot \frac{0.0072644182}{{x}^3}\right))_*}{x}}{(0.0003579942 * \left(\frac{{\left(\frac{1}{x}\right)}^3}{{\left({x}^3\right)}^3}\right) + \left((\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left({\left(\frac{1}{x}\right)}^3 \cdot \frac{0.0694555761}{{x}^3}\right))_* + (0.0008327945 * \left({\left({\left(\frac{1}{x}\right)}^3\right)}^3 \cdot \frac{1}{x}\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))_*} & \text{when } x \le -5233.3438f0 \\ \frac{\left((0.0001789971 * \left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^3 \cdot {x}^3\right)\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 \cdot {x}^3\right)\right))_*\right) \cdot \left(-x\right)}{-\left(0.0003579942 \cdot \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)\right)} & \text{when } x \le 15032.417f0 \\ \frac{\frac{(0.0001789971 * \left({\left({\left(\frac{1}{x}\right)}^3\right)}^3 \cdot \frac{1}{x}\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({\left(\frac{1}{x}\right)}^3 \cdot \frac{0.0072644182}{{x}^3}\right))_*}{x}}{(0.0003579942 * \left(\frac{{\left(\frac{1}{x}\right)}^3}{{\left({x}^3\right)}^3}\right) + \left((\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left({\left(\frac{1}{x}\right)}^3 \cdot \frac{0.0694555761}{{x}^3}\right))_* + (0.0008327945 * \left({\left({\left(\frac{1}{x}\right)}^3\right)}^3 \cdot \frac{1}{x}\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))_*} & \text{otherwise} \end{cases}\)

    if x < -5233.3438f0 or 15032.417f0 < 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-exp-log 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)}{\color{red}{(\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(\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)}{\color{blue}{e^{\log \left((\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)}}}\]
      30.9
    5. Applied add-exp-log to get
      \[\frac{\color{red}{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)}}{e^{\log \left((\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)}} \leadsto \frac{\color{blue}{e^{\log \left(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)\right)}}}{e^{\log \left((\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)}}\]
      30.9
    6. Applied div-exp to get
      \[\color{red}{\frac{e^{\log \left(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)\right)}}{e^{\log \left((\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)}}} \leadsto \color{blue}{e^{\log \left(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)\right) - \log \left((\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)}}\]
      30.9
    7. Applied simplify to get
      \[e^{\color{red}{\log \left(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)\right) - \log \left((\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)}} \leadsto e^{\color{blue}{\log \left(x \cdot \left((0.0001789971 * \left({\left({x}^3\right)}^3 \cdot x\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 \cdot {x}^3\right)\right))_*\right)\right) - \log \left((\left(2 \cdot 0.0001789971\right) * \left(\left({\left({x}^3\right)}^3 \cdot x\right) \cdot {x}^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}^3 \cdot 0.0694555761\right) \cdot {x}^3\right))_* + (0.0008327945 * \left({\left({x}^3\right)}^3 \cdot x\right) + \left((0.2909738639 * \left({x}^2 \cdot {x}^2\right) + \left((\left(x \cdot 0.7715471019\right) * x + 1)_*\right))_*\right))_*\right))_*\right)}}\]
      30.9
    8. Applied taylor to get
      \[e^{\log \left(x \cdot \left((0.0001789971 * \left({\left({x}^3\right)}^3 \cdot x\right) + \left((0.0424060604 * \left({x}^2 \cdot {x}^2\right) + \left((\left(x \cdot 0.1049934947\right) * x + 1)_*\right))_*\right))_* + (0.0005064034 * \left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) + \left(0.0072644182 \cdot \left({x}^3 \cdot {x}^3\right)\right))_*\right)\right) - \log \left((\left(2 \cdot 0.0001789971\right) * \left(\left({\left({x}^3\right)}^3 \cdot x\right) \cdot {x}^2\right) + \left((\left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) * 0.0140005442 + \left(\left({x}^3 \cdot 0.0694555761\right) \cdot {x}^3\right))_* + (0.0008327945 * \left({\left({x}^3\right)}^3 \cdot x\right) + \left((0.2909738639 * \left({x}^2 \cdot {x}^2\right) + \left((\left(x \cdot 0.7715471019\right) * x + 1)_*\right))_*\right))_*\right))_*\right)} \leadsto e^{\log \left((0.0001789971 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{x}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(0.0072644182 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2\right))_*\right) - \left(\log x + \log \left((0.0003579942 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{{x}^{3}}\right) + \left((0.0008327945 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{x}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2\right))_*\right))_*\right)\right)}\]
      17.2
    9. Taylor expanded around inf to get
      \[\color{red}{e^{\log \left((0.0001789971 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{x}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(0.0072644182 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2\right))_*\right) - \left(\log x + \log \left((0.0003579942 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{{x}^{3}}\right) + \left((0.0008327945 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{x}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2\right))_*\right))_*\right)\right)}} \leadsto \color{blue}{e^{\log \left((0.0001789971 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{x}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(0.0072644182 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2\right))_*\right) - \left(\log x + \log \left((0.0003579942 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{{x}^{3}}\right) + \left((0.0008327945 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{x}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2\right))_*\right))_*\right)\right)}}\]
      17.2
    10. Applied simplify to get
      \[e^{\log \left((0.0001789971 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{x}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(0.0072644182 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2\right))_*\right) - \left(\log x + \log \left((0.0003579942 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{{x}^{3}}\right) + \left((0.0008327945 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{x}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({\left(\frac{1}{x}\right)}^3\right)}^2\right))_*\right))_*\right)\right)} \leadsto \frac{\frac{(0.0001789971 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{x}\right) + \left((0.0424060604 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (0.0005064034 * \left(\frac{1}{{x}^{8}}\right) + \left(0.0072644182 \cdot \left({\left(\frac{1}{x}\right)}^3 \cdot {\left(\frac{1}{x}\right)}^3\right)\right))_*}{x}}{(0.0003579942 * \left(\frac{1 \cdot 1}{{x}^3 \cdot {\left({x}^3\right)}^3}\right) + \left((0.0008327945 * \left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{x}\right) + \left((0.2909738639 * \left(\frac{1}{{x}^{4}}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_* + (\left(\frac{1}{{x}^{8}}\right) * 0.0140005442 + \left(0.0694555761 \cdot \left({\left(\frac{1}{x}\right)}^3 \cdot {\left(\frac{1}{x}\right)}^3\right)\right))_*\right))_*}\]
      0.0

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

    if -5233.3438f0 < x < 15032.417f0

    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 \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))_*}}\]
      0.6
    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(\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)}{(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))_*}\]
      0.6
    4. Taylor expanded around 0 to get
      \[\frac{x \cdot \left((0.0005064034 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{\color{red}{(0.0003579942 * \left({\left({x}^2\right)}^3 \cdot {x}^{6}\right) + \left((\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({x}^2\right)}^3\right))_* + (0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*}} \leadsto \frac{x \cdot \left((0.0005064034 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{\color{blue}{(0.0003579942 * \left({\left({x}^2\right)}^3 \cdot {x}^{6}\right) + \left((\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({x}^2\right)}^3\right))_* + (0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*}}\]
      0.6
    5. Using strategy rm
      0.6
    6. Applied fma-udef to get
      \[\frac{x \cdot \left((0.0005064034 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{\color{red}{(0.0003579942 * \left({\left({x}^2\right)}^3 \cdot {x}^{6}\right) + \left((\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({x}^2\right)}^3\right))_* + (0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right))_*}} \leadsto \frac{x \cdot \left((0.0005064034 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{\color{blue}{0.0003579942 \cdot \left({\left({x}^2\right)}^3 \cdot {x}^{6}\right) + \left((\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({x}^2\right)}^3\right))_* + (0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}}\]
      0.2
    7. Using strategy rm
      0.2
    8. Applied frac-2neg to get
      \[\color{red}{\frac{x \cdot \left((0.0005064034 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{0.0003579942 \cdot \left({\left({x}^2\right)}^3 \cdot {x}^{6}\right) + \left((\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({x}^2\right)}^3\right))_* + (0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}} \leadsto \color{blue}{\frac{-x \cdot \left((0.0005064034 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}{-\left(0.0003579942 \cdot \left({\left({x}^2\right)}^3 \cdot {x}^{6}\right) + \left((\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({x}^2\right)}^3\right))_* + (0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)\right)}}\]
      0.2
    9. Applied simplify to get
      \[\frac{\color{red}{-x \cdot \left((0.0005064034 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left({\left(x \cdot x\right)}^3 \cdot 0.0072644182\right))_* + (0.0001789971 * \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + \left((0.0424060604 * \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)}}{-\left(0.0003579942 \cdot \left({\left({x}^2\right)}^3 \cdot {x}^{6}\right) + \left((\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({x}^2\right)}^3\right))_* + (0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)\right)} \leadsto \frac{\color{blue}{\left((0.0001789971 * \left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^3 \cdot {x}^3\right)\right) + \left((0.0424060604 * \left({x}^2 \cdot {x}^2\right) + \left((\left(x \cdot 0.1049934947\right) * x + 1)_*\right))_*\right))_* + (0.0005064034 * \left(\left({x}^2 \cdot {x}^2\right) \cdot \left({x}^2 \cdot {x}^2\right)\right) + \left(0.0072644182 \cdot \left({x}^3 \cdot {x}^3\right)\right))_*\right) \cdot \left(-x\right)}}{-\left(0.0003579942 \cdot \left({\left({x}^2\right)}^3 \cdot {x}^{6}\right) + \left((\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left({x}^2\right)}^3\right))_* + (0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_*\right)\right)}\]
      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))