\[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
Test:
Jmat.Real.dawson
Bits:
128 bits
Bits error versus x
Time: 36.6 s
Input Error: 28.7
Output Error: 0.2
Log:
Profile: 🕒
\(\begin{cases} (\left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{{x}^2 \cdot (0.0003579942 * \left(\frac{{\left(\frac{1}{{x}^2}\right)}^3}{{x}^{6}}\right) + \left((\left({\left(\frac{1}{x}\right)}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0008327945 * \left(\frac{1}{{x}^{10}}\right) + \left((0.2909738639 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}\right) * 0.0001789971 + \left(\frac{(0.0005064034 * \left({\left(\frac{1}{x}\right)}^{8}\right) + \left(0.0072644182 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0424060604 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*}{x \cdot (0.0003579942 * \left(\frac{{\left(\frac{1}{{x}^2}\right)}^3}{{x}^{6}}\right) + \left((\left({\left(\frac{1}{x}\right)}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0008327945 * \left(\frac{1}{{x}^{10}}\right) + \left((0.2909738639 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}\right))_* & \text{when } x \le -1.1392497874101738 \cdot 10^{+24} \\ (\left(\frac{{\left({x}^3\right)}^3 \cdot {x}^2}{(0.0003579942 * \left({x}^3 \cdot \left({x}^3 \cdot {x}^{6}\right)\right) + \left((0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(x \cdot 0.7715471019\right) * x + 1)_*\right))_*\right))_* + (\left({x}^{8}\right) * 0.0140005442 + \left({\left({x}^2\right)}^3 \cdot 0.0694555761\right))_*\right))_*}\right) * 0.0001789971 + \left(\frac{x}{(0.0003579942 * \left({x}^{6} \cdot {\left(x \cdot x\right)}^3\right) + \left((0.0008327945 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot {x}^{4}\right)\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_* + (\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_*\right))_*} \cdot \left((0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left(x \cdot x\right)}^3\right))_* + (0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right)\right))_* & \text{when } x \le 1.653196896254347 \cdot 10^{+29} \\ (\left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{{x}^2 \cdot (0.0003579942 * \left(\frac{{\left(\frac{1}{{x}^2}\right)}^3}{{x}^{6}}\right) + \left((\left({\left(\frac{1}{x}\right)}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0008327945 * \left(\frac{1}{{x}^{10}}\right) + \left((0.2909738639 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}\right) * 0.0001789971 + \left(\frac{(0.0005064034 * \left({\left(\frac{1}{x}\right)}^{8}\right) + \left(0.0072644182 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0424060604 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*}{x \cdot (0.0003579942 * \left(\frac{{\left(\frac{1}{{x}^2}\right)}^3}{{x}^{6}}\right) + \left((\left({\left(\frac{1}{x}\right)}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0008327945 * \left(\frac{1}{{x}^{10}}\right) + \left((0.2909738639 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}\right))_* & \text{otherwise} \end{cases}\)

    if x < -1.1392497874101738e+24 or 1.653196896254347e+29 < x

    1. Started with
      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
      62.9
    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))_*}}\]
      62.9
    3. Using strategy rm
      62.9
    4. 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))_* + \color{red}{(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))_* + \color{blue}{\left(0.0001789971 \cdot \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + (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))_*}\]
      62.9
    5. Applied simplify 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))_* + \left(\color{red}{0.0001789971 \cdot \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)} + (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))_* + \left(\color{blue}{\left({x}^3 \cdot {x}^3\right) \cdot \left(\left(x \cdot 0.0001789971\right) \cdot {x}^3\right)} + (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))_*}\]
      62.9
    6. 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))_* + \left(\left({x}^3 \cdot {x}^3\right) \cdot \left(\left(x \cdot 0.0001789971\right) \cdot {x}^3\right) + (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{(0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3\right))_* \cdot x}{(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))_*} + \left(\frac{(0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_* \cdot x}{(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))_*} + 0.0001789971 \cdot \frac{{\left({x}^3\right)}^{3} \cdot {x}^2}{(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))_*}\right)\]
      62.9
    7. Taylor expanded around 0 to get
      \[\color{red}{\frac{(0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3\right))_* \cdot x}{(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))_*} + \left(\frac{(0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_* \cdot x}{(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))_*} + 0.0001789971 \cdot \frac{{\left({x}^3\right)}^{3} \cdot {x}^2}{(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))_*}\right)} \leadsto \color{blue}{\frac{(0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3\right))_* \cdot x}{(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))_*} + \left(\frac{(0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_* \cdot x}{(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))_*} + 0.0001789971 \cdot \frac{{\left({x}^3\right)}^{3} \cdot {x}^2}{(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))_*}\right)}\]
      62.9
    8. Applied simplify to get
      \[\color{red}{\frac{(0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3\right))_* \cdot x}{(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))_*} + \left(\frac{(0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_* \cdot x}{(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))_*} + 0.0001789971 \cdot \frac{{\left({x}^3\right)}^{3} \cdot {x}^2}{(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))_*}\right)} \leadsto \color{blue}{(\left(\frac{{\left({x}^3\right)}^3 \cdot \left(x \cdot x\right)}{(0.0003579942 * \left({x}^{6} \cdot {\left(x \cdot x\right)}^3\right) + \left((0.0008327945 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot {x}^{4}\right)\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_* + (\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_*\right))_*}\right) * 0.0001789971 + \left(\frac{x}{(0.0003579942 * \left({x}^{6} \cdot {\left(x \cdot x\right)}^3\right) + \left((0.0008327945 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot {x}^{4}\right)\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_* + (\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_*\right))_*} \cdot \left((0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left(x \cdot x\right)}^3\right))_* + (0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right)\right))_*}\]
      62.9
    9. Applied taylor to get
      \[(\left(\frac{{\left({x}^3\right)}^3 \cdot \left(x \cdot x\right)}{(0.0003579942 * \left({x}^{6} \cdot {\left(x \cdot x\right)}^3\right) + \left((0.0008327945 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot {x}^{4}\right)\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_* + (\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_*\right))_*}\right) * 0.0001789971 + \left(\frac{x}{(0.0003579942 * \left({x}^{6} \cdot {\left(x \cdot x\right)}^3\right) + \left((0.0008327945 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot {x}^{4}\right)\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_* + (\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_*\right))_*} \cdot \left((0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left(x \cdot x\right)}^3\right))_* + (0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right)\right))_* \leadsto (\left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{{x}^2 \cdot (0.0003579942 * \left(\frac{{\left(\frac{1}{{x}^2}\right)}^3}{{x}^{6}}\right) + \left((\left({\left(\frac{1}{x}\right)}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0008327945 * \left(\frac{1}{{x}^{10}}\right) + \left((0.2909738639 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}\right) * 0.0001789971 + \left(\frac{(0.0005064034 * \left({\left(\frac{1}{x}\right)}^{8}\right) + \left(0.0072644182 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0424060604 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*}{x \cdot (0.0003579942 * \left(\frac{{\left(\frac{1}{{x}^2}\right)}^3}{{x}^{6}}\right) + \left((\left({\left(\frac{1}{x}\right)}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0008327945 * \left(\frac{1}{{x}^{10}}\right) + \left((0.2909738639 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}\right))_*\]
      0
    10. Taylor expanded around inf to get
      \[\color{red}{(\left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{{x}^2 \cdot (0.0003579942 * \left(\frac{{\left(\frac{1}{{x}^2}\right)}^3}{{x}^{6}}\right) + \left((\left({\left(\frac{1}{x}\right)}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0008327945 * \left(\frac{1}{{x}^{10}}\right) + \left((0.2909738639 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}\right) * 0.0001789971 + \left(\frac{(0.0005064034 * \left({\left(\frac{1}{x}\right)}^{8}\right) + \left(0.0072644182 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0424060604 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*}{x \cdot (0.0003579942 * \left(\frac{{\left(\frac{1}{{x}^2}\right)}^3}{{x}^{6}}\right) + \left((\left({\left(\frac{1}{x}\right)}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0008327945 * \left(\frac{1}{{x}^{10}}\right) + \left((0.2909738639 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}\right))_*} \leadsto \color{blue}{(\left(\frac{{\left({\left(\frac{1}{x}\right)}^3\right)}^3}{{x}^2 \cdot (0.0003579942 * \left(\frac{{\left(\frac{1}{{x}^2}\right)}^3}{{x}^{6}}\right) + \left((\left({\left(\frac{1}{x}\right)}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0008327945 * \left(\frac{1}{{x}^{10}}\right) + \left((0.2909738639 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}\right) * 0.0001789971 + \left(\frac{(0.0005064034 * \left({\left(\frac{1}{x}\right)}^{8}\right) + \left(0.0072644182 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0424060604 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.1049934947}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*}{x \cdot (0.0003579942 * \left(\frac{{\left(\frac{1}{{x}^2}\right)}^3}{{x}^{6}}\right) + \left((\left({\left(\frac{1}{x}\right)}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(\frac{1}{{x}^2}\right)}^3\right))_* + (0.0008327945 * \left(\frac{1}{{x}^{10}}\right) + \left((0.2909738639 * \left({\left(\frac{1}{x}\right)}^{4}\right) + \left((\left(\frac{0.7715471019}{x}\right) * \left(\frac{1}{x}\right) + 1)_*\right))_*\right))_*\right))_*}\right))_*}\]
      0

    if -1.1392497874101738e+24 < x < 1.653196896254347e+29

    1. Started with
      \[\frac{\left(\left(\left(\left(1 + 0.1049934947 \cdot \left(x \cdot x\right)\right) + 0.0424060604 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0072644182 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0005064034 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0001789971 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)}{\left(\left(\left(\left(\left(1 + 0.7715471019 \cdot \left(x \cdot x\right)\right) + 0.2909738639 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0694555761 \cdot \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0140005442 \cdot \left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + 0.0008327945 \cdot \left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)\right) + \left(2 \cdot 0.0001789971\right) \cdot \left(\left(\left(\left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot x\right)\right)} \cdot x\]
      0.3
    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))_*}}\]
      0.3
    3. Using strategy rm
      0.3
    4. 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))_* + \color{red}{(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))_* + \color{blue}{\left(0.0001789971 \cdot \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right) + (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))_*}\]
      0.3
    5. Applied simplify 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))_* + \left(\color{red}{0.0001789971 \cdot \left({\left(x \cdot x\right)}^3 \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)\right)} + (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))_* + \left(\color{blue}{\left({x}^3 \cdot {x}^3\right) \cdot \left(\left(x \cdot 0.0001789971\right) \cdot {x}^3\right)} + (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))_*}\]
      0.4
    6. 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))_* + \left(\left({x}^3 \cdot {x}^3\right) \cdot \left(\left(x \cdot 0.0001789971\right) \cdot {x}^3\right) + (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{(0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3\right))_* \cdot x}{(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))_*} + \left(\frac{(0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_* \cdot x}{(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))_*} + 0.0001789971 \cdot \frac{{\left({x}^3\right)}^{3} \cdot {x}^2}{(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))_*}\right)\]
      0.4
    7. Taylor expanded around 0 to get
      \[\color{red}{\frac{(0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3\right))_* \cdot x}{(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))_*} + \left(\frac{(0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_* \cdot x}{(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))_*} + 0.0001789971 \cdot \frac{{\left({x}^3\right)}^{3} \cdot {x}^2}{(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))_*}\right)} \leadsto \color{blue}{\frac{(0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3\right))_* \cdot x}{(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))_*} + \left(\frac{(0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_* \cdot x}{(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))_*} + 0.0001789971 \cdot \frac{{\left({x}^3\right)}^{3} \cdot {x}^2}{(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))_*}\right)}\]
      0.4
    8. Applied simplify to get
      \[\color{red}{\frac{(0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left({x}^2\right)}^3\right))_* \cdot x}{(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))_*} + \left(\frac{(0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_* \cdot x}{(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))_*} + 0.0001789971 \cdot \frac{{\left({x}^3\right)}^{3} \cdot {x}^2}{(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))_*}\right)} \leadsto \color{blue}{(\left(\frac{{\left({x}^3\right)}^3 \cdot \left(x \cdot x\right)}{(0.0003579942 * \left({x}^{6} \cdot {\left(x \cdot x\right)}^3\right) + \left((0.0008327945 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot {x}^{4}\right)\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_* + (\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_*\right))_*}\right) * 0.0001789971 + \left(\frac{x}{(0.0003579942 * \left({x}^{6} \cdot {\left(x \cdot x\right)}^3\right) + \left((0.0008327945 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot {x}^{4}\right)\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_* + (\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_*\right))_*} \cdot \left((0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left(x \cdot x\right)}^3\right))_* + (0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right)\right))_*}\]
      0.4
    9. Applied simplify to get
      \[(\color{red}{\left(\frac{{\left({x}^3\right)}^3 \cdot \left(x \cdot x\right)}{(0.0003579942 * \left({x}^{6} \cdot {\left(x \cdot x\right)}^3\right) + \left((0.0008327945 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot {x}^{4}\right)\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_* + (\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_*\right))_*}\right)} * 0.0001789971 + \left(\frac{x}{(0.0003579942 * \left({x}^{6} \cdot {\left(x \cdot x\right)}^3\right) + \left((0.0008327945 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot {x}^{4}\right)\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_* + (\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_*\right))_*} \cdot \left((0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left(x \cdot x\right)}^3\right))_* + (0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right)\right))_* \leadsto (\color{blue}{\left(\frac{{\left({x}^3\right)}^3 \cdot {x}^2}{(0.0003579942 * \left({x}^3 \cdot \left({x}^3 \cdot {x}^{6}\right)\right) + \left((0.0008327945 * \left({\left({x}^2\right)}^3 \cdot {x}^{4}\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(x \cdot 0.7715471019\right) * x + 1)_*\right))_*\right))_* + (\left({x}^{8}\right) * 0.0140005442 + \left({\left({x}^2\right)}^3 \cdot 0.0694555761\right))_*\right))_*}\right)} * 0.0001789971 + \left(\frac{x}{(0.0003579942 * \left({x}^{6} \cdot {\left(x \cdot x\right)}^3\right) + \left((0.0008327945 * \left(\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) \cdot \left(\left(x \cdot x\right) \cdot {x}^{4}\right)\right) + \left((0.2909738639 * \left({x}^{4}\right) + \left((\left(0.7715471019 \cdot x\right) * x + 1)_*\right))_*\right))_* + (\left({x}^{8}\right) * 0.0140005442 + \left(0.0694555761 \cdot {\left(x \cdot x\right)}^3\right))_*\right))_*} \cdot \left((0.0005064034 * \left({x}^{8}\right) + \left(0.0072644182 \cdot {\left(x \cdot x\right)}^3\right))_* + (0.0424060604 * \left({x}^{4}\right) + \left((\left(0.1049934947 \cdot x\right) * x + 1)_*\right))_*\right)\right))_*\]
      0.4

  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))