\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
Test:
Jmat.Real.erf
Bits:
128 bits
Bits error versus x
Time: 44.4 s
Input Error: 14.1
Output Error: 13.3
Log:
Profile: 🕒
\(\frac{{1}^{3} - {\left(\sqrt{{\left(\frac{\left(0.254829592 + \frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^3}\right) + \left(\frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911} + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right)}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}^3}\right)}^2}{\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} + 1\right) + {\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}\)
  1. Started with
    \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
    14.1
  2. Using strategy rm
    14.1
  3. Applied add-sqr-sqrt to get
    \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \color{red}{\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \color{blue}{{\left(\sqrt{\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429}\right)}^2}\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
    14.1
  4. Applied simplify to get
    \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\color{red}{\left(\sqrt{\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429}\right)}}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|} \leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\color{blue}{\left(\sqrt{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}\right)}}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
    14.1
  5. Using strategy rm
    14.1
  6. Applied flip3-- to get
    \[\color{red}{1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\left(\sqrt{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}\right)}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}} \leadsto \color{blue}{\frac{{1}^{3} - {\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\left(\sqrt{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}\right)}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{{1}^2 + \left({\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\left(\sqrt{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}\right)}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^2 + 1 \cdot \left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\left(\sqrt{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}\right)}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}}\]
    14.1
  7. Applied simplify to get
    \[\frac{{1}^{3} - {\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\left(\sqrt{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}\right)}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{\color{red}{{1}^2 + \left({\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\left(\sqrt{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}\right)}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^2 + 1 \cdot \left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\left(\sqrt{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}\right)}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)\right)}} \leadsto \frac{{1}^{3} - {\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\left(\sqrt{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}\right)}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}{\color{blue}{\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} + 1\right) + {\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}}\]
    14.1
  8. Using strategy rm
    14.1
  9. Applied add-sqr-sqrt to get
    \[\frac{{1}^{3} - \color{red}{{\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\left(\sqrt{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}\right)}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}}{\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} + 1\right) + {\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}^2} \leadsto \frac{{1}^{3} - \color{blue}{{\left(\sqrt{{\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\left(\sqrt{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}\right)}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}^2}}{\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} + 1\right) + {\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}\]
    13.3
  10. Applied simplify to get
    \[\frac{{1}^{3} - {\color{red}{\left(\sqrt{{\left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + {\left(\sqrt{\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1}}\right)}^2\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right)}}^2}{\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} + 1\right) + {\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}^2} \leadsto \frac{{1}^{3} - {\color{blue}{\left(\sqrt{{\left(\frac{\left(\left(\frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.421413741}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right) + {\left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1}\right)}^3 \cdot \left(\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1} + -1.453152027\right)\right) + 0.254829592}{\left(\left|x\right| \cdot 0.3275911 + 1\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}^3}\right)}}^2}{\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} + 1\right) + {\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}\]
    13.3
  11. Applied simplify to get
    \[\frac{{1}^{3} - {\left(\sqrt{\color{red}{{\left(\frac{\left(\left(\frac{-0.284496736}{\left|x\right| \cdot 0.3275911 + 1} + \frac{\frac{1.421413741}{\left|x\right| \cdot 0.3275911 + 1}}{\left|x\right| \cdot 0.3275911 + 1}\right) + {\left(\frac{1}{\left|x\right| \cdot 0.3275911 + 1}\right)}^3 \cdot \left(\frac{1.061405429}{\left|x\right| \cdot 0.3275911 + 1} + -1.453152027\right)\right) + 0.254829592}{\left(\left|x\right| \cdot 0.3275911 + 1\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}^3}}\right)}^2}{\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} + 1\right) + {\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}^2} \leadsto \frac{{1}^{3} - {\left(\sqrt{\color{blue}{{\left(\frac{\left(0.254829592 + \frac{-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}}{{\left(1 + \left|x\right| \cdot 0.3275911\right)}^3}\right) + \left(\frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911} + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right)}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}^3}}\right)}^2}{\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}} + 1\right) + {\left(\frac{\left(\left(0.254829592 + \frac{-0.284496736}{1 + \left|x\right| \cdot 0.3275911}\right) + \frac{\frac{1.421413741}{1 + \left|x\right| \cdot 0.3275911}}{1 + \left|x\right| \cdot 0.3275911}\right) + \left(-1.453152027 + \frac{1.061405429}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot {\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911}\right)}^3}{\left(1 + \left|x\right| \cdot 0.3275911\right) \cdot e^{\left|x\right| \cdot \left|x\right|}}\right)}^2}\]
    13.3

Original test:


(lambda ((x default))
  #:name "Jmat.Real.erf"
  (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))