Derivation

Split input into 3 regimes
if x < -3.3807721204784955e-16
1. Initial program 1.0
  \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
2. Using strategy rm
3. Applied add-log-exp1.0
  \[\leadsto \color{blue}{\log \left(e^{1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)}\]
4. Using strategy rm
5. Applied add-exp-log1.1
  \[\leadsto \color{blue}{e^{\log \left(\log \left(e^{1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)\right)}}\]
6. Using strategy rm
7. Applied exp-diff1.1
  \[\leadsto e^{\log \left(\log \color{blue}{\left(\frac{e^{1}}{e^{\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}}\right)}\right)}\]
8. Applied log-div1.0
  \[\leadsto e^{\log \color{blue}{\left(\log \left(e^{1}\right) - \log \left(e^{\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)\right)}}\]
9. Simplified1.0
  \[\leadsto e^{\log \left(\color{blue}{1} - \log \left(e^{\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)\right)}\]
if -3.3807721204784955e-16 < x < 2.9354363685255574e-17
1. Initial program 28.0
  \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
2. Using strategy rm
3. Applied add-log-exp28.0
  \[\leadsto \color{blue}{\log \left(e^{1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)}\]
4. Using strategy rm
5. Applied add-exp-log28.0
  \[\leadsto \color{blue}{e^{\log \left(\log \left(e^{1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)\right)}}\]
6. Taylor expanded around inf 28.0
  \[\leadsto e^{\log \color{blue}{\left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \left(1.061405429 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} + 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)}}\]
7. Using strategy rm
8. Applied flip-+28.0
  \[\leadsto e^{\log \left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \left(1.061405429 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}} + \color{blue}{\frac{\left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) - \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) \cdot \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)}{1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}}}\right)\right)}\]
9. Applied associate-*r/28.0
  \[\leadsto e^{\log \left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \left(\color{blue}{\frac{1.061405429 \cdot e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}}} + \frac{\left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) - \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) \cdot \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)}{1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}}\right)\right)}\]
10. Applied frac-add28.0
  \[\leadsto e^{\log \left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \color{blue}{\frac{\left(1.061405429 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(\left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) - \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) \cdot \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)}}\right)}\]
11. Applied flip3-+30.8
  \[\leadsto e^{\log \left(\color{blue}{\frac{{\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right)}^{3} + {\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)}^{3}}{\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) + \left(\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) - \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right)}} - \frac{\left(1.061405429 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(\left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) - \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) \cdot \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)}\right)}\]
12. Applied frac-sub25.6
  \[\leadsto e^{\log \color{blue}{\left(\frac{\left({\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right)}^{3} + {\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)}^{3}\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right) - \left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) + \left(\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) - \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right)\right) \cdot \left(\left(1.061405429 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(\left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) - \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) \cdot \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)}{\left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) + \left(\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) - \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right)\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)}\right)}}\]
13. Applied log-div25.6
  \[\leadsto e^{\color{blue}{\log \left(\left({\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right)}^{3} + {\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)}^{3}\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right) - \left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) + \left(\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) - \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right)\right) \cdot \left(\left(1.061405429 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(\left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) - \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) \cdot \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)\right) - \log \left(\left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) + \left(\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) - \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right)\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)}}\]
14. Applied exp-diff25.6
  \[\leadsto \color{blue}{\frac{e^{\log \left(\left({\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right)}^{3} + {\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)}^{3}\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right) - \left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) + \left(\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) - \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right)\right) \cdot \left(\left(1.061405429 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(\left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}\right) - \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) \cdot \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)\right)}}{e^{\log \left(\left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) + \left(\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right) - \left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right)\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} - 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)}}}\]
if 2.9354363685255574e-17 < x
1. Initial program 0.9
  \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
2. Using strategy rm
3. Applied add-log-exp0.9
  \[\leadsto \color{blue}{\log \left(e^{1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)}\]
4. Using strategy rm
5. Applied add-exp-log0.9
  \[\leadsto \color{blue}{e^{\log \left(\log \left(e^{1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\right)\right)}}\]
6. Taylor expanded around inf 0.9
  \[\leadsto e^{\log \color{blue}{\left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \left(1.061405429 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} + 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)}}\]
7. Using strategy rm
8. Applied pow10.9
  \[\leadsto e^{\log \color{blue}{\left({\left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \left(1.061405429 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} + 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)}^{1}\right)}}\]
9. Applied log-pow0.9
  \[\leadsto e^{\color{blue}{1 \cdot \log \left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \left(1.061405429 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} + 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)}}\]
10. Applied exp-prod0.9
  \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\log \left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \left(1.061405429 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} + 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)\right)}}\]
11. Simplified0.9
  \[\leadsto {\color{blue}{e}}^{\left(\log \left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \left(1.061405429 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} + 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)\right)}\]
Recombined 3 regimes into one program.
Final simplification12.5
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.3807721204784955 \cdot 10^{-16}:\\ \;\;\;\;e^{\log \left(1 - \log \left(e^{e^{-\left|x\right| \cdot \left|x\right|} \cdot \left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \left(1.061405429 \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|} + -1.453152027\right) \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right) + -0.284496736\right)\right) \cdot \frac{1}{1 + 0.3275911 \cdot \left|x\right|}\right)}\right)\right)}\\ \mathbf{elif}\;x \le 2.9354363685255574 \cdot 10^{-17}:\\ \;\;\;\;\frac{e^{\log \left(\left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{5} \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} - \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{1 + 0.3275911 \cdot \left|x\right|} \cdot 0.254829592\right)\right) \cdot \left({\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{4}} \cdot 1.453152027\right)}^{3} + {\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot 0.284496736 + 1\right)}^{3}\right) - \left(\left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} - \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{1 + 0.3275911 \cdot \left|x\right|} \cdot 0.254829592\right) \cdot \left(e^{-{\left(\left|x\right|\right)}^{2}} \cdot 1.061405429\right) + \left(\left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}}\right) \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}}\right) - \left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{1 + 0.3275911 \cdot \left|x\right|} \cdot 0.254829592\right) \cdot \left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{1 + 0.3275911 \cdot \left|x\right|} \cdot 0.254829592\right)\right) \cdot {\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{5}\right) \cdot \left(\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{4}} \cdot 1.453152027\right) \cdot \left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{4}} \cdot 1.453152027\right) + \left(\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot 0.284496736 + 1\right) \cdot \left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot 0.284496736 + 1\right) - \left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot 0.284496736 + 1\right) \cdot \left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{4}} \cdot 1.453152027\right)\right)\right)\right)}}{e^{\log \left(\left(\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{4}} \cdot 1.453152027\right) \cdot \left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{4}} \cdot 1.453152027\right) + \left(\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot 0.284496736 + 1\right) \cdot \left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot 0.284496736 + 1\right) - \left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot 0.284496736 + 1\right) \cdot \left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{4}} \cdot 1.453152027\right)\right)\right) \cdot \left({\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{5} \cdot \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} - \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{1 + 0.3275911 \cdot \left|x\right|} \cdot 0.254829592\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;{e}^{\left(\log \left(\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{4}} \cdot 1.453152027 + \left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot 0.284496736 + 1\right)\right) - \left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{5}} \cdot 1.061405429 + \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{3}} + \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{1 + 0.3275911 \cdot \left|x\right|} \cdot 0.254829592\right)\right)\right)\right)}\\ \end{array}\]

Error

Try it out

Derivation

`if x < -3.3807721204784955e-16`

`if -3.3807721204784955e-16 < x < 2.9354363685255574e-17`

`if 2.9354363685255574e-17 < x`

Runtime

In
Out