Error

Derivation

1. Initial program 14.0

   \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

2. Taylor expanded around -inf 14.0

   \[\leadsto \color{blue}{\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \left(1.061405429 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} + 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)}\]
3. Using strategy rm

4. Applied add-exp-log14.0

   \[\leadsto \color{blue}{e^{\log \left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \left(1.061405429 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}} + \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} + 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)}}\]
5. Using strategy rm

6. Applied add-cube-cbrt14.0

   \[\leadsto e^{\color{blue}{\left(\sqrt[3]{\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)} \cdot \sqrt[3]{\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) \cdot \sqrt[3]{\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)}}}\]

7. Applied exp-prod14.0

   \[\leadsto \color{blue}{{\left(e^{\sqrt[3]{\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)} \cdot \sqrt[3]{\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)}^{\left(\sqrt[3]{\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)}}\]
8. Using strategy rm

9. Applied associate-*r/14.0

   \[\leadsto {\left(e^{\sqrt[3]{\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)} \cdot \sqrt[3]{\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)}^{\left(\sqrt[3]{\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}} + \color{blue}{\frac{0.254829592 \cdot e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}}\right)\right)\right)}\right)}\]

10. Applied associate-*r/14.0

    \[\leadsto {\left(e^{\sqrt[3]{\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)} \cdot \sqrt[3]{\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)}^{\left(\sqrt[3]{\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(\color{blue}{\frac{1.421413741 \cdot e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}}} + \frac{0.254829592 \cdot e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right)\right)\right)}\right)}\]

11. Applied frac-add14.0

    \[\leadsto {\left(e^{\sqrt[3]{\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)} \cdot \sqrt[3]{\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)}^{\left(\sqrt[3]{\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 e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.254829592 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}}\right)\right)}\right)}\]

12. Applied associate-*r/14.0

    \[\leadsto {\left(e^{\sqrt[3]{\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)} \cdot \sqrt[3]{\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)}^{\left(\sqrt[3]{\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 e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.254829592 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)}\right)\right)}\right)}\]

13. Applied frac-add14.0

    \[\leadsto {\left(e^{\sqrt[3]{\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)} \cdot \sqrt[3]{\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)}^{\left(\sqrt[3]{\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({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(\left(1.421413741 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.254829592 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)\right)}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right)}}\right)}\right)}\]

14. Applied flip-+14.0

    \[\leadsto {\left(e^{\sqrt[3]{\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)} \cdot \sqrt[3]{\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)}^{\left(\sqrt[3]{\log \left(\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \color{blue}{\frac{\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right) - 1 \cdot 1}{0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} - 1}}\right) - \frac{\left(1.061405429 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(\left(1.421413741 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.254829592 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)\right)}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right)}\right)}\right)}\]

15. Applied associate-*r/14.0

    \[\leadsto {\left(e^{\sqrt[3]{\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)} \cdot \sqrt[3]{\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)}^{\left(\sqrt[3]{\log \left(\left(\color{blue}{\frac{1.453152027 \cdot e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}}} + \frac{\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right) - 1 \cdot 1}{0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} - 1}\right) - \frac{\left(1.061405429 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(\left(1.421413741 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.254829592 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)\right)}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right)}\right)}\right)}\]

16. Applied frac-add14.4

    \[\leadsto {\left(e^{\sqrt[3]{\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)} \cdot \sqrt[3]{\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)}^{\left(\sqrt[3]{\log \left(\color{blue}{\frac{\left(1.453152027 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\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(0.3275911 \cdot \left|x\right| + 1\right)}^{4} \cdot \left(\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right) - 1 \cdot 1\right)}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4} \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)}} - \frac{\left(1.061405429 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(\left(1.421413741 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.254829592 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)\right)}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right)}\right)}\right)}\]

17. Applied frac-sub12.2

    \[\leadsto {\left(e^{\sqrt[3]{\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)} \cdot \sqrt[3]{\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)}^{\left(\sqrt[3]{\log \color{blue}{\left(\frac{\left(\left(1.453152027 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\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(0.3275911 \cdot \left|x\right| + 1\right)}^{4} \cdot \left(\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right) - 1 \cdot 1\right)\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right)\right) - \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4} \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) \cdot \left(\left(1.061405429 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(\left(1.421413741 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.254829592 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)\right)\right)}{\left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4} \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) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right)\right)}\right)}}\right)}\]

18. Simplified12.2

    \[\leadsto {\left(e^{\sqrt[3]{\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)} \cdot \sqrt[3]{\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)}^{\left(\sqrt[3]{\log \left(\frac{\left(\left(1.453152027 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\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(0.3275911 \cdot \left|x\right| + 1\right)}^{4} \cdot \left(\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right) - 1 \cdot 1\right)\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right)\right) - \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4} \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) \cdot \left(\left(1.061405429 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left({\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.3275911 \cdot \left|x\right| + 1\right)\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} \cdot \left(\left(1.421413741 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(0.254829592 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)\right)\right)}{\color{blue}{\left(\left({\left((\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*\right)}^{5} \cdot {\left((\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*\right)}^{4}\right) \cdot {\left((\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*\right)}^{4}\right) \cdot (\left(\frac{{\left(e^{\left|x\right|}\right)}^{\left(-\left|x\right|\right)}}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_* \cdot (\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) \cdot 0.284496736 + -1)_*}}\right)}\right)}\]

19. Final simplification12.2

    \[\leadsto {\left(e^{\sqrt[3]{\log \left(\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} \cdot 1.453152027 + \left(1 + 0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) - \left(\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} \cdot 1.421413741 + 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) + 1.061405429 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}}\right)\right)} \cdot \sqrt[3]{\log \left(\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} \cdot 1.453152027 + \left(1 + 0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) - \left(\left(\frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} \cdot 1.421413741 + 0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1}\right) + 1.061405429 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}}\right)\right)}}\right)}^{\left(\sqrt[3]{\log \left(\frac{\left(\left(\left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right) \cdot \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}}\right) - 1\right) \cdot {\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) \cdot \left(1.453152027 \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)\right) \cdot \left(\left(\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}\right) \cdot {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}\right) - \left(\left(\left(e^{-{\left(\left|x\right|\right)}^{2}} \cdot 1.421413741\right) \cdot \left(0.3275911 \cdot \left|x\right| + 1\right) + {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3} \cdot \left(e^{-{\left(\left|x\right|\right)}^{2}} \cdot 0.254829592\right)\right) \cdot {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5} + \left(e^{-{\left(\left|x\right|\right)}^{2}} \cdot 1.061405429\right) \cdot \left(\left(0.3275911 \cdot \left|x\right| + 1\right) \cdot {\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}\right)\right) \cdot \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(0.3275911 \cdot \left|x\right| + 1\right)}^{4}\right)}{\left(\left({\left((\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*\right)}^{4} \cdot {\left((\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*\right)}^{5}\right) \cdot {\left((\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*\right)}^{4}\right) \cdot (\left(\frac{{\left(e^{\left|x\right|}\right)}^{\left(-\left|x\right|\right)}}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_* \cdot (\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) \cdot 0.284496736 + -1)_*}\right)}\right)}\]

Runtime

Time bar (total: 2.7m)Debug logProfile

herbie shell --seed 2018340 +o rules:numerics
(FPCore (x)
  :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)))))))