Error

Derivation

1. Initial program 13.9

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

3. Applied add-cbrt-cube13.9

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

4. Applied simplify13.9

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

6. Applied flip--13.9

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

8. Applied flip--13.8

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

10. Applied flip3--13.8

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

11. Applied simplify13.8

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

12. Applied simplify13.8

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

Runtime

Time bar (total: 7.0m)Debug logProfile

herbie shell --seed '#(1064173506 2580572819 2847706409 4129882574 1125180799 1845288547)' 
(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)))))))