Error

Derivation

1. Split input into 2 regimes

2. if x < -27.011360069309372 or 2.329938848652218e-05 < x

   1. Initial program 0.1

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

   2. Initial simplification0.1

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

   4. Applied add-cube-cbrt0.1

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

   6. Applied add-log-exp0.1

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

   8. Applied add-cube-cbrt0.1

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

   if -27.011360069309372 < x < 2.329938848652218e-05

   1. Initial program 27.7

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

   2. Initial simplification27.7

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

   3. Taylor expanded around -inf 27.7

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

   4. Simplified27.7

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

   6. Applied flip--27.7

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

   7. Applied flip3-+27.7

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

   8. Applied frac-add25.4

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

4. Final simplification12.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -27.011360069309372 \lor \neg \left(x \le 2.329938848652218 \cdot 10^{-05}\right):\\ \;\;\;\;\sqrt[3]{\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\sqrt[3]{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*} \cdot \left(\sqrt[3]{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*} \cdot \sqrt[3]{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*}\right)\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)} \cdot \left(\sqrt[3]{\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\sqrt[3]{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*} \cdot \left(\sqrt[3]{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*} \cdot \sqrt[3]{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*}\right)\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)} \cdot \sqrt[3]{\log \left(e^{(\left(\frac{-1}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\sqrt[3]{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*} \cdot \left(\sqrt[3]{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*} \cdot \sqrt[3]{(\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left((\left(\frac{1}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot \left(\frac{1.061405429}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*}\right)\right) + \left(\frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right))_*\right) + 1)_*}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(\left(\frac{1.453152027}{{\left((0.3275911 \cdot \left(\left|x\right|\right) + 1)_*\right)}^{4}} - \frac{\frac{1.421413741}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot e^{\left|x\right| \cdot \left(-\left|x\right|\right)}\right) \cdot \left(\left(\frac{1.453152027}{{\left((0.3275911 \cdot \left(\left|x\right|\right) + 1)_*\right)}^{4}} - \frac{\frac{1.421413741}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot e^{\left|x\right| \cdot \left(-\left|x\right|\right)}\right) - \left(e^{\left|x\right| \cdot \left(-\left|x\right|\right)} \cdot \left(\frac{1.061405429}{{\left((0.3275911 \cdot \left(\left|x\right|\right) + 1)_*\right)}^{5}} + \frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right)\right) \cdot \left(e^{\left|x\right| \cdot \left(-\left|x\right|\right)} \cdot \left(\frac{1.061405429}{{\left((0.3275911 \cdot \left(\left|x\right|\right) + 1)_*\right)}^{5}} + \frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right)\right)\right) \cdot \left(\frac{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|}}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|}}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + \left(1 - \frac{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|}}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right)\right) + \left(e^{\left|x\right| \cdot \left(-\left|x\right|\right)} \cdot \left(\frac{1.061405429}{{\left((0.3275911 \cdot \left(\left|x\right|\right) + 1)_*\right)}^{5}} + \frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) + \left(\frac{1.453152027}{{\left((0.3275911 \cdot \left(\left|x\right|\right) + 1)_*\right)}^{4}} - \frac{\frac{1.421413741}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot e^{\left|x\right| \cdot \left(-\left|x\right|\right)}\right) \cdot \left(1 + {\left(\frac{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|}}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right)}^{3}\right)}{\left(e^{\left|x\right| \cdot \left(-\left|x\right|\right)} \cdot \left(\frac{1.061405429}{{\left((0.3275911 \cdot \left(\left|x\right|\right) + 1)_*\right)}^{5}} + \frac{0.254829592}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) + \left(\frac{1.453152027}{{\left((0.3275911 \cdot \left(\left|x\right|\right) + 1)_*\right)}^{4}} - \frac{\frac{1.421413741}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right) \cdot e^{\left|x\right| \cdot \left(-\left|x\right|\right)}\right) \cdot \left(\frac{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|}}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} \cdot \frac{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|}}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*} + \left(1 - \frac{\frac{0.284496736}{e^{\left|x\right| \cdot \left|x\right|}}}{(0.3275911 \cdot \left(\left|x\right|\right) + 1)_* \cdot (0.3275911 \cdot \left(\left|x\right|\right) + 1)_*}\right)\right)}\\ \end{array}\]

Runtime

Time bar (total: 2.0m)Debug logProfile

herbie shell --seed 2018274 +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)))))))