Average Error: 14.1 → 2.3
Time: 2.1m
Precision: 64
Internal Precision: 384
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\sqrt{\left(1.453152027 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{4}} + \left(0.284496736 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{2}} + 1\right)\right) - \left(1.421413741 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{3}} + \left(0.254829592 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{0.3275911 \cdot \left|x\right| + 1} + 1.061405429 \cdot \frac{e^{-{\left(\left|x\right|\right)}^{2}}}{{\left(0.3275911 \cdot \left|x\right| + 1\right)}^{5}}\right)\right)} \cdot \sqrt{1 - \frac{(\left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} \cdot \sqrt[3]{(\left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) \cdot \left((\left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) \cdot \left(\frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*}\right) \cdot \left(\sqrt[3]{(\left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) \cdot \left((\left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) \cdot \left(\frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -1.453152027\right) + 1.421413741)_*\right) + -0.284496736)_*} \cdot \sqrt[3]{(\left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) \cdot \left((\left(\frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -1.453152027\right) \cdot \left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + 1.421413741)_*\right) + -0.284496736)_*}\right) + 0.254829592)_*}{\frac{e^{\left|x\right| \cdot \left|x\right|}}{\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}}}}\]

Error

Bits error versus x

Derivation

  1. Initial program 14.1

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

  3. Applied add-cube-cbrt14.1

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

  4. Applied simplify14.1

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

  5. Applied simplify14.1

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

  7. Applied add-log-exp14.1

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

  9. Applied add-sqr-sqrt14.1

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

  10. Applied exp-prod14.1

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

  11. Applied log-pow14.1

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

  12. Applied simplify14.1

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

  13. Taylor expanded around inf 2.3

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

Runtime

Time bar (total: 2.1m)Debug logProfile

herbie shell --seed '#(1070258749 1877548225 2229079127 1588002776 3179087814 1886870650)' +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)))))))