Average Error: 13.8 → 13.0
Time: 6.1m
Precision: 64
Internal Precision: 576
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\frac{\left(\sqrt[3]{(\left(\sqrt{{1}^{3}}\right) \cdot \left(\sqrt{{1}^{3}}\right) + \left(-\sqrt{{\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 (e^{\log_* (1 + (\left(\frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -1.453152027\right) \cdot \left(\frac{\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + \left(\frac{1.421413741}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -0.284496736\right))_*)} - 1)^*\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\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 (e^{\log_* (1 + (\left(\frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -1.453152027\right) \cdot \left(\frac{\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + \left(\frac{1.421413741}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -0.284496736\right))_*)} - 1)^*\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right))_*} \cdot \sqrt[3]{(\left(\sqrt{{1}^{3}}\right) \cdot \left(\sqrt{{1}^{3}}\right) + \left(-\sqrt{{\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 (e^{\log_* (1 + (\left(\frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -1.453152027\right) \cdot \left(\frac{\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + \left(\frac{1.421413741}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -0.284496736\right))_*)} - 1)^*\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\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 (e^{\log_* (1 + (\left(\frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -1.453152027\right) \cdot \left(\frac{\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + \left(\frac{1.421413741}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -0.284496736\right))_*)} - 1)^*\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right))_*}\right) \cdot \sqrt[3]{(\left(\sqrt{{1}^{3}}\right) \cdot \left(\sqrt{{1}^{3}}\right) + \left(-\sqrt{{\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 (e^{\log_* (1 + (\left(\frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -1.453152027\right) \cdot \left(\frac{\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + \left(\frac{1.421413741}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -0.284496736\right))_*)} - 1)^*\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}} \cdot \sqrt{{\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 (e^{\log_* (1 + (\left(\frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -1.453152027\right) \cdot \left(\frac{\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + \left(\frac{1.421413741}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -0.284496736\right))_*)} - 1)^*\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}^{3}}\right))_*} + \left({\left(\frac{(\left((\left(-1.453152027 + \frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) \cdot \left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_* \cdot (\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + \left(\frac{1.421413741}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -0.284496736\right))_*\right) \cdot \left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} \cdot \frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + \left(\frac{0.254829592}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right))_*}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3} - {\left(\frac{(\left((\left(-1.453152027 + \frac{1.061405429}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) \cdot \left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_* \cdot (\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + \left(\frac{1.421413741}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} + -0.284496736\right))_*\right) \cdot \left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*} \cdot \frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) + \left(\frac{0.254829592}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right))_*}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}\right)}{(\left(\frac{(\left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_* \cdot (\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right) \cdot \left((\left(\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_* \cdot (\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) + \left(-0.284496736 + \frac{1.421413741}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right))_*\right) + \left(\frac{0.254829592}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right))_*}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left((\left((\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)_* \cdot (\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) + \left(-0.284496736 + \frac{1.421413741}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}\right))_*\right) + 0.254829592)_*\right) \cdot \left(\frac{\frac{1}{(\left(\left|x\right|\right) \cdot 0.3275911 + 1)_*}}{e^{\left|x\right| \cdot \left|x\right|}}\right) + 1)_*\right) + 1)_*}\]

Error

Bits error versus x

Derivation

  1. Initial program 13.8

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

  3. Applied expm1-log1p-u13.8

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

  4. Applied simplify13.8

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

  6. Applied flip3--13.8

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

  7. Applied simplify13.8

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

  9. Applied add-sqr-sqrt13.0

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

  10. Applied add-sqr-sqrt13.0

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

  11. Applied prod-diff13.1

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

  12. Applied simplify13.0

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

  14. Applied add-cube-cbrt13.0

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

Runtime

Time bar (total: 6.1m)Debug logProfile

herbie shell --seed '#(1072840222 1305617769 1692503039 1353360431 4178980589 1488672652)' +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)))))))