Average Error: 13.7 → 12.6
Time: 3.3m
Precision: 64
Internal Precision: 128
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.0009669879910695 \cdot 10^{-17} \lor \neg \left(x \le 2.2459177707888453 \cdot 10^{-10}\right):\\ \;\;\;\;\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(-\left|x\right|\right) \cdot \left|x\right|} - e^{\left(-\left|x\right|\right) \cdot \left|x\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) + \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)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(e^{\left(-\left|x\right|\right) \cdot \left|x\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(-\left|x\right|\right) \cdot \left|x\right|}\right) \cdot \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\right) + \left(\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) + \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)_*}\right) \cdot \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(-\left|x\right|\right) \cdot \left|x\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(-\left|x\right|\right) \cdot \left|x\right|}\right) - \left(e^{\left(-\left|x\right|\right) \cdot \left|x\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(-\left|x\right|\right) \cdot \left|x\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)}{\left(\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) + \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)_*}\right) \cdot \left(e^{\left(-\left|x\right|\right) \cdot \left|x\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(-\left|x\right|\right) \cdot \left|x\right|}\right)}\\ \end{array}\]

Error

Bits error versus x

Derivation

  1. Split input into 2 regimes

  2. if x < -2.0009669879910695e-17 or 2.2459177707888453e-10 < x

    1. Initial program 0.8

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

    2. Simplified0.8

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

    3. Taylor expanded around -inf 0.8

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

    4. Simplified0.8

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

    6. Applied associate-+l+0.8

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

    8. Applied associate-+r+0.8

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

    if -2.0009669879910695e-17 < x < 2.2459177707888453e-10

    1. Initial program 28.0

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

    2. Simplified28.0

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

    3. Taylor expanded around -inf 28.0

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

    4. Simplified28.0

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

    6. Applied flip--28.0

      \[\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-+28.0

      \[\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-add25.6

      \[\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 simplification12.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.0009669879910695 \cdot 10^{-17} \lor \neg \left(x \le 2.2459177707888453 \cdot 10^{-10}\right):\\ \;\;\;\;\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(-\left|x\right|\right) \cdot \left|x\right|} - e^{\left(-\left|x\right|\right) \cdot \left|x\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) + \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)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(e^{\left(-\left|x\right|\right) \cdot \left|x\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(-\left|x\right|\right) \cdot \left|x\right|}\right) \cdot \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\right) + \left(\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) + \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)_*}\right) \cdot \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(-\left|x\right|\right) \cdot \left|x\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(-\left|x\right|\right) \cdot \left|x\right|}\right) - \left(e^{\left(-\left|x\right|\right) \cdot \left|x\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(-\left|x\right|\right) \cdot \left|x\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)}{\left(\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) + \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)_*}\right) \cdot \left(e^{\left(-\left|x\right|\right) \cdot \left|x\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(-\left|x\right|\right) \cdot \left|x\right|}\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019008 +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)))))))

Details

Time bar (total: 3.3m)Debug log

sample164.0ms

Algorithm
intervals

simplify238.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

238.0ms
(- 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))))))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.9b

localize51.0ms

Local error

Found 4 expressions with local error:

14.8b
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
0.5b
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
0.2b
(/ 1 (fma 0.3275911 (fabs x) 1))
0.2b
(/ 1 (fma 0.3275911 (fabs x) 1))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
4 → 56
Calls

4 calls. Slowest were:

1.0ms
(/ 1 (fma 0.3275911 (fabs x) 1))
1.0ms
(/ 1 (fma 0.3275911 (fabs x) 1))
0.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)

series580.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

360.0ms
(fma (/ -1 (exp (* (fabs x) (fabs x)))) (fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1))) 1)
174.0ms
(fma (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) 1.421413741) -0.284496736) (/ 0.254829592 (fma 0.3275911 (fabs x) 1)))
23.0ms
(/ 1 (fma 0.3275911 (fabs x) 1))
22.0ms
(/ 1 (fma 0.3275911 (fabs x) 1))

simplify1.5s

Counts
20 → 68
Calls

20 calls. Slowest were:

398.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (* 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 5))) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))
311.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (* 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 5))) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))
295.0ms
(- (+ (* 0.254829592 (/ 1 (+ (* 0.3275911 (fabs x)) 1))) (+ (* 1.061405429 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 5))) (* 1.421413741 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 3))))) (+ (* 0.284496736 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 2))) (* 1.453152027 (/ 1 (pow (+ (* 0.3275911 (fabs x)) 1) 4)))))

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.8b

localize56.0ms

Local error

Found 4 expressions with local error:

14.8b
(+ (+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1) (- (* (exp (* (- (fabs x)) (fabs x))) (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4)) (/ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))))))
0.2b
(/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))
0.2b
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4))
0.1b
(/ 1.421413741 (fma 0.3275911 (fabs x) 1))

rewrite599.0ms

Algorithm
rewrite-expression-head
Counts
4 → 246
Calls

4 calls. Slowest were:

577.0ms
(+ (+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1) (- (* (exp (* (- (fabs x)) (fabs x))) (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4)) (/ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))))))
2.0ms
(/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))
2.0ms
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4))

series890.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

787.0ms
(+ (+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1) (- (* (exp (* (- (fabs x)) (fabs x))) (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4)) (/ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))))))
46.0ms
(/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))
38.0ms
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4))
19.0ms
(/ 1.421413741 (fma 0.3275911 (fabs x) 1))

simplify1.3m

Counts
313 → 258
Calls

313 calls. Slowest were:

955.0ms
(* (cbrt (+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1)) (cbrt (+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1)))
904.0ms
(* (+ (* (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)))) (- (* 1 1) (* (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1))) (exp (* (fabs x) (fabs x))))
830.0ms
(* (- (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1) (* (* (exp (* (fabs x) (fabs x))) (* (pow (fma 0.3275911 (fabs x) 1) 4) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)))) (exp (* (fabs x) (fabs x)))))

prune8.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.5b

localize47.0ms

Local error

Found 4 expressions with local error:

14.8b
(+ (+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1) (- (* (exp (* (- (fabs x)) (fabs x))) (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4)) (/ (* (* (cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))))))
0.3b
(cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))
0.3b
(cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))
0.3b
(cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Counts
4 → 216
Calls

4 calls. Slowest were:

167.0ms
(+ (+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1) (- (* (exp (* (- (fabs x)) (fabs x))) (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4)) (/ (* (* (cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))))))
1.0ms
(cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))
1.0ms
(cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))

series1.7s

Counts
4 → 12
Calls

4 calls. Slowest were:

1.0s
(+ (+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1) (- (* (exp (* (- (fabs x)) (fabs x))) (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4)) (/ (* (* (cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1))) (cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))) (cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))))))
232.0ms
(cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))
229.0ms
(cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))
204.0ms
(cbrt (/ 1.421413741 (fma 0.3275911 (fabs x) 1)))

simplify1.1m

Counts
289 → 228
Calls

289 calls. Slowest were:

1.1s
(* (cbrt (+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1)) (cbrt (+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1)))
1.1s
(* (- (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1) (* (exp (* (fabs x) (fabs x))) (* (exp (* (fabs x) (fabs x))) (* (fma 0.3275911 (fabs x) 1) (pow (fma 0.3275911 (fabs x) 1) 5)))))
888.0ms
(* (+ (* (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)))) (- (* 1 1) (* (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 1))) (exp (* (fabs x) (fabs x))))

prune7.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) (+ 1 (- (* (exp (* (- (fabs x)) (fabs x))) (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4)) (/ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5)))))))
0.8b
(+ 1 (- (* (exp (* (- (fabs x)) (fabs x))) (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4)) (/ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))))))
0.2b
(/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))
0.2b
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4))

rewrite141.0ms

Algorithm
rewrite-expression-head
Counts
4 → 146
Calls

4 calls. Slowest were:

96.0ms
(+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) (+ 1 (- (* (exp (* (- (fabs x)) (fabs x))) (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4)) (/ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5)))))))
36.0ms
(+ 1 (- (* (exp (* (- (fabs x)) (fabs x))) (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4)) (/ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))))))
2.0ms
(/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))

series1.6s

Counts
4 → 12
Calls

4 calls. Slowest were:

843.0ms
(+ (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) (+ 1 (- (* (exp (* (- (fabs x)) (fabs x))) (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4)) (/ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5)))))))
651.0ms
(+ 1 (- (* (exp (* (- (fabs x)) (fabs x))) (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4)) (/ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))))))
67.0ms
(/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5))
48.0ms
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1) 4))

simplify21.4s

Counts
111 → 158
Calls

111 calls. Slowest were:

994.0ms
(sqrt (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))
809.0ms
(* (cbrt (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)))) (cbrt (/ (/ 0.284496736 (exp (* (fabs x) (fabs x)))) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)))))
519.0ms
(- (* (exp (* (- (fabs x)) (fabs x))) (fma (- (/ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) (fma 0.3275911 (fabs x) 1))) (/ 1 (fma 0.3275911 (fabs x) 1)) (* (/ (/ 1.421413741 (fma 0.3275911 (fabs x) 1)) (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))))) (* (exp (* (- (fabs x)) (fabs x))) (+ (/ 0.254829592 (fma 0.3275911 (fabs x) 1)) (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1) 5)))))

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.4b

regimes415.0ms

Accuracy

93.4% (0.1b remaining)

Error of 12.6b against oracle of 12.5b and baseline of 13.7b

bsearch981.0ms

end0.0ms

sample2.5s

Algorithm
intervals