Average Error: 13.8 → 13.8
Time: 54.0s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[e^{\log \left(1 - e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1 \cdot \left(\log \left({\left(e^{\frac{1}{1 \cdot 1 - 0.3275911000000000239396058532292954623699 \cdot \left(0.3275911000000000239396058532292954623699 \cdot {\left(\left|x\right|\right)}^{2}\right)}}\right)}^{\left(1.061405428999999900341322245367337018251 \cdot \left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)\right)}\right) + -1.453152027000000012790792425221297889948\right)}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right)\right)\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right)}\]
1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
e^{\log \left(1 - e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1 \cdot \left(\log \left({\left(e^{\frac{1}{1 \cdot 1 - 0.3275911000000000239396058532292954623699 \cdot \left(0.3275911000000000239396058532292954623699 \cdot {\left(\left|x\right|\right)}^{2}\right)}}\right)}^{\left(1.061405428999999900341322245367337018251 \cdot \left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)\right)}\right) + -1.453152027000000012790792425221297889948\right)}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right)\right)\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right)}
double f(double x) {
        double r244782 = 1.0;
        double r244783 = 0.3275911;
        double r244784 = x;
        double r244785 = fabs(r244784);
        double r244786 = r244783 * r244785;
        double r244787 = r244782 + r244786;
        double r244788 = r244782 / r244787;
        double r244789 = 0.254829592;
        double r244790 = -0.284496736;
        double r244791 = 1.421413741;
        double r244792 = -1.453152027;
        double r244793 = 1.061405429;
        double r244794 = r244788 * r244793;
        double r244795 = r244792 + r244794;
        double r244796 = r244788 * r244795;
        double r244797 = r244791 + r244796;
        double r244798 = r244788 * r244797;
        double r244799 = r244790 + r244798;
        double r244800 = r244788 * r244799;
        double r244801 = r244789 + r244800;
        double r244802 = r244788 * r244801;
        double r244803 = r244785 * r244785;
        double r244804 = -r244803;
        double r244805 = exp(r244804);
        double r244806 = r244802 * r244805;
        double r244807 = r244782 - r244806;
        return r244807;
}
↓
double f(double x) {
        double r244808 = 1.0;
        double r244809 = x;
        double r244810 = fabs(r244809);
        double r244811 = 2.0;
        double r244812 = pow(r244810, r244811);
        double r244813 = -r244812;
        double r244814 = exp(r244813);
        double r244815 = 0.254829592;
        double r244816 = 0.3275911;
        double r244817 = r244816 * r244810;
        double r244818 = r244808 + r244817;
        double r244819 = r244808 / r244818;
        double r244820 = -0.284496736;
        double r244821 = r244808 * r244808;
        double r244822 = r244816 * r244812;
        double r244823 = r244816 * r244822;
        double r244824 = r244821 - r244823;
        double r244825 = r244808 / r244824;
        double r244826 = exp(r244825);
        double r244827 = 1.061405429;
        double r244828 = r244808 - r244817;
        double r244829 = r244827 * r244828;
        double r244830 = pow(r244826, r244829);
        double r244831 = log(r244830);
        double r244832 = -1.453152027;
        double r244833 = r244831 + r244832;
        double r244834 = r244808 * r244833;
        double r244835 = r244834 / r244818;
        double r244836 = 1.421413741;
        double r244837 = r244835 + r244836;
        double r244838 = r244819 * r244837;
        double r244839 = r244820 + r244838;
        double r244840 = r244819 * r244839;
        double r244841 = r244815 + r244840;
        double r244842 = r244841 * r244819;
        double r244843 = r244814 * r244842;
        double r244844 = r244808 - r244843;
        double r244845 = log(r244844);
        double r244846 = exp(r244845);
        return r244846;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.8

    \[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  2. Using strategy rm

  3. Applied flip-+13.8

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{\color{blue}{\frac{1 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)}{1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  4. Applied associate-/r/13.8

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \color{blue}{\left(\frac{1}{1 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)\right)} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  5. Simplified13.8

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \left(\color{blue}{\frac{1}{1 \cdot 1 - \left({\left(\left|x\right|\right)}^{2} \cdot 0.3275911000000000239396058532292954623699\right) \cdot 0.3275911000000000239396058532292954623699}} \cdot \left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  6. Using strategy rm

  7. Applied add-exp-log13.8

    \[\leadsto \color{blue}{e^{\log \left(1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \left(\frac{1}{1 \cdot 1 - \left({\left(\left|x\right|\right)}^{2} \cdot 0.3275911000000000239396058532292954623699\right) \cdot 0.3275911000000000239396058532292954623699} \cdot \left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}}\]

  8. Simplified13.8

    \[\leadsto e^{\color{blue}{\log \left(1 - e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\left(-1.453152027000000012790792425221297889948 + \frac{1}{1 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot 0.3275911000000000239396058532292954623699\right) \cdot {\left(\left|x\right|\right)}^{2}} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right)\right)\right)\right)}}\]
  9. Using strategy rm

  10. Applied add-log-exp13.8

    \[\leadsto e^{\log \left(1 - e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\left(-1.453152027000000012790792425221297889948 + \color{blue}{\log \left(e^{\frac{1}{1 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot 0.3275911000000000239396058532292954623699\right) \cdot {\left(\left|x\right|\right)}^{2}} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)}\right)}\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right)\right)\right)\right)}\]

  11. Simplified13.8

    \[\leadsto e^{\log \left(1 - e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\frac{1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\left(-1.453152027000000012790792425221297889948 + \log \color{blue}{\left({\left(e^{\frac{1}{1 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot {\left(\left|x\right|\right)}^{2}\right) \cdot 0.3275911000000000239396058532292954623699}}\right)}^{\left(1.061405428999999900341322245367337018251 \cdot \left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)\right)}\right)}\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right)\right)\right)\right)}\]

  12. Final simplification13.8

    \[\leadsto e^{\log \left(1 - e^{-{\left(\left|x\right|\right)}^{2}} \cdot \left(\left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1 \cdot \left(\log \left({\left(e^{\frac{1}{1 \cdot 1 - 0.3275911000000000239396058532292954623699 \cdot \left(0.3275911000000000239396058532292954623699 \cdot {\left(\left|x\right|\right)}^{2}\right)}}\right)}^{\left(1.061405428999999900341322245367337018251 \cdot \left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)\right)}\right) + -1.453152027000000012790792425221297889948\right)}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right)\right)\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)\right)}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x)
  :name "Jmat.Real.erf"
  (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))