Average Error: 13.9 → 13.9
Time: 52.3s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot -0.2844967359999999723108032867457950487733\right) + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
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|}
↓
1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot -0.2844967359999999723108032867457950487733\right) + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\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 \cdot 1 - \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot \left(0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)} \cdot \left(\left(1 - 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
double f(double x) {
        double r252751 = 1.0;
        double r252752 = 0.3275911;
        double r252753 = x;
        double r252754 = fabs(r252753);
        double r252755 = r252752 * r252754;
        double r252756 = r252751 + r252755;
        double r252757 = r252751 / r252756;
        double r252758 = 0.254829592;
        double r252759 = -0.284496736;
        double r252760 = 1.421413741;
        double r252761 = -1.453152027;
        double r252762 = 1.061405429;
        double r252763 = r252757 * r252762;
        double r252764 = r252761 + r252763;
        double r252765 = r252757 * r252764;
        double r252766 = r252760 + r252765;
        double r252767 = r252757 * r252766;
        double r252768 = r252759 + r252767;
        double r252769 = r252757 * r252768;
        double r252770 = r252758 + r252769;
        double r252771 = r252757 * r252770;
        double r252772 = r252754 * r252754;
        double r252773 = -r252772;
        double r252774 = exp(r252773);
        double r252775 = r252771 * r252774;
        double r252776 = r252751 - r252775;
        return r252776;
}
↓
double f(double x) {
        double r252777 = 1.0;
        double r252778 = 0.3275911;
        double r252779 = x;
        double r252780 = fabs(r252779);
        double r252781 = r252778 * r252780;
        double r252782 = r252777 + r252781;
        double r252783 = r252777 / r252782;
        double r252784 = 0.254829592;
        double r252785 = -0.284496736;
        double r252786 = r252783 * r252785;
        double r252787 = r252784 + r252786;
        double r252788 = 1.421413741;
        double r252789 = -1.453152027;
        double r252790 = r252777 * r252777;
        double r252791 = r252781 * r252781;
        double r252792 = r252790 - r252791;
        double r252793 = r252777 / r252792;
        double r252794 = r252777 - r252781;
        double r252795 = 1.061405429;
        double r252796 = r252794 * r252795;
        double r252797 = r252793 * r252796;
        double r252798 = r252789 + r252797;
        double r252799 = r252783 * r252798;
        double r252800 = r252788 + r252799;
        double r252801 = r252783 * r252800;
        double r252802 = r252783 * r252801;
        double r252803 = r252787 + r252802;
        double r252804 = r252783 * r252803;
        double r252805 = r252780 * r252780;
        double r252806 = -r252805;
        double r252807 = exp(r252806);
        double r252808 = r252804 * r252807;
        double r252809 = r252777 - r252808;
        return r252809;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.9

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

  3. Applied flip-+13.9

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

  4. Applied associate-/r/13.9

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

  5. Applied associate-*l*13.9

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

  7. Applied distribute-lft-in13.9

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

  8. Applied associate-+r+13.9

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

  9. Final simplification13.9

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

Reproduce

herbie shell --seed 2019306 
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1 (* (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ 0.25482959199999999 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ -0.284496735999999972 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ 1.42141374100000006 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ -1.45315202700000001 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) 1.0614054289999999))))))))) (exp (- (* (fabs x) (fabs x)))))))