Average Error: 14.0 → 14.0
Time: 22.4s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[1 - \frac{1 \cdot \frac{\log \left(e^{0.2548295919999999936678136691625695675611} \cdot e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\]
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 - \frac{1 \cdot \frac{\log \left(e^{0.2548295919999999936678136691625695675611} \cdot e^{\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{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}
double f(double x) {
        double r168490 = 1.0;
        double r168491 = 0.3275911;
        double r168492 = x;
        double r168493 = fabs(r168492);
        double r168494 = r168491 * r168493;
        double r168495 = r168490 + r168494;
        double r168496 = r168490 / r168495;
        double r168497 = 0.254829592;
        double r168498 = -0.284496736;
        double r168499 = 1.421413741;
        double r168500 = -1.453152027;
        double r168501 = 1.061405429;
        double r168502 = r168496 * r168501;
        double r168503 = r168500 + r168502;
        double r168504 = r168496 * r168503;
        double r168505 = r168499 + r168504;
        double r168506 = r168496 * r168505;
        double r168507 = r168498 + r168506;
        double r168508 = r168496 * r168507;
        double r168509 = r168497 + r168508;
        double r168510 = r168496 * r168509;
        double r168511 = r168493 * r168493;
        double r168512 = -r168511;
        double r168513 = exp(r168512);
        double r168514 = r168510 * r168513;
        double r168515 = r168490 - r168514;
        return r168515;
}
↓
double f(double x) {
        double r168516 = 1.0;
        double r168517 = 0.254829592;
        double r168518 = exp(r168517);
        double r168519 = 0.3275911;
        double r168520 = x;
        double r168521 = fabs(r168520);
        double r168522 = r168519 * r168521;
        double r168523 = r168516 + r168522;
        double r168524 = r168516 / r168523;
        double r168525 = -0.284496736;
        double r168526 = 1.421413741;
        double r168527 = -1.453152027;
        double r168528 = sqrt(r168516);
        double r168529 = cbrt(r168523);
        double r168530 = r168529 * r168529;
        double r168531 = r168528 / r168530;
        double r168532 = r168528 / r168529;
        double r168533 = r168531 * r168532;
        double r168534 = 1.061405429;
        double r168535 = r168533 * r168534;
        double r168536 = r168527 + r168535;
        double r168537 = r168524 * r168536;
        double r168538 = r168526 + r168537;
        double r168539 = r168524 * r168538;
        double r168540 = r168525 + r168539;
        double r168541 = r168524 * r168540;
        double r168542 = exp(r168541);
        double r168543 = r168518 * r168542;
        double r168544 = log(r168543);
        double r168545 = r168521 * r168521;
        double r168546 = exp(r168545);
        double r168547 = r168544 / r168546;
        double r168548 = r168516 * r168547;
        double r168549 = r168548 / r168523;
        double r168550 = r168516 - r168549;
        return r168550;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.0

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

  2. Simplified14.0

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

  4. Applied add-log-exp14.0

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

  5. Applied add-log-exp14.0

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

  6. Applied sum-log14.0

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

  7. Simplified14.0

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

  9. Applied exp-sum14.0

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

  11. Applied add-cube-cbrt14.0

    \[\leadsto 1 - \frac{1 \cdot \frac{\log \left(e^{0.2548295919999999936678136691625695675611} \cdot e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{\color{blue}{\left(\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) \cdot \sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\]

  12. Applied add-sqr-sqrt14.0

    \[\leadsto 1 - \frac{1 \cdot \frac{\log \left(e^{0.2548295919999999936678136691625695675611} \cdot e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{\left(\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) \cdot \sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\]

  13. Applied times-frac14.0

    \[\leadsto 1 - \frac{1 \cdot \frac{\log \left(e^{0.2548295919999999936678136691625695675611} \cdot e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \color{blue}{\left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right)} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\]

  14. Final simplification14.0

    \[\leadsto 1 - \frac{1 \cdot \frac{\log \left(e^{0.2548295919999999936678136691625695675611} \cdot e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) \cdot 1.061405428999999900341322245367337018251\right)\right)\right)}\right)}{e^{\left|x\right| \cdot \left|x\right|}}}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\]

Reproduce

herbie shell --seed 2019235 
(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)))))))