Jmat.Real.erf

Average Error: 13.9 → 13.9

Time: 26.5s

Precision: 64

Math

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

↓

\[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\sqrt{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\sqrt{1} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251 + -1.453152027000000012790792425221297889948\right)\right)}{{\left(\sqrt{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)}^{\frac{2}{3}} \cdot {\left(\sqrt{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)}^{\frac{2}{3}}}\right) + -0.2844967359999999723108032867457950487733\right) + 0.2548295919999999936678136691625695675611} \cdot \sqrt{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\sqrt{1} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251 + -1.453152027000000012790792425221297889948\right)\right)}{{\left(1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)}^{\frac{2}{3}}}\right) + -0.2844967359999999723108032867457950487733\right) + 0.2548295919999999936678136691625695675611}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

C

double f(double x) {
        double r161402 = 1.0;
        double r161403 = 0.3275911;
        double r161404 = x;
        double r161405 = fabs(r161404);
        double r161406 = r161403 * r161405;
        double r161407 = r161402 + r161406;
        double r161408 = r161402 / r161407;
        double r161409 = 0.254829592;
        double r161410 = -0.284496736;
        double r161411 = 1.421413741;
        double r161412 = -1.453152027;
        double r161413 = 1.061405429;
        double r161414 = r161408 * r161413;
        double r161415 = r161412 + r161414;
        double r161416 = r161408 * r161415;
        double r161417 = r161411 + r161416;
        double r161418 = r161408 * r161417;
        double r161419 = r161410 + r161418;
        double r161420 = r161408 * r161419;
        double r161421 = r161409 + r161420;
        double r161422 = r161408 * r161421;
        double r161423 = r161405 * r161405;
        double r161424 = -r161423;
        double r161425 = exp(r161424);
        double r161426 = r161422 * r161425;
        double r161427 = r161402 - r161426;
        return r161427;
}

↓

double f(double x) {
        double r161428 = 1.0;
        double r161429 = 0.3275911;
        double r161430 = x;
        double r161431 = fabs(r161430);
        double r161432 = r161429 * r161431;
        double r161433 = r161428 + r161432;
        double r161434 = r161428 / r161433;
        double r161435 = 1.421413741;
        double r161436 = sqrt(r161428);
        double r161437 = cbrt(r161433);
        double r161438 = r161436 / r161437;
        double r161439 = 1.061405429;
        double r161440 = r161434 * r161439;
        double r161441 = -1.453152027;
        double r161442 = r161440 + r161441;
        double r161443 = r161438 * r161442;
        double r161444 = r161436 * r161443;
        double r161445 = sqrt(r161433);
        double r161446 = 0.6666666666666666;
        double r161447 = pow(r161445, r161446);
        double r161448 = r161447 * r161447;
        double r161449 = r161444 / r161448;
        double r161450 = r161435 + r161449;
        double r161451 = r161434 * r161450;
        double r161452 = -0.284496736;
        double r161453 = r161451 + r161452;
        double r161454 = r161434 * r161453;
        double r161455 = 0.254829592;
        double r161456 = r161454 + r161455;
        double r161457 = sqrt(r161456);
        double r161458 = pow(r161433, r161446);
        double r161459 = r161444 / r161458;
        double r161460 = r161435 + r161459;
        double r161461 = r161434 * r161460;
        double r161462 = r161461 + r161452;
        double r161463 = r161434 * r161462;
        double r161464 = r161463 + r161455;
        double r161465 = sqrt(r161464);
        double r161466 = r161457 * r161465;
        double r161467 = r161434 * r161466;
        double r161468 = r161431 * r161431;
        double r161469 = -r161468;
        double r161470 = exp(r161469);
        double r161471 = r161467 * r161470;
        double r161472 = r161428 - r161471;
        return r161472;
}

Error

Bits error versus x

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 add-cbrt-cube 13.9

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

4. Applied add-cbrt-cube 13.9

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

5. Applied cbrt-undiv 13.9

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

6. Simplified 13.9

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

8. Applied add-cube-cbrt 13.9

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

9. Applied add-sqr-sqrt 13.9

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

10. Applied times-frac 13.9

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

11. Applied associate-*l* 13.9

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

12. Simplified 13.9

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

14. Applied add-sqr-sqrt 13.9

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

15. Simplified 13.9

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\color{blue}{\sqrt{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\sqrt{1} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251 + -1.453152027000000012790792425221297889948\right)\right)}{{\left(1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)}^{\frac{2}{3}}}\right) + -0.2844967359999999723108032867457950487733\right) + 0.2548295919999999936678136691625695675611}} \cdot \sqrt{0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251 + -1.453152027000000012790792425221297889948\right)\right)\right)\right)}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

16. Simplified 13.9

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\sqrt{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\sqrt{1} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251 + -1.453152027000000012790792425221297889948\right)\right)}{{\left(1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)}^{\frac{2}{3}}}\right) + -0.2844967359999999723108032867457950487733\right) + 0.2548295919999999936678136691625695675611} \cdot \color{blue}{\sqrt{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\sqrt{1} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251 + -1.453152027000000012790792425221297889948\right)\right)}{{\left(1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)}^{\frac{2}{3}}}\right) + -0.2844967359999999723108032867457950487733\right) + 0.2548295919999999936678136691625695675611}}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
17. Using strategy rm

18. Applied add-sqr-sqrt 13.9

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\sqrt{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\sqrt{1} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251 + -1.453152027000000012790792425221297889948\right)\right)}{{\color{blue}{\left(\sqrt{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \sqrt{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)}}^{\frac{2}{3}}}\right) + -0.2844967359999999723108032867457950487733\right) + 0.2548295919999999936678136691625695675611} \cdot \sqrt{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\sqrt{1} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251 + -1.453152027000000012790792425221297889948\right)\right)}{{\left(1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)}^{\frac{2}{3}}}\right) + -0.2844967359999999723108032867457950487733\right) + 0.2548295919999999936678136691625695675611}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

19. Applied unpow-prod-down 13.9

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\sqrt{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\sqrt{1} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251 + -1.453152027000000012790792425221297889948\right)\right)}{\color{blue}{{\left(\sqrt{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)}^{\frac{2}{3}} \cdot {\left(\sqrt{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)}^{\frac{2}{3}}}}\right) + -0.2844967359999999723108032867457950487733\right) + 0.2548295919999999936678136691625695675611} \cdot \sqrt{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\sqrt{1} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251 + -1.453152027000000012790792425221297889948\right)\right)}{{\left(1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)}^{\frac{2}{3}}}\right) + -0.2844967359999999723108032867457950487733\right) + 0.2548295919999999936678136691625695675611}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

20. Final simplification 13.9

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\sqrt{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\sqrt{1} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251 + -1.453152027000000012790792425221297889948\right)\right)}{{\left(\sqrt{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)}^{\frac{2}{3}} \cdot {\left(\sqrt{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right)}^{\frac{2}{3}}}\right) + -0.2844967359999999723108032867457950487733\right) + 0.2548295919999999936678136691625695675611} \cdot \sqrt{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{\sqrt{1} \cdot \left(\frac{\sqrt{1}}{\sqrt[3]{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}} \cdot \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251 + -1.453152027000000012790792425221297889948\right)\right)}{{\left(1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|\right)}^{\frac{2}{3}}}\right) + -0.2844967359999999723108032867457950487733\right) + 0.2548295919999999936678136691625695675611}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 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)))))))