Jmat.Real.erf

Average Error: 13.8 → 13.0

Time: 37.6s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r8848420 = 1.0;
        double r8848421 = 0.3275911;
        double r8848422 = x;
        double r8848423 = fabs(r8848422);
        double r8848424 = r8848421 * r8848423;
        double r8848425 = r8848420 + r8848424;
        double r8848426 = r8848420 / r8848425;
        double r8848427 = 0.254829592;
        double r8848428 = -0.284496736;
        double r8848429 = 1.421413741;
        double r8848430 = -1.453152027;
        double r8848431 = 1.061405429;
        double r8848432 = r8848426 * r8848431;
        double r8848433 = r8848430 + r8848432;
        double r8848434 = r8848426 * r8848433;
        double r8848435 = r8848429 + r8848434;
        double r8848436 = r8848426 * r8848435;
        double r8848437 = r8848428 + r8848436;
        double r8848438 = r8848426 * r8848437;
        double r8848439 = r8848427 + r8848438;
        double r8848440 = r8848426 * r8848439;
        double r8848441 = r8848423 * r8848423;
        double r8848442 = -r8848441;
        double r8848443 = exp(r8848442);
        double r8848444 = r8848440 * r8848443;
        double r8848445 = r8848420 - r8848444;
        return r8848445;
}

↓

double f(double x) {
        double r8848446 = 1.0;
        double r8848447 = sqrt(r8848446);
        double r8848448 = 3.0;
        double r8848449 = pow(r8848447, r8848448);
        double r8848450 = pow(r8848449, r8848448);
        double r8848451 = x;
        double r8848452 = fabs(r8848451);
        double r8848453 = -r8848452;
        double r8848454 = r8848453 * r8848452;
        double r8848455 = exp(r8848454);
        double r8848456 = 0.3275911;
        double r8848457 = r8848452 * r8848456;
        double r8848458 = r8848446 + r8848457;
        double r8848459 = r8848446 / r8848458;
        double r8848460 = exp(r8848459);
        double r8848461 = log(r8848460);
        double r8848462 = 1.061405429;
        double r8848463 = r8848461 * r8848462;
        double r8848464 = -1.453152027;
        double r8848465 = r8848463 + r8848464;
        double r8848466 = r8848459 * r8848465;
        double r8848467 = 1.421413741;
        double r8848468 = r8848466 + r8848467;
        double r8848469 = r8848468 * r8848459;
        double r8848470 = -0.284496736;
        double r8848471 = r8848469 + r8848470;
        double r8848472 = r8848471 * r8848459;
        double r8848473 = 0.254829592;
        double r8848474 = r8848472 + r8848473;
        double r8848475 = r8848459 * r8848474;
        double r8848476 = r8848455 * r8848475;
        double r8848477 = pow(r8848476, r8848448);
        double r8848478 = sqrt(r8848477);
        double r8848479 = pow(r8848478, r8848448);
        double r8848480 = r8848450 - r8848479;
        double r8848481 = r8848449 * r8848478;
        double r8848482 = r8848478 * r8848478;
        double r8848483 = r8848481 + r8848482;
        double r8848484 = r8848449 * r8848449;
        double r8848485 = r8848483 + r8848484;
        double r8848486 = r8848480 / r8848485;
        double r8848487 = r8848478 + r8848449;
        double r8848488 = r8848486 * r8848487;
        double r8848489 = r8848476 * r8848446;
        double r8848490 = r8848476 * r8848476;
        double r8848491 = r8848489 + r8848490;
        double r8848492 = r8848446 * r8848446;
        double r8848493 = r8848491 + r8848492;
        double r8848494 = r8848488 / r8848493;
        return r8848494;
}

Error

Bits error versus x

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 add-log-exp 13.8

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

5. Applied flip3-- 13.8

   \[\leadsto \color{blue}{\frac{{1}^{3} - {\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}}{1 \cdot 1 + \left(\left(\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 + \log \left(e^{\frac{1}{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|}\right) \cdot \left(\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 + \log \left(e^{\frac{1}{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|}\right) + 1 \cdot \left(\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 + \log \left(e^{\frac{1}{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|}\right)\right)}}\]
6. Using strategy rm

7. Applied add-sqr-sqrt 13.0

   \[\leadsto \frac{{1}^{3} - \color{blue}{\sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}} \cdot \sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}}}}{1 \cdot 1 + \left(\left(\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 + \log \left(e^{\frac{1}{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|}\right) \cdot \left(\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 + \log \left(e^{\frac{1}{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|}\right) + 1 \cdot \left(\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 + \log \left(e^{\frac{1}{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|}\right)\right)}\]

8. Applied add-sqr-sqrt 13.0

   \[\leadsto \frac{{\color{blue}{\left(\sqrt{1} \cdot \sqrt{1}\right)}}^{3} - \sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}} \cdot \sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}}}{1 \cdot 1 + \left(\left(\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 + \log \left(e^{\frac{1}{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|}\right) \cdot \left(\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 + \log \left(e^{\frac{1}{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|}\right) + 1 \cdot \left(\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 + \log \left(e^{\frac{1}{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|}\right)\right)}\]

9. Applied unpow-prod-down 13.0

   \[\leadsto \frac{\color{blue}{{\left(\sqrt{1}\right)}^{3} \cdot {\left(\sqrt{1}\right)}^{3}} - \sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}} \cdot \sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}}}{1 \cdot 1 + \left(\left(\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 + \log \left(e^{\frac{1}{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|}\right) \cdot \left(\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 + \log \left(e^{\frac{1}{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|}\right) + 1 \cdot \left(\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 + \log \left(e^{\frac{1}{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|}\right)\right)}\]

10. Applied difference-of-squares 13.0

    \[\leadsto \frac{\color{blue}{\left({\left(\sqrt{1}\right)}^{3} + \sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}}\right) \cdot \left({\left(\sqrt{1}\right)}^{3} - \sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}}\right)}}{1 \cdot 1 + \left(\left(\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 + \log \left(e^{\frac{1}{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|}\right) \cdot \left(\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 + \log \left(e^{\frac{1}{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|}\right) + 1 \cdot \left(\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 + \log \left(e^{\frac{1}{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|}\right)\right)}\]
11. Using strategy rm

12. Applied flip3-- 13.0

    \[\leadsto \frac{\left({\left(\sqrt{1}\right)}^{3} + \sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}}\right) \cdot \color{blue}{\frac{{\left({\left(\sqrt{1}\right)}^{3}\right)}^{3} - {\left(\sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}}\right)}^{3}}{{\left(\sqrt{1}\right)}^{3} \cdot {\left(\sqrt{1}\right)}^{3} + \left(\sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}} \cdot \sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}} + {\left(\sqrt{1}\right)}^{3} \cdot \sqrt{{\left(\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 + \log \left(e^{\frac{1}{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|}\right)}^{3}}\right)}}}{1 \cdot 1 + \left(\left(\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 + \log \left(e^{\frac{1}{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|}\right) \cdot \left(\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 + \log \left(e^{\frac{1}{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|}\right) + 1 \cdot \left(\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 + \log \left(e^{\frac{1}{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|}\right)\right)}\]

13. Final simplification 13.0

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

Reproduce

herbie shell --seed 2019179 
(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)))))))