Average Error: 13.7 → 12.9
Time: 58.8s
Precision: 64
\[1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\frac{\frac{{\left({\left(\sqrt{1}\right)}^{3}\right)}^{3} - {\left(\sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}}\right)}^{3}}{\left(\sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{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(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}} + \sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}} \cdot {\left(\sqrt{1}\right)}^{3}\right) + {\left(\sqrt{1}\right)}^{3} \cdot {\left(\sqrt{1}\right)}^{3}} \cdot \left({\left(\sqrt{1}\right)}^{3} + \sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}}\right)}{\left(1 \cdot \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right) + \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right)\right) + 1 \cdot 1}\]
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(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}}\right)}^{3}}{\left(\sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{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(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}} + \sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}} \cdot {\left(\sqrt{1}\right)}^{3}\right) + {\left(\sqrt{1}\right)}^{3} \cdot {\left(\sqrt{1}\right)}^{3}} \cdot \left({\left(\sqrt{1}\right)}^{3} + \sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right)}^{3}}\right)}{\left(1 \cdot \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right) + \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right) \cdot \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \left(\left(1.061405428999999900341322245367337018251 \cdot \log \left(e^{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}\right) + -1.453152027000000012790792425221297889948\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} + 1.421413741000000063863240029604639858007\right) \cdot \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}\right) + 0.2548295919999999936678136691625695675611\right) \cdot \frac{\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|}}{e^{\left|x\right| \cdot \left|x\right|}}\right)\right) + 1 \cdot 1}
double f(double x) {
        double r8148476 = 1.0;
        double r8148477 = 0.3275911;
        double r8148478 = x;
        double r8148479 = fabs(r8148478);
        double r8148480 = r8148477 * r8148479;
        double r8148481 = r8148476 + r8148480;
        double r8148482 = r8148476 / r8148481;
        double r8148483 = 0.254829592;
        double r8148484 = -0.284496736;
        double r8148485 = 1.421413741;
        double r8148486 = -1.453152027;
        double r8148487 = 1.061405429;
        double r8148488 = r8148482 * r8148487;
        double r8148489 = r8148486 + r8148488;
        double r8148490 = r8148482 * r8148489;
        double r8148491 = r8148485 + r8148490;
        double r8148492 = r8148482 * r8148491;
        double r8148493 = r8148484 + r8148492;
        double r8148494 = r8148482 * r8148493;
        double r8148495 = r8148483 + r8148494;
        double r8148496 = r8148482 * r8148495;
        double r8148497 = r8148479 * r8148479;
        double r8148498 = -r8148497;
        double r8148499 = exp(r8148498);
        double r8148500 = r8148496 * r8148499;
        double r8148501 = r8148476 - r8148500;
        return r8148501;
}
↓
double f(double x) {
        double r8148502 = 1.0;
        double r8148503 = sqrt(r8148502);
        double r8148504 = 3.0;
        double r8148505 = pow(r8148503, r8148504);
        double r8148506 = pow(r8148505, r8148504);
        double r8148507 = 0.3275911;
        double r8148508 = x;
        double r8148509 = fabs(r8148508);
        double r8148510 = r8148507 * r8148509;
        double r8148511 = r8148502 + r8148510;
        double r8148512 = r8148502 / r8148511;
        double r8148513 = -0.284496736;
        double r8148514 = 1.061405429;
        double r8148515 = exp(r8148512);
        double r8148516 = log(r8148515);
        double r8148517 = r8148514 * r8148516;
        double r8148518 = -1.453152027;
        double r8148519 = r8148517 + r8148518;
        double r8148520 = r8148519 * r8148512;
        double r8148521 = 1.421413741;
        double r8148522 = r8148520 + r8148521;
        double r8148523 = r8148522 * r8148512;
        double r8148524 = r8148513 + r8148523;
        double r8148525 = r8148512 * r8148524;
        double r8148526 = 0.254829592;
        double r8148527 = r8148525 + r8148526;
        double r8148528 = r8148509 * r8148509;
        double r8148529 = exp(r8148528);
        double r8148530 = r8148512 / r8148529;
        double r8148531 = r8148527 * r8148530;
        double r8148532 = pow(r8148531, r8148504);
        double r8148533 = sqrt(r8148532);
        double r8148534 = pow(r8148533, r8148504);
        double r8148535 = r8148506 - r8148534;
        double r8148536 = r8148533 * r8148533;
        double r8148537 = r8148533 * r8148505;
        double r8148538 = r8148536 + r8148537;
        double r8148539 = r8148505 * r8148505;
        double r8148540 = r8148538 + r8148539;
        double r8148541 = r8148535 / r8148540;
        double r8148542 = r8148505 + r8148533;
        double r8148543 = r8148541 * r8148542;
        double r8148544 = r8148502 * r8148531;
        double r8148545 = r8148531 * r8148531;
        double r8148546 = r8148544 + r8148545;
        double r8148547 = r8148502 * r8148502;
        double r8148548 = r8148546 + r8148547;
        double r8148549 = r8148543 / r8148548;
        return r8148549;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.7

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

  2. Simplified13.7

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

  4. Applied add-log-exp13.7

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

  6. Applied flip3--13.7

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

  8. Applied add-sqr-sqrt12.9

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

  9. Applied add-sqr-sqrt12.9

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

  10. Applied unpow-prod-down12.9

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

  11. Applied difference-of-squares12.9

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

  13. Applied flip3--12.9

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

  14. Final simplification12.9

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

Reproduce

herbie shell --seed 2019200 
(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)))))))