Average Error: 14.0 → 13.2
Time: 34.0s
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{\left({\left(\sqrt{1}\right)}^{3} + \sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}}\right) \cdot \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{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}}\right)}^{3}}{\left({\left(\sqrt{1}\right)}^{6} + {\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}\right) + {\left(\sqrt{1}\right)}^{3} \cdot \sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}}{1 \cdot 1 + \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}} + 1\right)}\]
1 - \left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-0.2844967359999999723108032867457950487733 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(1.421413741000000063863240029604639858007 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(-1.453152027000000012790792425221297889948 + \frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot 1.061405428999999900341322245367337018251\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
\frac{\left({\left(\sqrt{1}\right)}^{3} + \sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}}\right) \cdot \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{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}}\right)}^{3}}{\left({\left(\sqrt{1}\right)}^{6} + {\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}\right) + {\left(\sqrt{1}\right)}^{3} \cdot \sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}}{1 \cdot 1 + \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}} + 1\right)}
double f(double x) {
        double r155471 = 1.0;
        double r155472 = 0.3275911;
        double r155473 = x;
        double r155474 = fabs(r155473);
        double r155475 = r155472 * r155474;
        double r155476 = r155471 + r155475;
        double r155477 = r155471 / r155476;
        double r155478 = 0.254829592;
        double r155479 = -0.284496736;
        double r155480 = 1.421413741;
        double r155481 = -1.453152027;
        double r155482 = 1.061405429;
        double r155483 = r155477 * r155482;
        double r155484 = r155481 + r155483;
        double r155485 = r155477 * r155484;
        double r155486 = r155480 + r155485;
        double r155487 = r155477 * r155486;
        double r155488 = r155479 + r155487;
        double r155489 = r155477 * r155488;
        double r155490 = r155478 + r155489;
        double r155491 = r155477 * r155490;
        double r155492 = r155474 * r155474;
        double r155493 = -r155492;
        double r155494 = exp(r155493);
        double r155495 = r155491 * r155494;
        double r155496 = r155471 - r155495;
        return r155496;
}
↓
double f(double x) {
        double r155497 = 1.0;
        double r155498 = sqrt(r155497);
        double r155499 = 3.0;
        double r155500 = pow(r155498, r155499);
        double r155501 = 0.3275911;
        double r155502 = x;
        double r155503 = fabs(r155502);
        double r155504 = r155501 * r155503;
        double r155505 = r155497 + r155504;
        double r155506 = r155497 / r155505;
        double r155507 = 0.254829592;
        double r155508 = 1.061405429;
        double r155509 = r155504 + r155497;
        double r155510 = pow(r155509, r155499);
        double r155511 = r155508 / r155510;
        double r155512 = 1.421413741;
        double r155513 = r155512 / r155509;
        double r155514 = r155511 + r155513;
        double r155515 = 0.284496736;
        double r155516 = 1.453152027;
        double r155517 = 2.0;
        double r155518 = pow(r155509, r155517);
        double r155519 = r155516 / r155518;
        double r155520 = r155515 + r155519;
        double r155521 = r155514 - r155520;
        double r155522 = r155521 * r155497;
        double r155523 = r155522 / r155509;
        double r155524 = r155507 + r155523;
        double r155525 = r155506 * r155524;
        double r155526 = pow(r155503, r155517);
        double r155527 = -r155526;
        double r155528 = exp(r155527);
        double r155529 = r155525 * r155528;
        double r155530 = pow(r155529, r155499);
        double r155531 = sqrt(r155530);
        double r155532 = r155500 + r155531;
        double r155533 = pow(r155500, r155499);
        double r155534 = pow(r155531, r155499);
        double r155535 = r155533 - r155534;
        double r155536 = 6.0;
        double r155537 = pow(r155498, r155536);
        double r155538 = r155537 + r155530;
        double r155539 = r155500 * r155531;
        double r155540 = r155538 + r155539;
        double r155541 = r155535 / r155540;
        double r155542 = r155532 * r155541;
        double r155543 = r155497 * r155497;
        double r155544 = r155529 + r155497;
        double r155545 = r155529 * r155544;
        double r155546 = r155543 + r155545;
        double r155547 = r155542 / r155546;
        return r155547;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.0

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

  2. Taylor expanded around 0 14.0

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

  3. Simplified14.0

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

  5. Applied flip3--14.0

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

  6. Simplified14.0

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

  7. Simplified14.0

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

  9. Applied add-sqr-sqrt13.2

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

  10. Applied add-sqr-sqrt13.2

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

  11. Applied unpow-prod-down13.2

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

  12. Applied difference-of-squares13.3

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

  14. Applied flip3--13.2

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

  15. Simplified13.2

    \[\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{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}}\right) \cdot \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{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}}\right)}^{3}}{\color{blue}{\left({\left(\sqrt{1}\right)}^{6} + {\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}\right) + {\left(\sqrt{1}\right)}^{3} \cdot \sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}}}{1 \cdot 1 + \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}} + 1\right)}\]

  16. Final simplification13.2

    \[\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{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}}\right) \cdot \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{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}}\right)}^{3}}{\left({\left(\sqrt{1}\right)}^{6} + {\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}\right) + {\left(\sqrt{1}\right)}^{3} \cdot \sqrt{{\left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right)}^{3}}}}{1 \cdot 1 + \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}}\right) \cdot \left(\left(\frac{1}{1 + 0.3275911000000000239396058532292954623699 \cdot \left|x\right|} \cdot \left(0.2548295919999999936678136691625695675611 + \frac{\left(\left(\frac{1.061405428999999900341322245367337018251}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{3}} + \frac{1.421413741000000063863240029604639858007}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right) - \left(0.2844967359999999723108032867457950487733 + \frac{1.453152027000000012790792425221297889948}{{\left(0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1\right)}^{2}}\right)\right) \cdot 1}{0.3275911000000000239396058532292954623699 \cdot \left|x\right| + 1}\right)\right) \cdot e^{-{\left(\left|x\right|\right)}^{2}} + 1\right)}\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1 (* (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ 0.25482959199999999 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ -0.284496735999999972 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ 1.42141374100000006 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) (+ -1.45315202700000001 (* (/ 1 (+ 1 (* 0.32759110000000002 (fabs x)))) 1.0614054289999999))))))))) (exp (- (* (fabs x) (fabs x)))))))