Average Error: 13.4 → 13.4
Time: 2.1m
Precision: 64
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[1 - \left(\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(1.421413741 + \left(-1.453152027 + \frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot 1.061405429\right) \cdot \frac{1}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot \left(\sqrt{\left(1 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1}{1 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}} \cdot \sqrt{\left(1 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1}{1 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}}\right)\right) + \left(\frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot -0.284496736 + 0.254829592\right)\right) \cdot \frac{1}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
1 - \left(\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(1.421413741 + \left(-1.453152027 + \frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot 1.061405429\right) \cdot \frac{1}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot \left(\sqrt{\left(1 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1}{1 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}} \cdot \sqrt{\left(1 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1}{1 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}}\right)\right) + \left(\frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot -0.284496736 + 0.254829592\right)\right) \cdot \frac{1}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
double f(double x) {
        double r7132576 = 1.0;
        double r7132577 = 0.3275911;
        double r7132578 = x;
        double r7132579 = fabs(r7132578);
        double r7132580 = r7132577 * r7132579;
        double r7132581 = r7132576 + r7132580;
        double r7132582 = r7132576 / r7132581;
        double r7132583 = 0.254829592;
        double r7132584 = -0.284496736;
        double r7132585 = 1.421413741;
        double r7132586 = -1.453152027;
        double r7132587 = 1.061405429;
        double r7132588 = r7132582 * r7132587;
        double r7132589 = r7132586 + r7132588;
        double r7132590 = r7132582 * r7132589;
        double r7132591 = r7132585 + r7132590;
        double r7132592 = r7132582 * r7132591;
        double r7132593 = r7132584 + r7132592;
        double r7132594 = r7132582 * r7132593;
        double r7132595 = r7132583 + r7132594;
        double r7132596 = r7132582 * r7132595;
        double r7132597 = r7132579 * r7132579;
        double r7132598 = -r7132597;
        double r7132599 = exp(r7132598);
        double r7132600 = r7132596 * r7132599;
        double r7132601 = r7132576 - r7132600;
        return r7132601;
}
↓
double f(double x) {
        double r7132602 = 1.0;
        double r7132603 = x;
        double r7132604 = fabs(r7132603);
        double r7132605 = 0.3275911;
        double r7132606 = r7132604 * r7132605;
        double r7132607 = r7132602 + r7132606;
        double r7132608 = r7132602 / r7132607;
        double r7132609 = 1.421413741;
        double r7132610 = -1.453152027;
        double r7132611 = 1.061405429;
        double r7132612 = r7132608 * r7132611;
        double r7132613 = r7132610 + r7132612;
        double r7132614 = r7132613 * r7132608;
        double r7132615 = r7132609 + r7132614;
        double r7132616 = r7132602 - r7132606;
        double r7132617 = r7132606 * r7132606;
        double r7132618 = r7132602 - r7132617;
        double r7132619 = r7132602 / r7132618;
        double r7132620 = r7132616 * r7132619;
        double r7132621 = sqrt(r7132620);
        double r7132622 = r7132621 * r7132621;
        double r7132623 = r7132615 * r7132622;
        double r7132624 = r7132608 * r7132623;
        double r7132625 = -0.284496736;
        double r7132626 = r7132608 * r7132625;
        double r7132627 = 0.254829592;
        double r7132628 = r7132626 + r7132627;
        double r7132629 = r7132624 + r7132628;
        double r7132630 = r7132629 * r7132608;
        double r7132631 = r7132604 * r7132604;
        double r7132632 = -r7132631;
        double r7132633 = exp(r7132632);
        double r7132634 = r7132630 * r7132633;
        double r7132635 = r7132602 - r7132634;
        return r7132635;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.4

    \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  2. Using strategy rm

  3. Applied distribute-lft-in13.4

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \color{blue}{\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot -0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  4. Applied associate-+r+13.4

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \color{blue}{\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot -0.284496736\right) + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  5. Using strategy rm

  6. Applied flip-+13.4

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot -0.284496736\right) + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\frac{1}{\color{blue}{\frac{1 \cdot 1 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)}{1 - 0.3275911 \cdot \left|x\right|}}} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  7. Applied associate-/r/13.4

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot -0.284496736\right) + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\color{blue}{\left(\frac{1}{1 \cdot 1 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)\right)} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt13.4

    \[\leadsto 1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot -0.284496736\right) + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(\color{blue}{\left(\sqrt{\frac{1}{1 \cdot 1 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)} \cdot \sqrt{\frac{1}{1 \cdot 1 - \left(0.3275911 \cdot \left|x\right|\right) \cdot \left(0.3275911 \cdot \left|x\right|\right)} \cdot \left(1 - 0.3275911 \cdot \left|x\right|\right)}\right)} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

  10. Final simplification13.4

    \[\leadsto 1 - \left(\left(\frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot \left(\left(1.421413741 + \left(-1.453152027 + \frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot 1.061405429\right) \cdot \frac{1}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot \left(\sqrt{\left(1 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1}{1 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}} \cdot \sqrt{\left(1 - \left|x\right| \cdot 0.3275911\right) \cdot \frac{1}{1 - \left(\left|x\right| \cdot 0.3275911\right) \cdot \left(\left|x\right| \cdot 0.3275911\right)}}\right)\right) + \left(\frac{1}{1 + \left|x\right| \cdot 0.3275911} \cdot -0.284496736 + 0.254829592\right)\right) \cdot \frac{1}{1 + \left|x\right| \cdot 0.3275911}\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]

Reproduce

herbie shell --seed 2019143 
(FPCore (x)
  :name "Jmat.Real.erf"
  (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))