Average Error: 59.8 → 0.9
Time: 1.5m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\frac{\frac{{\left(0.5 + \left(z - -6\right)\right)}^{z}}{\sqrt[3]{{\left(\sqrt{0.5 + \left(z - -6\right)}\right)}^{\left(1 - 0.5\right)}} \cdot \sqrt[3]{{\left(\sqrt{0.5 + \left(z - -6\right)}\right)}^{\left(1 - 0.5\right)}}} \cdot \frac{\sqrt{2 \cdot \pi}}{\sqrt[3]{{\left(\sqrt{0.5 + \left(z - -6\right)}\right)}^{\left(1 - 0.5\right)}}}}{{\left(\sqrt{0.5 + \left(z - -6\right)}\right)}^{\left(1 - 0.5\right)}} \cdot \frac{\left(\left(\left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right) + \frac{12.507343278686905}{z + 4}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{2 + z} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right)}{e^{0.5 + \left(z - -6\right)}}\]
\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)
↓
\frac{\frac{{\left(0.5 + \left(z - -6\right)\right)}^{z}}{\sqrt[3]{{\left(\sqrt{0.5 + \left(z - -6\right)}\right)}^{\left(1 - 0.5\right)}} \cdot \sqrt[3]{{\left(\sqrt{0.5 + \left(z - -6\right)}\right)}^{\left(1 - 0.5\right)}}} \cdot \frac{\sqrt{2 \cdot \pi}}{\sqrt[3]{{\left(\sqrt{0.5 + \left(z - -6\right)}\right)}^{\left(1 - 0.5\right)}}}}{{\left(\sqrt{0.5 + \left(z - -6\right)}\right)}^{\left(1 - 0.5\right)}} \cdot \frac{\left(\left(\left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right) + \frac{12.507343278686905}{z + 4}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{2 + z} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right)}{e^{0.5 + \left(z - -6\right)}}
double f(double z) {
        double r3417541 = atan2(1.0, 0.0);
        double r3417542 = 2.0;
        double r3417543 = r3417541 * r3417542;
        double r3417544 = sqrt(r3417543);
        double r3417545 = z;
        double r3417546 = 1.0;
        double r3417547 = r3417545 - r3417546;
        double r3417548 = 7.0;
        double r3417549 = r3417547 + r3417548;
        double r3417550 = 0.5;
        double r3417551 = r3417549 + r3417550;
        double r3417552 = r3417547 + r3417550;
        double r3417553 = pow(r3417551, r3417552);
        double r3417554 = r3417544 * r3417553;
        double r3417555 = -r3417551;
        double r3417556 = exp(r3417555);
        double r3417557 = r3417554 * r3417556;
        double r3417558 = 0.9999999999998099;
        double r3417559 = 676.5203681218851;
        double r3417560 = r3417547 + r3417546;
        double r3417561 = r3417559 / r3417560;
        double r3417562 = r3417558 + r3417561;
        double r3417563 = -1259.1392167224028;
        double r3417564 = r3417547 + r3417542;
        double r3417565 = r3417563 / r3417564;
        double r3417566 = r3417562 + r3417565;
        double r3417567 = 771.3234287776531;
        double r3417568 = 3.0;
        double r3417569 = r3417547 + r3417568;
        double r3417570 = r3417567 / r3417569;
        double r3417571 = r3417566 + r3417570;
        double r3417572 = -176.6150291621406;
        double r3417573 = 4.0;
        double r3417574 = r3417547 + r3417573;
        double r3417575 = r3417572 / r3417574;
        double r3417576 = r3417571 + r3417575;
        double r3417577 = 12.507343278686905;
        double r3417578 = 5.0;
        double r3417579 = r3417547 + r3417578;
        double r3417580 = r3417577 / r3417579;
        double r3417581 = r3417576 + r3417580;
        double r3417582 = -0.13857109526572012;
        double r3417583 = 6.0;
        double r3417584 = r3417547 + r3417583;
        double r3417585 = r3417582 / r3417584;
        double r3417586 = r3417581 + r3417585;
        double r3417587 = 9.984369578019572e-06;
        double r3417588 = r3417587 / r3417549;
        double r3417589 = r3417586 + r3417588;
        double r3417590 = 1.5056327351493116e-07;
        double r3417591 = 8.0;
        double r3417592 = r3417547 + r3417591;
        double r3417593 = r3417590 / r3417592;
        double r3417594 = r3417589 + r3417593;
        double r3417595 = r3417557 * r3417594;
        return r3417595;
}
↓
double f(double z) {
        double r3417596 = 0.5;
        double r3417597 = z;
        double r3417598 = -6.0;
        double r3417599 = r3417597 - r3417598;
        double r3417600 = r3417596 + r3417599;
        double r3417601 = pow(r3417600, r3417597);
        double r3417602 = sqrt(r3417600);
        double r3417603 = 1.0;
        double r3417604 = r3417603 - r3417596;
        double r3417605 = pow(r3417602, r3417604);
        double r3417606 = cbrt(r3417605);
        double r3417607 = r3417606 * r3417606;
        double r3417608 = r3417601 / r3417607;
        double r3417609 = 2.0;
        double r3417610 = atan2(1.0, 0.0);
        double r3417611 = r3417609 * r3417610;
        double r3417612 = sqrt(r3417611);
        double r3417613 = r3417612 / r3417606;
        double r3417614 = r3417608 * r3417613;
        double r3417615 = r3417614 / r3417605;
        double r3417616 = -176.6150291621406;
        double r3417617 = 3.0;
        double r3417618 = r3417597 + r3417617;
        double r3417619 = r3417616 / r3417618;
        double r3417620 = -0.13857109526572012;
        double r3417621 = -5.0;
        double r3417622 = r3417597 - r3417621;
        double r3417623 = r3417620 / r3417622;
        double r3417624 = r3417619 + r3417623;
        double r3417625 = 12.507343278686905;
        double r3417626 = 4.0;
        double r3417627 = r3417597 + r3417626;
        double r3417628 = r3417625 / r3417627;
        double r3417629 = r3417624 + r3417628;
        double r3417630 = 9.984369578019572e-06;
        double r3417631 = r3417630 / r3417599;
        double r3417632 = r3417629 + r3417631;
        double r3417633 = 1.5056327351493116e-07;
        double r3417634 = -7.0;
        double r3417635 = r3417597 - r3417634;
        double r3417636 = r3417633 / r3417635;
        double r3417637 = 771.3234287776531;
        double r3417638 = r3417609 + r3417597;
        double r3417639 = r3417637 / r3417638;
        double r3417640 = 0.9999999999998099;
        double r3417641 = 676.5203681218851;
        double r3417642 = r3417641 / r3417597;
        double r3417643 = r3417640 + r3417642;
        double r3417644 = r3417639 + r3417643;
        double r3417645 = -1259.1392167224028;
        double r3417646 = r3417597 + r3417603;
        double r3417647 = r3417645 / r3417646;
        double r3417648 = r3417644 + r3417647;
        double r3417649 = r3417636 + r3417648;
        double r3417650 = r3417632 + r3417649;
        double r3417651 = exp(r3417600);
        double r3417652 = r3417650 / r3417651;
        double r3417653 = r3417615 * r3417652;
        return r3417653;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.8

    \[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]

  2. Simplified0.9

    \[\leadsto \color{blue}{\left({\left(\left(z - -6\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{\left(z - -6\right) + 0.5}}}\]
  3. Using strategy rm

  4. Applied associate-+l-0.8

    \[\leadsto \left({\left(\left(z - -6\right) + 0.5\right)}^{\color{blue}{\left(z - \left(1 - 0.5\right)\right)}} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{\left(z - -6\right) + 0.5}}\]

  5. Applied pow-sub0.9

    \[\leadsto \left(\color{blue}{\frac{{\left(\left(z - -6\right) + 0.5\right)}^{z}}{{\left(\left(z - -6\right) + 0.5\right)}^{\left(1 - 0.5\right)}}} \cdot \sqrt{\pi \cdot 2}\right) \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{\left(z - -6\right) + 0.5}}\]

  6. Applied associate-*l/0.8

    \[\leadsto \color{blue}{\frac{{\left(\left(z - -6\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{{\left(\left(z - -6\right) + 0.5\right)}^{\left(1 - 0.5\right)}}} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{\left(z - -6\right) + 0.5}}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.8

    \[\leadsto \frac{{\left(\left(z - -6\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{{\color{blue}{\left(\sqrt{\left(z - -6\right) + 0.5} \cdot \sqrt{\left(z - -6\right) + 0.5}\right)}}^{\left(1 - 0.5\right)}} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{\left(z - -6\right) + 0.5}}\]

  9. Applied unpow-prod-down0.9

    \[\leadsto \frac{{\left(\left(z - -6\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{\color{blue}{{\left(\sqrt{\left(z - -6\right) + 0.5}\right)}^{\left(1 - 0.5\right)} \cdot {\left(\sqrt{\left(z - -6\right) + 0.5}\right)}^{\left(1 - 0.5\right)}}} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{\left(z - -6\right) + 0.5}}\]

  10. Applied associate-/r*0.9

    \[\leadsto \color{blue}{\frac{\frac{{\left(\left(z - -6\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{{\left(\sqrt{\left(z - -6\right) + 0.5}\right)}^{\left(1 - 0.5\right)}}}{{\left(\sqrt{\left(z - -6\right) + 0.5}\right)}^{\left(1 - 0.5\right)}}} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{\left(z - -6\right) + 0.5}}\]
  11. Using strategy rm

  12. Applied add-cube-cbrt1.0

    \[\leadsto \frac{\frac{{\left(\left(z - -6\right) + 0.5\right)}^{z} \cdot \sqrt{\pi \cdot 2}}{\color{blue}{\left(\sqrt[3]{{\left(\sqrt{\left(z - -6\right) + 0.5}\right)}^{\left(1 - 0.5\right)}} \cdot \sqrt[3]{{\left(\sqrt{\left(z - -6\right) + 0.5}\right)}^{\left(1 - 0.5\right)}}\right) \cdot \sqrt[3]{{\left(\sqrt{\left(z - -6\right) + 0.5}\right)}^{\left(1 - 0.5\right)}}}}}{{\left(\sqrt{\left(z - -6\right) + 0.5}\right)}^{\left(1 - 0.5\right)}} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{\left(z - -6\right) + 0.5}}\]

  13. Applied times-frac0.9

    \[\leadsto \frac{\color{blue}{\frac{{\left(\left(z - -6\right) + 0.5\right)}^{z}}{\sqrt[3]{{\left(\sqrt{\left(z - -6\right) + 0.5}\right)}^{\left(1 - 0.5\right)}} \cdot \sqrt[3]{{\left(\sqrt{\left(z - -6\right) + 0.5}\right)}^{\left(1 - 0.5\right)}}} \cdot \frac{\sqrt{\pi \cdot 2}}{\sqrt[3]{{\left(\sqrt{\left(z - -6\right) + 0.5}\right)}^{\left(1 - 0.5\right)}}}}}{{\left(\sqrt{\left(z - -6\right) + 0.5}\right)}^{\left(1 - 0.5\right)}} \cdot \frac{\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{z + 2} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right) + \left(\left(\frac{12.507343278686905}{z + 4} + \left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right)\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right)}{e^{\left(z - -6\right) + 0.5}}\]

  14. Final simplification0.9

    \[\leadsto \frac{\frac{{\left(0.5 + \left(z - -6\right)\right)}^{z}}{\sqrt[3]{{\left(\sqrt{0.5 + \left(z - -6\right)}\right)}^{\left(1 - 0.5\right)}} \cdot \sqrt[3]{{\left(\sqrt{0.5 + \left(z - -6\right)}\right)}^{\left(1 - 0.5\right)}}} \cdot \frac{\sqrt{2 \cdot \pi}}{\sqrt[3]{{\left(\sqrt{0.5 + \left(z - -6\right)}\right)}^{\left(1 - 0.5\right)}}}}{{\left(\sqrt{0.5 + \left(z - -6\right)}\right)}^{\left(1 - 0.5\right)}} \cdot \frac{\left(\left(\left(\frac{-176.6150291621406}{z + 3} + \frac{-0.13857109526572012}{z - -5}\right) + \frac{12.507343278686905}{z + 4}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right) + \left(\frac{1.5056327351493116 \cdot 10^{-07}}{z - -7} + \left(\left(\frac{771.3234287776531}{2 + z} + \left(0.9999999999998099 + \frac{676.5203681218851}{z}\right)\right) + \frac{-1259.1392167224028}{z + 1}\right)\right)}{e^{0.5 + \left(z - -6\right)}}\]

Reproduce

herbie shell --seed 2019151 
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8)))))