Average Error: 59.9 → 0.9
Time: 4.5m
Precision: 64
\[\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}^{\left(\left(z - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(z - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(z - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(z - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(z - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(z - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(z - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(z - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(z - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(z - 1\right) + 8}\right)\]
↓
\[\left(\frac{{\left(0.5 + \left(z - -6\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{\sqrt{e^{0.5 + \left(z - -6\right)}}} \cdot \frac{\sqrt{2 \cdot \pi}}{\sqrt{e^{0.5 + \left(z - -6\right)}}}\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{z - -1} + \left(\left(\frac{771.3234287776531}{2 + z} + \frac{676.5203681218851}{z}\right) + 0.9999999999998099\right)\right) + \frac{-176.6150291621406}{3 + z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z + 7} + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right) + \left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{\left(z - -6\right) + -1}\right)\right)\right)\]
\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)
↓
\left(\frac{{\left(0.5 + \left(z - -6\right)\right)}^{\left(0.5 + \left(z - 1\right)\right)}}{\sqrt{e^{0.5 + \left(z - -6\right)}}} \cdot \frac{\sqrt{2 \cdot \pi}}{\sqrt{e^{0.5 + \left(z - -6\right)}}}\right) \cdot \left(\left(\left(\frac{-1259.1392167224028}{z - -1} + \left(\left(\frac{771.3234287776531}{2 + z} + \frac{676.5203681218851}{z}\right) + 0.9999999999998099\right)\right) + \frac{-176.6150291621406}{3 + z}\right) + \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{z + 7} + \frac{9.984369578019572 \cdot 10^{-06}}{z - -6}\right) + \left(\frac{12.507343278686905}{z + 4} + \frac{-0.13857109526572012}{\left(z - -6\right) + -1}\right)\right)\right)
double f(double z) {
        double r12364523 = atan2(1.0, 0.0);
        double r12364524 = 2.0;
        double r12364525 = r12364523 * r12364524;
        double r12364526 = sqrt(r12364525);
        double r12364527 = z;
        double r12364528 = 1.0;
        double r12364529 = r12364527 - r12364528;
        double r12364530 = 7.0;
        double r12364531 = r12364529 + r12364530;
        double r12364532 = 0.5;
        double r12364533 = r12364531 + r12364532;
        double r12364534 = r12364529 + r12364532;
        double r12364535 = pow(r12364533, r12364534);
        double r12364536 = r12364526 * r12364535;
        double r12364537 = -r12364533;
        double r12364538 = exp(r12364537);
        double r12364539 = r12364536 * r12364538;
        double r12364540 = 0.9999999999998099;
        double r12364541 = 676.5203681218851;
        double r12364542 = r12364529 + r12364528;
        double r12364543 = r12364541 / r12364542;
        double r12364544 = r12364540 + r12364543;
        double r12364545 = -1259.1392167224028;
        double r12364546 = r12364529 + r12364524;
        double r12364547 = r12364545 / r12364546;
        double r12364548 = r12364544 + r12364547;
        double r12364549 = 771.3234287776531;
        double r12364550 = 3.0;
        double r12364551 = r12364529 + r12364550;
        double r12364552 = r12364549 / r12364551;
        double r12364553 = r12364548 + r12364552;
        double r12364554 = -176.6150291621406;
        double r12364555 = 4.0;
        double r12364556 = r12364529 + r12364555;
        double r12364557 = r12364554 / r12364556;
        double r12364558 = r12364553 + r12364557;
        double r12364559 = 12.507343278686905;
        double r12364560 = 5.0;
        double r12364561 = r12364529 + r12364560;
        double r12364562 = r12364559 / r12364561;
        double r12364563 = r12364558 + r12364562;
        double r12364564 = -0.13857109526572012;
        double r12364565 = 6.0;
        double r12364566 = r12364529 + r12364565;
        double r12364567 = r12364564 / r12364566;
        double r12364568 = r12364563 + r12364567;
        double r12364569 = 9.984369578019572e-06;
        double r12364570 = r12364569 / r12364531;
        double r12364571 = r12364568 + r12364570;
        double r12364572 = 1.5056327351493116e-07;
        double r12364573 = 8.0;
        double r12364574 = r12364529 + r12364573;
        double r12364575 = r12364572 / r12364574;
        double r12364576 = r12364571 + r12364575;
        double r12364577 = r12364539 * r12364576;
        return r12364577;
}
↓
double f(double z) {
        double r12364578 = 0.5;
        double r12364579 = z;
        double r12364580 = -6.0;
        double r12364581 = r12364579 - r12364580;
        double r12364582 = r12364578 + r12364581;
        double r12364583 = 1.0;
        double r12364584 = r12364579 - r12364583;
        double r12364585 = r12364578 + r12364584;
        double r12364586 = pow(r12364582, r12364585);
        double r12364587 = exp(r12364582);
        double r12364588 = sqrt(r12364587);
        double r12364589 = r12364586 / r12364588;
        double r12364590 = 2.0;
        double r12364591 = atan2(1.0, 0.0);
        double r12364592 = r12364590 * r12364591;
        double r12364593 = sqrt(r12364592);
        double r12364594 = r12364593 / r12364588;
        double r12364595 = r12364589 * r12364594;
        double r12364596 = -1259.1392167224028;
        double r12364597 = -1.0;
        double r12364598 = r12364579 - r12364597;
        double r12364599 = r12364596 / r12364598;
        double r12364600 = 771.3234287776531;
        double r12364601 = r12364590 + r12364579;
        double r12364602 = r12364600 / r12364601;
        double r12364603 = 676.5203681218851;
        double r12364604 = r12364603 / r12364579;
        double r12364605 = r12364602 + r12364604;
        double r12364606 = 0.9999999999998099;
        double r12364607 = r12364605 + r12364606;
        double r12364608 = r12364599 + r12364607;
        double r12364609 = -176.6150291621406;
        double r12364610 = 3.0;
        double r12364611 = r12364610 + r12364579;
        double r12364612 = r12364609 / r12364611;
        double r12364613 = r12364608 + r12364612;
        double r12364614 = 1.5056327351493116e-07;
        double r12364615 = 7.0;
        double r12364616 = r12364579 + r12364615;
        double r12364617 = r12364614 / r12364616;
        double r12364618 = 9.984369578019572e-06;
        double r12364619 = r12364618 / r12364581;
        double r12364620 = r12364617 + r12364619;
        double r12364621 = 12.507343278686905;
        double r12364622 = 4.0;
        double r12364623 = r12364579 + r12364622;
        double r12364624 = r12364621 / r12364623;
        double r12364625 = -0.13857109526572012;
        double r12364626 = r12364581 + r12364597;
        double r12364627 = r12364625 / r12364626;
        double r12364628 = r12364624 + r12364627;
        double r12364629 = r12364620 + r12364628;
        double r12364630 = r12364613 + r12364629;
        double r12364631 = r12364595 * r12364630;
        return r12364631;
}

Error

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.9

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

  2. Simplified1.1

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

  4. Applied add-sqr-sqrt1.1

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

  5. Applied times-frac0.9

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

  6. Final simplification0.9

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

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(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)))))