Jmat.Real.gamma, branch z greater than 0.5

Average Error: 59.8 → 0.9

Time: 5.6m

Precision: 64

• could not determine a ground truth for program body

  1. z = 4.035271246258652e+292

Math

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

↓

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

C

double f(double z) {
        double r16781420 = atan2(1.0, 0.0);
        double r16781421 = 2.0;
        double r16781422 = r16781420 * r16781421;
        double r16781423 = sqrt(r16781422);
        double r16781424 = z;
        double r16781425 = 1.0;
        double r16781426 = r16781424 - r16781425;
        double r16781427 = 7.0;
        double r16781428 = r16781426 + r16781427;
        double r16781429 = 0.5;
        double r16781430 = r16781428 + r16781429;
        double r16781431 = r16781426 + r16781429;
        double r16781432 = pow(r16781430, r16781431);
        double r16781433 = r16781423 * r16781432;
        double r16781434 = -r16781430;
        double r16781435 = exp(r16781434);
        double r16781436 = r16781433 * r16781435;
        double r16781437 = 0.9999999999998099;
        double r16781438 = 676.5203681218851;
        double r16781439 = r16781426 + r16781425;
        double r16781440 = r16781438 / r16781439;
        double r16781441 = r16781437 + r16781440;
        double r16781442 = -1259.1392167224028;
        double r16781443 = r16781426 + r16781421;
        double r16781444 = r16781442 / r16781443;
        double r16781445 = r16781441 + r16781444;
        double r16781446 = 771.3234287776531;
        double r16781447 = 3.0;
        double r16781448 = r16781426 + r16781447;
        double r16781449 = r16781446 / r16781448;
        double r16781450 = r16781445 + r16781449;
        double r16781451 = -176.6150291621406;
        double r16781452 = 4.0;
        double r16781453 = r16781426 + r16781452;
        double r16781454 = r16781451 / r16781453;
        double r16781455 = r16781450 + r16781454;
        double r16781456 = 12.507343278686905;
        double r16781457 = 5.0;
        double r16781458 = r16781426 + r16781457;
        double r16781459 = r16781456 / r16781458;
        double r16781460 = r16781455 + r16781459;
        double r16781461 = -0.13857109526572012;
        double r16781462 = 6.0;
        double r16781463 = r16781426 + r16781462;
        double r16781464 = r16781461 / r16781463;
        double r16781465 = r16781460 + r16781464;
        double r16781466 = 9.984369578019572e-06;
        double r16781467 = r16781466 / r16781428;
        double r16781468 = r16781465 + r16781467;
        double r16781469 = 1.5056327351493116e-07;
        double r16781470 = 8.0;
        double r16781471 = r16781426 + r16781470;
        double r16781472 = r16781469 / r16781471;
        double r16781473 = r16781468 + r16781472;
        double r16781474 = r16781436 * r16781473;
        return r16781474;
}

↓

double f(double z) {
        double r16781475 = atan2(1.0, 0.0);
        double r16781476 = 2.0;
        double r16781477 = r16781475 * r16781476;
        double r16781478 = sqrt(r16781477);
        double r16781479 = -0.13857109526572012;
        double r16781480 = z;
        double r16781481 = 5.0;
        double r16781482 = r16781480 + r16781481;
        double r16781483 = r16781479 / r16781482;
        double r16781484 = 1.5056327351493116e-07;
        double r16781485 = 7.0;
        double r16781486 = r16781480 + r16781485;
        double r16781487 = r16781484 / r16781486;
        double r16781488 = 771.3234287776531;
        double r16781489 = r16781476 + r16781480;
        double r16781490 = r16781488 / r16781489;
        double r16781491 = r16781487 + r16781490;
        double r16781492 = 12.507343278686905;
        double r16781493 = 4.0;
        double r16781494 = r16781480 + r16781493;
        double r16781495 = r16781492 / r16781494;
        double r16781496 = 9.984369578019572e-06;
        double r16781497 = 6.0;
        double r16781498 = r16781497 + r16781480;
        double r16781499 = r16781496 / r16781498;
        double r16781500 = r16781495 + r16781499;
        double r16781501 = r16781491 + r16781500;
        double r16781502 = 676.5203681218851;
        double r16781503 = r16781502 / r16781480;
        double r16781504 = 0.9999999999998099;
        double r16781505 = -176.6150291621406;
        double r16781506 = 3.0;
        double r16781507 = r16781480 + r16781506;
        double r16781508 = r16781505 / r16781507;
        double r16781509 = r16781504 + r16781508;
        double r16781510 = r16781503 + r16781509;
        double r16781511 = -1259.1392167224028;
        double r16781512 = 1.0;
        double r16781513 = r16781512 + r16781480;
        double r16781514 = r16781511 / r16781513;
        double r16781515 = r16781510 + r16781514;
        double r16781516 = r16781501 + r16781515;
        double r16781517 = r16781483 + r16781516;
        double r16781518 = 0.5;
        double r16781519 = r16781480 + r16781518;
        double r16781520 = exp(r16781519);
        double r16781521 = r16781519 + r16781497;
        double r16781522 = cbrt(r16781521);
        double r16781523 = r16781522 * r16781522;
        double r16781524 = sqrt(r16781523);
        double r16781525 = r16781480 - r16781512;
        double r16781526 = r16781518 + r16781525;
        double r16781527 = pow(r16781524, r16781526);
        double r16781528 = r16781520 / r16781527;
        double r16781529 = sqrt(r16781521);
        double r16781530 = pow(r16781529, r16781526);
        double r16781531 = exp(r16781497);
        double r16781532 = sqrt(r16781522);
        double r16781533 = pow(r16781532, r16781526);
        double r16781534 = r16781531 / r16781533;
        double r16781535 = r16781530 / r16781534;
        double r16781536 = r16781528 / r16781535;
        double r16781537 = r16781512 / r16781536;
        double r16781538 = r16781517 * r16781537;
        double r16781539 = r16781478 * r16781538;
        return r16781539;
}

Error

Bits error versus z

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. Simplified 1.2

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

3. Simplified 0.9

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

5. Applied add-sqr-sqrt 0.9

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

6. Applied unpow-prod-down 0.9

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

7. Applied exp-sum 0.9

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

8. Applied times-frac 0.9

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

10. Applied div-inv 1.6

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

11. Applied associate-*l* 1.5

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

12. Simplified 0.9

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

14. Applied add-cube-cbrt 0.9

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

15. Applied sqrt-prod 0.9

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

16. Applied unpow-prod-down 0.9

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

17. Applied exp-sum 0.9

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

18. Applied times-frac 0.9

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

19. Applied associate-/l* 0.9

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

20. Final simplification 0.9

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

Reproduce

herbie shell --seed 2019130 
(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)))))