Jmat.Real.gamma, branch z less than 0.5

Average Error: 1.8 → 0.6

Time: 2.4m

Precision: 64

• could not determine a ground truth for program body

  1. z = -5.528985092060166e+69

Math

\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

↓

\[\frac{\frac{\mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right), \frac{771.3234287776531346025876700878143310547}{3 - z}, {\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)}^{2}\right) \cdot \left(\left(\left(\left(5 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(8 - z\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) + \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt[3]{\left(\pi \cdot 2\right) \cdot \sqrt{\pi \cdot 2}}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

C

double f(double z) {
        double r158599 = atan2(1.0, 0.0);
        double r158600 = z;
        double r158601 = r158599 * r158600;
        double r158602 = sin(r158601);
        double r158603 = r158599 / r158602;
        double r158604 = 2.0;
        double r158605 = r158599 * r158604;
        double r158606 = sqrt(r158605);
        double r158607 = 1.0;
        double r158608 = r158607 - r158600;
        double r158609 = r158608 - r158607;
        double r158610 = 7.0;
        double r158611 = r158609 + r158610;
        double r158612 = 0.5;
        double r158613 = r158611 + r158612;
        double r158614 = r158609 + r158612;
        double r158615 = pow(r158613, r158614);
        double r158616 = r158606 * r158615;
        double r158617 = -r158613;
        double r158618 = exp(r158617);
        double r158619 = r158616 * r158618;
        double r158620 = 0.9999999999998099;
        double r158621 = 676.5203681218851;
        double r158622 = r158609 + r158607;
        double r158623 = r158621 / r158622;
        double r158624 = r158620 + r158623;
        double r158625 = -1259.1392167224028;
        double r158626 = r158609 + r158604;
        double r158627 = r158625 / r158626;
        double r158628 = r158624 + r158627;
        double r158629 = 771.3234287776531;
        double r158630 = 3.0;
        double r158631 = r158609 + r158630;
        double r158632 = r158629 / r158631;
        double r158633 = r158628 + r158632;
        double r158634 = -176.6150291621406;
        double r158635 = 4.0;
        double r158636 = r158609 + r158635;
        double r158637 = r158634 / r158636;
        double r158638 = r158633 + r158637;
        double r158639 = 12.507343278686905;
        double r158640 = 5.0;
        double r158641 = r158609 + r158640;
        double r158642 = r158639 / r158641;
        double r158643 = r158638 + r158642;
        double r158644 = -0.13857109526572012;
        double r158645 = 6.0;
        double r158646 = r158609 + r158645;
        double r158647 = r158644 / r158646;
        double r158648 = r158643 + r158647;
        double r158649 = 9.984369578019572e-06;
        double r158650 = r158649 / r158611;
        double r158651 = r158648 + r158650;
        double r158652 = 1.5056327351493116e-07;
        double r158653 = 8.0;
        double r158654 = r158609 + r158653;
        double r158655 = r158652 / r158654;
        double r158656 = r158651 + r158655;
        double r158657 = r158619 * r158656;
        double r158658 = r158603 * r158657;
        return r158658;
}

↓

double f(double z) {
        double r158659 = 771.3234287776531;
        double r158660 = 3.0;
        double r158661 = z;
        double r158662 = r158660 - r158661;
        double r158663 = r158659 / r158662;
        double r158664 = -176.6150291621406;
        double r158665 = 4.0;
        double r158666 = r158665 - r158661;
        double r158667 = r158664 / r158666;
        double r158668 = 0.9999999999998099;
        double r158669 = 676.5203681218851;
        double r158670 = 1.0;
        double r158671 = r158670 - r158661;
        double r158672 = r158669 / r158671;
        double r158673 = r158668 + r158672;
        double r158674 = r158667 + r158673;
        double r158675 = r158663 - r158674;
        double r158676 = r158673 + r158667;
        double r158677 = 2.0;
        double r158678 = pow(r158676, r158677);
        double r158679 = fma(r158675, r158663, r158678);
        double r158680 = 5.0;
        double r158681 = r158680 - r158661;
        double r158682 = 7.0;
        double r158683 = r158682 - r158661;
        double r158684 = r158681 * r158683;
        double r158685 = 6.0;
        double r158686 = r158685 - r158661;
        double r158687 = 8.0;
        double r158688 = r158687 - r158661;
        double r158689 = r158686 * r158688;
        double r158690 = r158684 * r158689;
        double r158691 = -1259.1392167224028;
        double r158692 = r158690 * r158691;
        double r158693 = r158679 * r158692;
        double r158694 = 3.0;
        double r158695 = pow(r158674, r158694);
        double r158696 = pow(r158663, r158694);
        double r158697 = r158695 + r158696;
        double r158698 = -r158661;
        double r158699 = r158698 + r158682;
        double r158700 = r158699 * r158686;
        double r158701 = r158700 * r158688;
        double r158702 = r158701 * r158681;
        double r158703 = r158663 * r158675;
        double r158704 = fma(r158674, r158674, r158703);
        double r158705 = 12.507343278686905;
        double r158706 = 1.5056327351493116e-07;
        double r158707 = 9.984369578019572e-06;
        double r158708 = -0.13857109526572012;
        double r158709 = r158699 * r158708;
        double r158710 = fma(r158707, r158686, r158709);
        double r158711 = r158688 * r158710;
        double r158712 = fma(r158706, r158700, r158711);
        double r158713 = r158681 * r158712;
        double r158714 = fma(r158705, r158701, r158713);
        double r158715 = r158704 * r158714;
        double r158716 = fma(r158697, r158702, r158715);
        double r158717 = 2.0;
        double r158718 = r158698 + r158717;
        double r158719 = r158716 * r158718;
        double r158720 = r158693 + r158719;
        double r158721 = r158718 * r158704;
        double r158722 = r158721 * r158702;
        double r158723 = r158720 / r158722;
        double r158724 = 0.5;
        double r158725 = r158724 + r158699;
        double r158726 = exp(r158725);
        double r158727 = r158723 / r158726;
        double r158728 = atan2(1.0, 0.0);
        double r158729 = r158728 * r158661;
        double r158730 = sin(r158729);
        double r158731 = r158728 / r158730;
        double r158732 = r158728 * r158717;
        double r158733 = sqrt(r158732);
        double r158734 = r158732 * r158733;
        double r158735 = cbrt(r158734);
        double r158736 = r158731 * r158735;
        double r158737 = r158698 + r158724;
        double r158738 = pow(r158725, r158737);
        double r158739 = r158736 * r158738;
        double r158740 = r158727 * r158739;
        return r158740;
}

Error

Bits error versus z

Derivation

1. Initial program 1.8

   \[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.139216722402807135949842631816864014}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531346025876700878143310547}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621405870046146446838974952698}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.50734327868690520801919774385169148445}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.1385710952657201178173096423051902092993}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

2. Simplified 2.2

   \[\leadsto \color{blue}{\frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \left(\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6}}{\left(-z\right) + 7} + \frac{-0.1385710952657201178173096423051902092993}{6 + \left(-z\right)}\right)\right)\right)\right)}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)}\]
3. Using strategy rm

4. Applied frac-add 2.2

   \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \left(\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7}}{8 + \left(-z\right)} + \color{blue}{\frac{9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(6 + \left(-z\right)\right) + \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993}{\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)}}\right)\right)\right)}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

5. Applied frac-add 2.2

   \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right) + \left(\frac{12.50734327868690520801919774385169148445}{5 + \left(-z\right)} + \color{blue}{\frac{1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right) + \left(8 + \left(-z\right)\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(6 + \left(-z\right)\right) + \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)}{\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)}}\right)\right)}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

6. Applied frac-add 2.2

   \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right) + \color{blue}{\frac{12.50734327868690520801919774385169148445 \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right) + \left(5 + \left(-z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right) + \left(8 + \left(-z\right)\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(6 + \left(-z\right)\right) + \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)}{\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)}}\right)}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

7. Applied flip3-+ 1.1

   \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \left(\color{blue}{\frac{{\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}^{3}}{\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}} + \frac{12.50734327868690520801919774385169148445 \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right) + \left(5 + \left(-z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right) + \left(8 + \left(-z\right)\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(6 + \left(-z\right)\right) + \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)}{\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)}\right)}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

8. Applied frac-add 1.1

   \[\leadsto \frac{\frac{-1259.139216722402807135949842631816864014}{\left(-z\right) + 2} + \color{blue}{\frac{\left({\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}^{3}\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)\right) + \left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(12.50734327868690520801919774385169148445 \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right) + \left(5 + \left(-z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right) + \left(8 + \left(-z\right)\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(6 + \left(-z\right)\right) + \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)}{\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)\right)}}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

9. Applied frac-add 1.1

   \[\leadsto \frac{\color{blue}{\frac{-1259.139216722402807135949842631816864014 \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)\right)\right) + \left(\left(-z\right) + 2\right) \cdot \left(\left({\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)}^{3}\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)\right) + \left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(12.50734327868690520801919774385169148445 \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right) + \left(5 + \left(-z\right)\right) \cdot \left(1.505632735149311617592788074479481785772 \cdot 10^{-7} \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right) + \left(8 + \left(-z\right)\right) \cdot \left(9.984369578019571583242346146658263705831 \cdot 10^{-6} \cdot \left(6 + \left(-z\right)\right) + \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right)}{\left(\left(-z\right) + 2\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)\right)\right)}}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

10. Simplified 0.6

    \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(5 - z\right)\right) \cdot \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right), \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)}}{\left(\left(-z\right) + 2\right) \cdot \left(\left(\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) + \left(\frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)} - \left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 + \left(-z\right)}\right) \cdot \frac{771.3234287776531346025876700878143310547}{3 + \left(-z\right)}\right)\right) \cdot \left(\left(5 + \left(-z\right)\right) \cdot \left(\left(8 + \left(-z\right)\right) \cdot \left(\left(\left(-z\right) + 7\right) \cdot \left(6 + \left(-z\right)\right)\right)\right)\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

11. Simplified 0.6

    \[\leadsto \frac{\frac{\mathsf{fma}\left(-1259.139216722402807135949842631816864014, \left(\mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(5 - z\right)\right) \cdot \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right), \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)\right)}{\color{blue}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]
12. Using strategy rm

13. Applied fma-udef 1.1

    \[\leadsto \frac{\frac{\color{blue}{-1259.139216722402807135949842631816864014 \cdot \left(\left(\mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \left(5 - z\right)\right) \cdot \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right)\right) + \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)}}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

14. Simplified 1.1

    \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right), \frac{771.3234287776531346025876700878143310547}{3 - z}, {\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)}^{2}\right) \cdot \left(\left(\left(\left(5 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(8 - z\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right)} + \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt{\pi \cdot 2}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]
15. Using strategy rm

16. Applied add-cbrt-cube 1.1

    \[\leadsto \frac{\frac{\mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right), \frac{771.3234287776531346025876700878143310547}{3 - z}, {\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)}^{2}\right) \cdot \left(\left(\left(\left(5 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(8 - z\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) + \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \color{blue}{\sqrt[3]{\left(\sqrt{\pi \cdot 2} \cdot \sqrt{\pi \cdot 2}\right) \cdot \sqrt{\pi \cdot 2}}}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

17. Simplified 0.6

    \[\leadsto \frac{\frac{\mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right), \frac{771.3234287776531346025876700878143310547}{3 - z}, {\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)}^{2}\right) \cdot \left(\left(\left(\left(5 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(8 - z\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) + \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt[3]{\color{blue}{\left(\pi \cdot 2\right) \cdot \sqrt{\pi \cdot 2}}}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

18. Final simplification 0.6

    \[\leadsto \frac{\frac{\mathsf{fma}\left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right), \frac{771.3234287776531346025876700878143310547}{3 - z}, {\left(\left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right) + \frac{-176.6150291621405870046146446838974952698}{4 - z}\right)}^{2}\right) \cdot \left(\left(\left(\left(5 - z\right) \cdot \left(7 - z\right)\right) \cdot \left(\left(6 - z\right) \cdot \left(8 - z\right)\right)\right) \cdot -1259.139216722402807135949842631816864014\right) + \mathsf{fma}\left({\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)}^{3} + {\left(\frac{771.3234287776531346025876700878143310547}{3 - z}\right)}^{3}, \left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right), \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right) \cdot \mathsf{fma}\left(12.50734327868690520801919774385169148445, \left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right), \left(5 - z\right) \cdot \mathsf{fma}\left(1.505632735149311617592788074479481785772 \cdot 10^{-7}, \left(\left(-z\right) + 7\right) \cdot \left(6 - z\right), \left(8 - z\right) \cdot \mathsf{fma}\left(9.984369578019571583242346146658263705831 \cdot 10^{-6}, 6 - z, \left(\left(-z\right) + 7\right) \cdot -0.1385710952657201178173096423051902092993\right)\right)\right)\right) \cdot \left(\left(-z\right) + 2\right)}{\left(\left(\left(-z\right) + 2\right) \cdot \mathsf{fma}\left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right), \frac{771.3234287776531346025876700878143310547}{3 - z} \cdot \left(\frac{771.3234287776531346025876700878143310547}{3 - z} - \left(\frac{-176.6150291621405870046146446838974952698}{4 - z} + \left(0.9999999999998099298181841732002794742584 + \frac{676.5203681218850988443591631948947906494}{1 - z}\right)\right)\right)\right)\right) \cdot \left(\left(\left(\left(\left(-z\right) + 7\right) \cdot \left(6 - z\right)\right) \cdot \left(8 - z\right)\right) \cdot \left(5 - z\right)\right)}}{e^{0.5 + \left(\left(-z\right) + 7\right)}} \cdot \left(\left(\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \sqrt[3]{\left(\pi \cdot 2\right) \cdot \sqrt{\pi \cdot 2}}\right) \cdot {\left(0.5 + \left(\left(-z\right) + 7\right)\right)}^{\left(\left(-z\right) + 0.5\right)}\right)\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z less than 0.5"
  :precision binary64
  (* (/ PI (sin (* PI z))) (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- (- 1 z) 1) 7) 0.5) (+ (- (- 1 z) 1) 0.5))) (exp (- (+ (+ (- (- 1 z) 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- (- 1 z) 1) 1))) (/ -1259.1392167224028 (+ (- (- 1 z) 1) 2))) (/ 771.3234287776531 (+ (- (- 1 z) 1) 3))) (/ -176.6150291621406 (+ (- (- 1 z) 1) 4))) (/ 12.507343278686905 (+ (- (- 1 z) 1) 5))) (/ -0.13857109526572012 (+ (- (- 1 z) 1) 6))) (/ 9.984369578019572e-06 (+ (- (- 1 z) 1) 7))) (/ 1.5056327351493116e-07 (+ (- (- 1 z) 1) 8))))))