Average Error: 29.5 → 5.3
Time: 23.1s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -39196859320496969268875775641921781760 \lor \neg \left(z \le 1.879850085979871535558211275291510018991 \cdot 10^{-14}\right):\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}
↓
\begin{array}{l}
\mathbf{if}\;z \le -39196859320496969268875775641921781760 \lor \neg \left(z \le 1.879850085979871535558211275291510018991 \cdot 10^{-14}\right):\\
\;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r275759 = x;
        double r275760 = y;
        double r275761 = z;
        double r275762 = 3.13060547623;
        double r275763 = r275761 * r275762;
        double r275764 = 11.1667541262;
        double r275765 = r275763 + r275764;
        double r275766 = r275765 * r275761;
        double r275767 = t;
        double r275768 = r275766 + r275767;
        double r275769 = r275768 * r275761;
        double r275770 = a;
        double r275771 = r275769 + r275770;
        double r275772 = r275771 * r275761;
        double r275773 = b;
        double r275774 = r275772 + r275773;
        double r275775 = r275760 * r275774;
        double r275776 = 15.234687407;
        double r275777 = r275761 + r275776;
        double r275778 = r275777 * r275761;
        double r275779 = 31.4690115749;
        double r275780 = r275778 + r275779;
        double r275781 = r275780 * r275761;
        double r275782 = 11.9400905721;
        double r275783 = r275781 + r275782;
        double r275784 = r275783 * r275761;
        double r275785 = 0.607771387771;
        double r275786 = r275784 + r275785;
        double r275787 = r275775 / r275786;
        double r275788 = r275759 + r275787;
        return r275788;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r275789 = z;
        double r275790 = -3.919685932049697e+37;
        bool r275791 = r275789 <= r275790;
        double r275792 = 1.8798500859798715e-14;
        bool r275793 = r275789 <= r275792;
        double r275794 = !r275793;
        bool r275795 = r275791 || r275794;
        double r275796 = x;
        double r275797 = 3.13060547623;
        double r275798 = y;
        double r275799 = r275797 * r275798;
        double r275800 = t;
        double r275801 = r275800 * r275798;
        double r275802 = 2.0;
        double r275803 = pow(r275789, r275802);
        double r275804 = r275801 / r275803;
        double r275805 = r275799 + r275804;
        double r275806 = 36.527041698806414;
        double r275807 = r275798 / r275789;
        double r275808 = r275806 * r275807;
        double r275809 = r275805 - r275808;
        double r275810 = r275796 + r275809;
        double r275811 = r275789 * r275797;
        double r275812 = 11.1667541262;
        double r275813 = r275811 + r275812;
        double r275814 = r275813 * r275789;
        double r275815 = r275814 + r275800;
        double r275816 = r275815 * r275789;
        double r275817 = a;
        double r275818 = r275816 + r275817;
        double r275819 = r275818 * r275789;
        double r275820 = b;
        double r275821 = r275819 + r275820;
        double r275822 = r275798 * r275821;
        double r275823 = 15.234687407;
        double r275824 = r275789 + r275823;
        double r275825 = r275824 * r275789;
        double r275826 = 31.4690115749;
        double r275827 = r275825 + r275826;
        double r275828 = r275827 * r275789;
        double r275829 = 11.9400905721;
        double r275830 = r275828 + r275829;
        double r275831 = r275830 * r275789;
        double r275832 = 0.607771387771;
        double r275833 = r275831 + r275832;
        double r275834 = r275822 / r275833;
        double r275835 = r275796 + r275834;
        double r275836 = r275795 ? r275810 : r275835;
        return r275836;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.5
Target1.0
Herbie5.3
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252631754123144978817242590467 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914286795694558389038333165002 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.919685932049697e+37 or 1.8798500859798715e-14 < z

    1. Initial program 56.6

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]

    2. Taylor expanded around inf 9.5

      \[\leadsto x + \color{blue}{\left(\left(3.130605476229999961645944495103321969509 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right)}\]

    if -3.919685932049697e+37 < z < 1.8798500859798715e-14

    1. Initial program 0.8

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification5.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -39196859320496969268875775641921781760 \lor \neg \left(z \le 1.879850085979871535558211275291510018991 \cdot 10^{-14}\right):\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\\ \end{array}\]

Reproduce

herbie shell --seed 2019294 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (if (< z -6.4993449962526318e53) (+ x (* (+ (- 3.13060547622999996 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1))) (if (< z 7.0669654369142868e59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687406999999) z) 31.469011574900001) z) 11.940090572100001) z) 0.60777138777100004) (+ (* (+ (* (+ (* (+ (* z 3.13060547622999996) 11.166754126200001) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547622999996 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547622999996) 11.166754126200001) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687406999999) z) 31.469011574900001) z) 11.940090572100001) z) 0.60777138777100004))))