Average Error: 29.4 → 1.2
Time: 30.0s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -8.012125234246043972472451502679502100871 \cdot 10^{48}:\\ \;\;\;\;\left(\left(\frac{t}{z} \cdot \frac{y}{z} + 3.130605476229999961645944495103321969509 \cdot y\right) - \frac{36.52704169880641416057187598198652267456}{\frac{z}{y}}\right) + x\\ \mathbf{elif}\;z \le 6604017825197738179408704188920627200:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(11.94009057210000079862766142468899488449 + \left(31.46901157490000144889563671313226222992 + z \cdot \left(z + 15.2346874069999991263557603815570473671\right)\right) \cdot z\right) + 0.6077713877710000378584709324059076607227}{b + \left(z \cdot \left(t + \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right) \cdot z\right) + a\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{t}{z} \cdot \frac{y}{z} + 3.130605476229999961645944495103321969509 \cdot y\right) - \frac{36.52704169880641416057187598198652267456}{\frac{z}{y}}\right) + x\\ \end{array}\]
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 -8.012125234246043972472451502679502100871 \cdot 10^{48}:\\
\;\;\;\;\left(\left(\frac{t}{z} \cdot \frac{y}{z} + 3.130605476229999961645944495103321969509 \cdot y\right) - \frac{36.52704169880641416057187598198652267456}{\frac{z}{y}}\right) + x\\

\mathbf{elif}\;z \le 6604017825197738179408704188920627200:\\
\;\;\;\;x + \frac{y}{\frac{z \cdot \left(11.94009057210000079862766142468899488449 + \left(31.46901157490000144889563671313226222992 + z \cdot \left(z + 15.2346874069999991263557603815570473671\right)\right) \cdot z\right) + 0.6077713877710000378584709324059076607227}{b + \left(z \cdot \left(t + \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right) \cdot z\right) + a\right) \cdot z}}\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\frac{t}{z} \cdot \frac{y}{z} + 3.130605476229999961645944495103321969509 \cdot y\right) - \frac{36.52704169880641416057187598198652267456}{\frac{z}{y}}\right) + x\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r22400797 = x;
        double r22400798 = y;
        double r22400799 = z;
        double r22400800 = 3.13060547623;
        double r22400801 = r22400799 * r22400800;
        double r22400802 = 11.1667541262;
        double r22400803 = r22400801 + r22400802;
        double r22400804 = r22400803 * r22400799;
        double r22400805 = t;
        double r22400806 = r22400804 + r22400805;
        double r22400807 = r22400806 * r22400799;
        double r22400808 = a;
        double r22400809 = r22400807 + r22400808;
        double r22400810 = r22400809 * r22400799;
        double r22400811 = b;
        double r22400812 = r22400810 + r22400811;
        double r22400813 = r22400798 * r22400812;
        double r22400814 = 15.234687407;
        double r22400815 = r22400799 + r22400814;
        double r22400816 = r22400815 * r22400799;
        double r22400817 = 31.4690115749;
        double r22400818 = r22400816 + r22400817;
        double r22400819 = r22400818 * r22400799;
        double r22400820 = 11.9400905721;
        double r22400821 = r22400819 + r22400820;
        double r22400822 = r22400821 * r22400799;
        double r22400823 = 0.607771387771;
        double r22400824 = r22400822 + r22400823;
        double r22400825 = r22400813 / r22400824;
        double r22400826 = r22400797 + r22400825;
        return r22400826;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r22400827 = z;
        double r22400828 = -8.012125234246044e+48;
        bool r22400829 = r22400827 <= r22400828;
        double r22400830 = t;
        double r22400831 = r22400830 / r22400827;
        double r22400832 = y;
        double r22400833 = r22400832 / r22400827;
        double r22400834 = r22400831 * r22400833;
        double r22400835 = 3.13060547623;
        double r22400836 = r22400835 * r22400832;
        double r22400837 = r22400834 + r22400836;
        double r22400838 = 36.527041698806414;
        double r22400839 = r22400827 / r22400832;
        double r22400840 = r22400838 / r22400839;
        double r22400841 = r22400837 - r22400840;
        double r22400842 = x;
        double r22400843 = r22400841 + r22400842;
        double r22400844 = 6.604017825197738e+36;
        bool r22400845 = r22400827 <= r22400844;
        double r22400846 = 11.9400905721;
        double r22400847 = 31.4690115749;
        double r22400848 = 15.234687407;
        double r22400849 = r22400827 + r22400848;
        double r22400850 = r22400827 * r22400849;
        double r22400851 = r22400847 + r22400850;
        double r22400852 = r22400851 * r22400827;
        double r22400853 = r22400846 + r22400852;
        double r22400854 = r22400827 * r22400853;
        double r22400855 = 0.607771387771;
        double r22400856 = r22400854 + r22400855;
        double r22400857 = b;
        double r22400858 = r22400835 * r22400827;
        double r22400859 = 11.1667541262;
        double r22400860 = r22400858 + r22400859;
        double r22400861 = r22400860 * r22400827;
        double r22400862 = r22400830 + r22400861;
        double r22400863 = r22400827 * r22400862;
        double r22400864 = a;
        double r22400865 = r22400863 + r22400864;
        double r22400866 = r22400865 * r22400827;
        double r22400867 = r22400857 + r22400866;
        double r22400868 = r22400856 / r22400867;
        double r22400869 = r22400832 / r22400868;
        double r22400870 = r22400842 + r22400869;
        double r22400871 = r22400845 ? r22400870 : r22400843;
        double r22400872 = r22400829 ? r22400843 : r22400871;
        return r22400872;
}

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

Original29.4
Target1.1
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252631754123144978817242590467 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914286795694558389038333165002 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -8.012125234246044e+48 or 6.604017825197738e+36 < z

    1. Initial program 60.4

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

    2. Taylor expanded around inf 8.5

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

    3. Simplified1.5

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

    if -8.012125234246044e+48 < z < 6.604017825197738e+36

    1. Initial program 1.8

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

    3. Applied associate-/l*0.9

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -8.012125234246043972472451502679502100871 \cdot 10^{48}:\\ \;\;\;\;\left(\left(\frac{t}{z} \cdot \frac{y}{z} + 3.130605476229999961645944495103321969509 \cdot y\right) - \frac{36.52704169880641416057187598198652267456}{\frac{z}{y}}\right) + x\\ \mathbf{elif}\;z \le 6604017825197738179408704188920627200:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(11.94009057210000079862766142468899488449 + \left(31.46901157490000144889563671313226222992 + z \cdot \left(z + 15.2346874069999991263557603815570473671\right)\right) \cdot z\right) + 0.6077713877710000378584709324059076607227}{b + \left(z \cdot \left(t + \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right) \cdot z\right) + a\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{t}{z} \cdot \frac{y}{z} + 3.130605476229999961645944495103321969509 \cdot y\right) - \frac{36.52704169880641416057187598198652267456}{\frac{z}{y}}\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0))) (if (< z 7.066965436914287e+59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771) (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))