Average Error: 30.2 → 1.1
Time: 24.1s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.807302090294030027556419953822894801612 \cdot 10^{70} \lor \neg \left(z \le 548437100344291305854952900722667028480\right):\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{\frac{t}{z}}{z}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\left(z \cdot \left(31.46901157490000144889563671313226222992 + \left(z + 15.2346874069999991263557603815570473671\right) \cdot z\right) + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227} \cdot \left(z \cdot \left(a + z \cdot \left(z \cdot \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right) + t\right)\right) + b\right)\right) \cdot y\\ \end{array}\]
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 -3.807302090294030027556419953822894801612 \cdot 10^{70} \lor \neg \left(z \le 548437100344291305854952900722667028480\right):\\
\;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{\frac{t}{z}}{z}\right) \cdot y\\

\mathbf{else}:\\
\;\;\;\;x + \left(\frac{1}{\left(z \cdot \left(31.46901157490000144889563671313226222992 + \left(z + 15.2346874069999991263557603815570473671\right) \cdot z\right) + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227} \cdot \left(z \cdot \left(a + z \cdot \left(z \cdot \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right) + t\right)\right) + b\right)\right) \cdot y\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r352822 = x;
        double r352823 = y;
        double r352824 = z;
        double r352825 = 3.13060547623;
        double r352826 = r352824 * r352825;
        double r352827 = 11.1667541262;
        double r352828 = r352826 + r352827;
        double r352829 = r352828 * r352824;
        double r352830 = t;
        double r352831 = r352829 + r352830;
        double r352832 = r352831 * r352824;
        double r352833 = a;
        double r352834 = r352832 + r352833;
        double r352835 = r352834 * r352824;
        double r352836 = b;
        double r352837 = r352835 + r352836;
        double r352838 = r352823 * r352837;
        double r352839 = 15.234687407;
        double r352840 = r352824 + r352839;
        double r352841 = r352840 * r352824;
        double r352842 = 31.4690115749;
        double r352843 = r352841 + r352842;
        double r352844 = r352843 * r352824;
        double r352845 = 11.9400905721;
        double r352846 = r352844 + r352845;
        double r352847 = r352846 * r352824;
        double r352848 = 0.607771387771;
        double r352849 = r352847 + r352848;
        double r352850 = r352838 / r352849;
        double r352851 = r352822 + r352850;
        return r352851;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r352852 = z;
        double r352853 = -3.80730209029403e+70;
        bool r352854 = r352852 <= r352853;
        double r352855 = 5.484371003442913e+38;
        bool r352856 = r352852 <= r352855;
        double r352857 = !r352856;
        bool r352858 = r352854 || r352857;
        double r352859 = x;
        double r352860 = 3.13060547623;
        double r352861 = 36.527041698806414;
        double r352862 = r352861 / r352852;
        double r352863 = r352860 - r352862;
        double r352864 = t;
        double r352865 = r352864 / r352852;
        double r352866 = r352865 / r352852;
        double r352867 = r352863 + r352866;
        double r352868 = y;
        double r352869 = r352867 * r352868;
        double r352870 = r352859 + r352869;
        double r352871 = 1.0;
        double r352872 = 31.4690115749;
        double r352873 = 15.234687407;
        double r352874 = r352852 + r352873;
        double r352875 = r352874 * r352852;
        double r352876 = r352872 + r352875;
        double r352877 = r352852 * r352876;
        double r352878 = 11.9400905721;
        double r352879 = r352877 + r352878;
        double r352880 = r352879 * r352852;
        double r352881 = 0.607771387771;
        double r352882 = r352880 + r352881;
        double r352883 = r352871 / r352882;
        double r352884 = a;
        double r352885 = r352860 * r352852;
        double r352886 = 11.1667541262;
        double r352887 = r352885 + r352886;
        double r352888 = r352852 * r352887;
        double r352889 = r352888 + r352864;
        double r352890 = r352852 * r352889;
        double r352891 = r352884 + r352890;
        double r352892 = r352852 * r352891;
        double r352893 = b;
        double r352894 = r352892 + r352893;
        double r352895 = r352883 * r352894;
        double r352896 = r352895 * r352868;
        double r352897 = r352859 + r352896;
        double r352898 = r352858 ? r352870 : r352897;
        return r352898;
}

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

Original30.2
Target0.8
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252631754123144978817242590467 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914286795694558389038333165002 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.80730209029403e+70 or 5.484371003442913e+38 < z

    1. Initial program 61.7

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

    2. Simplified60.5

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

    3. Taylor expanded around inf 0.7

      \[\leadsto x + \color{blue}{\left(\left(\frac{t}{{z}^{2}} + 3.130605476229999961645944495103321969509\right) - 36.52704169880641416057187598198652267456 \cdot \frac{1}{z}\right)} \cdot y\]

    4. Simplified0.7

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

    if -3.80730209029403e+70 < z < 5.484371003442913e+38

    1. Initial program 2.9

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

    2. Simplified1.3

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

    4. Applied div-inv1.3

      \[\leadsto x + \color{blue}{\left(\left(z \cdot \left(a + z \cdot \left(t + \left(11.16675412620000074070958362426608800888 + z \cdot 3.130605476229999961645944495103321969509\right) \cdot z\right)\right) + b\right) \cdot \frac{1}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.2346874069999991263557603815570473671\right) + 31.46901157490000144889563671313226222992\right) + 11.94009057210000079862766142468899488449\right) + 0.6077713877710000378584709324059076607227}\right)} \cdot y\]

    5. Simplified1.3

      \[\leadsto x + \left(\left(z \cdot \left(a + z \cdot \left(t + \left(11.16675412620000074070958362426608800888 + z \cdot 3.130605476229999961645944495103321969509\right) \cdot z\right)\right) + b\right) \cdot \color{blue}{\frac{1}{0.6077713877710000378584709324059076607227 + \left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z}}\right) \cdot y\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.807302090294030027556419953822894801612 \cdot 10^{70} \lor \neg \left(z \le 548437100344291305854952900722667028480\right):\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{\frac{t}{z}}{z}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\left(z \cdot \left(31.46901157490000144889563671313226222992 + \left(z + 15.2346874069999991263557603815570473671\right) \cdot z\right) + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227} \cdot \left(z \cdot \left(a + z \cdot \left(z \cdot \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right) + t\right)\right) + b\right)\right) \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(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))))