Average Error: 30.0 → 4.9
Time: 22.5s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.983991909224869626959693820538238066719 \cdot 10^{68} \lor \neg \left(z \le 26781923308.5818939208984375\right):\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\left(\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227\right) \cdot \frac{1}{b + \left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z}}\\ \end{array}\]
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 -6.983991909224869626959693820538238066719 \cdot 10^{68} \lor \neg \left(z \le 26781923308.5818939208984375\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}{\left(\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227\right) \cdot \frac{1}{b + \left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r228865 = x;
        double r228866 = y;
        double r228867 = z;
        double r228868 = 3.13060547623;
        double r228869 = r228867 * r228868;
        double r228870 = 11.1667541262;
        double r228871 = r228869 + r228870;
        double r228872 = r228871 * r228867;
        double r228873 = t;
        double r228874 = r228872 + r228873;
        double r228875 = r228874 * r228867;
        double r228876 = a;
        double r228877 = r228875 + r228876;
        double r228878 = r228877 * r228867;
        double r228879 = b;
        double r228880 = r228878 + r228879;
        double r228881 = r228866 * r228880;
        double r228882 = 15.234687407;
        double r228883 = r228867 + r228882;
        double r228884 = r228883 * r228867;
        double r228885 = 31.4690115749;
        double r228886 = r228884 + r228885;
        double r228887 = r228886 * r228867;
        double r228888 = 11.9400905721;
        double r228889 = r228887 + r228888;
        double r228890 = r228889 * r228867;
        double r228891 = 0.607771387771;
        double r228892 = r228890 + r228891;
        double r228893 = r228881 / r228892;
        double r228894 = r228865 + r228893;
        return r228894;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r228895 = z;
        double r228896 = -6.98399190922487e+68;
        bool r228897 = r228895 <= r228896;
        double r228898 = 26781923308.581894;
        bool r228899 = r228895 <= r228898;
        double r228900 = !r228899;
        bool r228901 = r228897 || r228900;
        double r228902 = x;
        double r228903 = 3.13060547623;
        double r228904 = y;
        double r228905 = r228903 * r228904;
        double r228906 = t;
        double r228907 = r228906 * r228904;
        double r228908 = 2.0;
        double r228909 = pow(r228895, r228908);
        double r228910 = r228907 / r228909;
        double r228911 = r228905 + r228910;
        double r228912 = 36.527041698806414;
        double r228913 = r228904 / r228895;
        double r228914 = r228912 * r228913;
        double r228915 = r228911 - r228914;
        double r228916 = r228902 + r228915;
        double r228917 = 15.234687407;
        double r228918 = r228895 + r228917;
        double r228919 = r228918 * r228895;
        double r228920 = 31.4690115749;
        double r228921 = r228919 + r228920;
        double r228922 = r228921 * r228895;
        double r228923 = 11.9400905721;
        double r228924 = r228922 + r228923;
        double r228925 = r228924 * r228895;
        double r228926 = 0.607771387771;
        double r228927 = r228925 + r228926;
        double r228928 = 1.0;
        double r228929 = b;
        double r228930 = r228895 * r228903;
        double r228931 = 11.1667541262;
        double r228932 = r228930 + r228931;
        double r228933 = r228932 * r228895;
        double r228934 = r228933 + r228906;
        double r228935 = r228934 * r228895;
        double r228936 = a;
        double r228937 = r228935 + r228936;
        double r228938 = r228937 * r228895;
        double r228939 = r228929 + r228938;
        double r228940 = r228928 / r228939;
        double r228941 = r228927 * r228940;
        double r228942 = r228904 / r228941;
        double r228943 = r228902 + r228942;
        double r228944 = r228901 ? r228916 : r228943;
        return r228944;
}

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

Original30.0
Target1.0
Herbie4.9
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252631754123144978817242590467 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914286795694558389038333165002 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -6.98399190922487e+68 or 26781923308.581894 < z

    1. Initial program 59.7

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

    2. Taylor expanded around inf 9.0

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

    if -6.98399190922487e+68 < z < 26781923308.581894

    1. Initial program 2.3

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

    3. Applied associate-/l*1.0

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

    5. Applied div-inv1.0

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

    6. Simplified1.0

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

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.983991909224869626959693820538238066719 \cdot 10^{68} \lor \neg \left(z \le 26781923308.5818939208984375\right):\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\left(\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227\right) \cdot \frac{1}{b + \left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(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 -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1))) (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)))))

  (+ 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))))