Average Error: 29.8 → 1.3
Time: 22.0s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.351770489844849963440765979757572867159 \cdot 10^{56} \lor \neg \left(z \le 128535262688296208\right):\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} - 36.52704169880641416057187598198652267456\right) + 3.130605476229999961645944495103321969509 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
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 -3.351770489844849963440765979757572867159 \cdot 10^{56} \lor \neg \left(z \le 128535262688296208\right):\\
\;\;\;\;x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} - 36.52704169880641416057187598198652267456\right) + 3.130605476229999961645944495103321969509 \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;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}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r253892 = x;
        double r253893 = y;
        double r253894 = z;
        double r253895 = 3.13060547623;
        double r253896 = r253894 * r253895;
        double r253897 = 11.1667541262;
        double r253898 = r253896 + r253897;
        double r253899 = r253898 * r253894;
        double r253900 = t;
        double r253901 = r253899 + r253900;
        double r253902 = r253901 * r253894;
        double r253903 = a;
        double r253904 = r253902 + r253903;
        double r253905 = r253904 * r253894;
        double r253906 = b;
        double r253907 = r253905 + r253906;
        double r253908 = r253893 * r253907;
        double r253909 = 15.234687407;
        double r253910 = r253894 + r253909;
        double r253911 = r253910 * r253894;
        double r253912 = 31.4690115749;
        double r253913 = r253911 + r253912;
        double r253914 = r253913 * r253894;
        double r253915 = 11.9400905721;
        double r253916 = r253914 + r253915;
        double r253917 = r253916 * r253894;
        double r253918 = 0.607771387771;
        double r253919 = r253917 + r253918;
        double r253920 = r253908 / r253919;
        double r253921 = r253892 + r253920;
        return r253921;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r253922 = z;
        double r253923 = -3.35177048984485e+56;
        bool r253924 = r253922 <= r253923;
        double r253925 = 1.2853526268829621e+17;
        bool r253926 = r253922 <= r253925;
        double r253927 = !r253926;
        bool r253928 = r253924 || r253927;
        double r253929 = x;
        double r253930 = y;
        double r253931 = r253930 / r253922;
        double r253932 = t;
        double r253933 = r253932 / r253922;
        double r253934 = 36.527041698806414;
        double r253935 = r253933 - r253934;
        double r253936 = r253931 * r253935;
        double r253937 = 3.13060547623;
        double r253938 = r253937 * r253930;
        double r253939 = r253936 + r253938;
        double r253940 = r253929 + r253939;
        double r253941 = 15.234687407;
        double r253942 = r253922 + r253941;
        double r253943 = r253942 * r253922;
        double r253944 = 31.4690115749;
        double r253945 = r253943 + r253944;
        double r253946 = r253945 * r253922;
        double r253947 = 11.9400905721;
        double r253948 = r253946 + r253947;
        double r253949 = r253948 * r253922;
        double r253950 = 0.607771387771;
        double r253951 = r253949 + r253950;
        double r253952 = r253922 * r253937;
        double r253953 = 11.1667541262;
        double r253954 = r253952 + r253953;
        double r253955 = r253954 * r253922;
        double r253956 = r253955 + r253932;
        double r253957 = r253956 * r253922;
        double r253958 = a;
        double r253959 = r253957 + r253958;
        double r253960 = r253959 * r253922;
        double r253961 = b;
        double r253962 = r253960 + r253961;
        double r253963 = r253951 / r253962;
        double r253964 = r253930 / r253963;
        double r253965 = r253929 + r253964;
        double r253966 = r253928 ? r253940 : r253965;
        return r253966;
}

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

Original29.8
Target1.0
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252631754123144978817242590467 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914286795694558389038333165002 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.35177048984485e+56 or 1.2853526268829621e+17 < z

    1. Initial program 59.6

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

    3. Applied add-cube-cbrt59.6

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

    4. Applied associate-*r*59.6

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

    5. Taylor expanded around inf 8.6

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

    6. Simplified1.9

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

    if -3.35177048984485e+56 < z < 1.2853526268829621e+17

    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*0.7

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.351770489844849963440765979757572867159 \cdot 10^{56} \lor \neg \left(z \le 128535262688296208\right):\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} - 36.52704169880641416057187598198652267456\right) + 3.130605476229999961645944495103321969509 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))))