Average Error: 29.8 → 5.0
Time: 6.9s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.1208553628708948 \cdot 10^{66} \lor \neg \left(z \le 1.0008220399133623 \cdot 10^{35}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004} \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.1208553628708948 \cdot 10^{66} \lor \neg \left(z \le 1.0008220399133623 \cdot 10^{35}\right):\\
\;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004} \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r394920 = x;
        double r394921 = y;
        double r394922 = z;
        double r394923 = 3.13060547623;
        double r394924 = r394922 * r394923;
        double r394925 = 11.1667541262;
        double r394926 = r394924 + r394925;
        double r394927 = r394926 * r394922;
        double r394928 = t;
        double r394929 = r394927 + r394928;
        double r394930 = r394929 * r394922;
        double r394931 = a;
        double r394932 = r394930 + r394931;
        double r394933 = r394932 * r394922;
        double r394934 = b;
        double r394935 = r394933 + r394934;
        double r394936 = r394921 * r394935;
        double r394937 = 15.234687407;
        double r394938 = r394922 + r394937;
        double r394939 = r394938 * r394922;
        double r394940 = 31.4690115749;
        double r394941 = r394939 + r394940;
        double r394942 = r394941 * r394922;
        double r394943 = 11.9400905721;
        double r394944 = r394942 + r394943;
        double r394945 = r394944 * r394922;
        double r394946 = 0.607771387771;
        double r394947 = r394945 + r394946;
        double r394948 = r394936 / r394947;
        double r394949 = r394920 + r394948;
        return r394949;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r394950 = z;
        double r394951 = -1.1208553628708948e+66;
        bool r394952 = r394950 <= r394951;
        double r394953 = 1.0008220399133623e+35;
        bool r394954 = r394950 <= r394953;
        double r394955 = !r394954;
        bool r394956 = r394952 || r394955;
        double r394957 = x;
        double r394958 = 3.13060547623;
        double r394959 = y;
        double r394960 = r394958 * r394959;
        double r394961 = t;
        double r394962 = r394961 * r394959;
        double r394963 = 2.0;
        double r394964 = pow(r394950, r394963);
        double r394965 = r394962 / r394964;
        double r394966 = r394960 + r394965;
        double r394967 = 36.527041698806414;
        double r394968 = r394959 / r394950;
        double r394969 = r394967 * r394968;
        double r394970 = r394966 - r394969;
        double r394971 = r394957 + r394970;
        double r394972 = 15.234687407;
        double r394973 = r394950 + r394972;
        double r394974 = r394973 * r394950;
        double r394975 = 31.4690115749;
        double r394976 = r394974 + r394975;
        double r394977 = r394976 * r394950;
        double r394978 = 11.9400905721;
        double r394979 = r394977 + r394978;
        double r394980 = r394979 * r394950;
        double r394981 = 0.607771387771;
        double r394982 = r394980 + r394981;
        double r394983 = r394959 / r394982;
        double r394984 = r394950 * r394958;
        double r394985 = 11.1667541262;
        double r394986 = r394984 + r394985;
        double r394987 = r394986 * r394950;
        double r394988 = r394987 + r394961;
        double r394989 = r394988 * r394950;
        double r394990 = a;
        double r394991 = r394989 + r394990;
        double r394992 = r394991 * r394950;
        double r394993 = b;
        double r394994 = r394992 + r394993;
        double r394995 = r394983 * r394994;
        double r394996 = r394957 + r394995;
        double r394997 = r394956 ? r394971 : r394996;
        return r394997;
}

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
Target1.1
Herbie5.0
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.1208553628708948e+66 or 1.0008220399133623e+35 < z

    1. Initial program 60.9

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]

    2. Taylor expanded around inf 8.8

      \[\leadsto x + \color{blue}{\left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    if -1.1208553628708948e+66 < z < 1.0008220399133623e+35

    1. Initial program 2.8

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
    2. Using strategy rm

    3. Applied associate-/l*1.4

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]
    4. Using strategy rm

    5. Applied associate-/r/1.7

      \[\leadsto x + \color{blue}{\frac{y}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004} \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification5.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.1208553628708948 \cdot 10^{66} \lor \neg \left(z \le 1.0008220399133623 \cdot 10^{35}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004} \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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))))