Average Error: 29.1 → 4.3
Time: 8.5s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.4368664720283841 \cdot 10^{58} \lor \neg \left(z \le 5.2812053084356365 \cdot 10^{38}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\frac{\left({\left(z \cdot 3.13060547622999996\right)}^{3} + {11.166754126200001}^{3}\right) \cdot z}{\left(z \cdot 3.13060547622999996\right) \cdot \left(z \cdot 3.13060547622999996\right) + \left(11.166754126200001 \cdot 11.166754126200001 - \left(z \cdot 3.13060547622999996\right) \cdot 11.166754126200001\right)} + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
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 -2.4368664720283841 \cdot 10^{58} \lor \neg \left(z \le 5.2812053084356365 \cdot 10^{38}\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}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\frac{\left({\left(z \cdot 3.13060547622999996\right)}^{3} + {11.166754126200001}^{3}\right) \cdot z}{\left(z \cdot 3.13060547622999996\right) \cdot \left(z \cdot 3.13060547622999996\right) + \left(11.166754126200001 \cdot 11.166754126200001 - \left(z \cdot 3.13060547622999996\right) \cdot 11.166754126200001\right)} + 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 r389897 = x;
        double r389898 = y;
        double r389899 = z;
        double r389900 = 3.13060547623;
        double r389901 = r389899 * r389900;
        double r389902 = 11.1667541262;
        double r389903 = r389901 + r389902;
        double r389904 = r389903 * r389899;
        double r389905 = t;
        double r389906 = r389904 + r389905;
        double r389907 = r389906 * r389899;
        double r389908 = a;
        double r389909 = r389907 + r389908;
        double r389910 = r389909 * r389899;
        double r389911 = b;
        double r389912 = r389910 + r389911;
        double r389913 = r389898 * r389912;
        double r389914 = 15.234687407;
        double r389915 = r389899 + r389914;
        double r389916 = r389915 * r389899;
        double r389917 = 31.4690115749;
        double r389918 = r389916 + r389917;
        double r389919 = r389918 * r389899;
        double r389920 = 11.9400905721;
        double r389921 = r389919 + r389920;
        double r389922 = r389921 * r389899;
        double r389923 = 0.607771387771;
        double r389924 = r389922 + r389923;
        double r389925 = r389913 / r389924;
        double r389926 = r389897 + r389925;
        return r389926;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r389927 = z;
        double r389928 = -2.436866472028384e+58;
        bool r389929 = r389927 <= r389928;
        double r389930 = 5.2812053084356365e+38;
        bool r389931 = r389927 <= r389930;
        double r389932 = !r389931;
        bool r389933 = r389929 || r389932;
        double r389934 = x;
        double r389935 = 3.13060547623;
        double r389936 = y;
        double r389937 = r389935 * r389936;
        double r389938 = t;
        double r389939 = r389938 * r389936;
        double r389940 = 2.0;
        double r389941 = pow(r389927, r389940);
        double r389942 = r389939 / r389941;
        double r389943 = r389937 + r389942;
        double r389944 = 36.527041698806414;
        double r389945 = r389936 / r389927;
        double r389946 = r389944 * r389945;
        double r389947 = r389943 - r389946;
        double r389948 = r389934 + r389947;
        double r389949 = 15.234687407;
        double r389950 = r389927 + r389949;
        double r389951 = r389950 * r389927;
        double r389952 = 31.4690115749;
        double r389953 = r389951 + r389952;
        double r389954 = r389953 * r389927;
        double r389955 = 11.9400905721;
        double r389956 = r389954 + r389955;
        double r389957 = r389956 * r389927;
        double r389958 = 0.607771387771;
        double r389959 = r389957 + r389958;
        double r389960 = r389927 * r389935;
        double r389961 = 3.0;
        double r389962 = pow(r389960, r389961);
        double r389963 = 11.1667541262;
        double r389964 = pow(r389963, r389961);
        double r389965 = r389962 + r389964;
        double r389966 = r389965 * r389927;
        double r389967 = r389960 * r389960;
        double r389968 = r389963 * r389963;
        double r389969 = r389960 * r389963;
        double r389970 = r389968 - r389969;
        double r389971 = r389967 + r389970;
        double r389972 = r389966 / r389971;
        double r389973 = r389972 + r389938;
        double r389974 = r389973 * r389927;
        double r389975 = a;
        double r389976 = r389974 + r389975;
        double r389977 = r389976 * r389927;
        double r389978 = b;
        double r389979 = r389977 + r389978;
        double r389980 = r389959 / r389979;
        double r389981 = r389936 / r389980;
        double r389982 = r389934 + r389981;
        double r389983 = r389933 ? r389948 : r389982;
        return r389983;
}

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

Original29.1
Target1.0
Herbie4.3
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.436866472028384e+58 or 5.2812053084356365e+38 < z

    1. Initial program 61.0

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

    2. Taylor expanded around inf 8.3

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

    if -2.436866472028384e+58 < z < 5.2812053084356365e+38

    1. Initial program 2.4

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

    3. Applied associate-/l*1.0

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

    5. Applied flip3-+1.0

      \[\leadsto x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\color{blue}{\frac{{\left(z \cdot 3.13060547622999996\right)}^{3} + {11.166754126200001}^{3}}{\left(z \cdot 3.13060547622999996\right) \cdot \left(z \cdot 3.13060547622999996\right) + \left(11.166754126200001 \cdot 11.166754126200001 - \left(z \cdot 3.13060547622999996\right) \cdot 11.166754126200001\right)}} \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\]

    6. Applied associate-*l/1.0

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

  4. Final simplification4.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.4368664720283841 \cdot 10^{58} \lor \neg \left(z \le 5.2812053084356365 \cdot 10^{38}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\frac{\left({\left(z \cdot 3.13060547622999996\right)}^{3} + {11.166754126200001}^{3}\right) \cdot z}{\left(z \cdot 3.13060547622999996\right) \cdot \left(z \cdot 3.13060547622999996\right) + \left(11.166754126200001 \cdot 11.166754126200001 - \left(z \cdot 3.13060547622999996\right) \cdot 11.166754126200001\right)} + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020039 
(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))))