Average Error: 28.6 → 1.1
Time: 27.0s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.4707468883041915 \cdot 10^{+53}:\\ \;\;\;\;\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + \frac{t}{z} \cdot \frac{y}{z}\right) + x\\ \mathbf{elif}\;z \le 3.7272833098172985 \cdot 10^{+62}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot \left(a + z \cdot \left(z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right) + t\right)\right)}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + \frac{t}{z} \cdot \frac{y}{z}\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.4707468883041915 \cdot 10^{+53}:\\
\;\;\;\;\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + \frac{t}{z} \cdot \frac{y}{z}\right) + x\\

\mathbf{elif}\;z \le 3.7272833098172985 \cdot 10^{+62}:\\
\;\;\;\;x + y \cdot \frac{b + z \cdot \left(a + z \cdot \left(z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right) + t\right)\right)}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right) \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + \frac{t}{z} \cdot \frac{y}{z}\right) + x\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r17787924 = x;
        double r17787925 = y;
        double r17787926 = z;
        double r17787927 = 3.13060547623;
        double r17787928 = r17787926 * r17787927;
        double r17787929 = 11.1667541262;
        double r17787930 = r17787928 + r17787929;
        double r17787931 = r17787930 * r17787926;
        double r17787932 = t;
        double r17787933 = r17787931 + r17787932;
        double r17787934 = r17787933 * r17787926;
        double r17787935 = a;
        double r17787936 = r17787934 + r17787935;
        double r17787937 = r17787936 * r17787926;
        double r17787938 = b;
        double r17787939 = r17787937 + r17787938;
        double r17787940 = r17787925 * r17787939;
        double r17787941 = 15.234687407;
        double r17787942 = r17787926 + r17787941;
        double r17787943 = r17787942 * r17787926;
        double r17787944 = 31.4690115749;
        double r17787945 = r17787943 + r17787944;
        double r17787946 = r17787945 * r17787926;
        double r17787947 = 11.9400905721;
        double r17787948 = r17787946 + r17787947;
        double r17787949 = r17787948 * r17787926;
        double r17787950 = 0.607771387771;
        double r17787951 = r17787949 + r17787950;
        double r17787952 = r17787940 / r17787951;
        double r17787953 = r17787924 + r17787952;
        return r17787953;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r17787954 = z;
        double r17787955 = -1.4707468883041915e+53;
        bool r17787956 = r17787954 <= r17787955;
        double r17787957 = y;
        double r17787958 = 3.13060547623;
        double r17787959 = r17787957 * r17787958;
        double r17787960 = r17787957 / r17787954;
        double r17787961 = 36.527041698806414;
        double r17787962 = r17787960 * r17787961;
        double r17787963 = r17787959 - r17787962;
        double r17787964 = t;
        double r17787965 = r17787964 / r17787954;
        double r17787966 = r17787965 * r17787960;
        double r17787967 = r17787963 + r17787966;
        double r17787968 = x;
        double r17787969 = r17787967 + r17787968;
        double r17787970 = 3.7272833098172985e+62;
        bool r17787971 = r17787954 <= r17787970;
        double r17787972 = b;
        double r17787973 = a;
        double r17787974 = 11.1667541262;
        double r17787975 = r17787958 * r17787954;
        double r17787976 = r17787974 + r17787975;
        double r17787977 = r17787954 * r17787976;
        double r17787978 = r17787977 + r17787964;
        double r17787979 = r17787954 * r17787978;
        double r17787980 = r17787973 + r17787979;
        double r17787981 = r17787954 * r17787980;
        double r17787982 = r17787972 + r17787981;
        double r17787983 = 0.607771387771;
        double r17787984 = 11.9400905721;
        double r17787985 = 31.4690115749;
        double r17787986 = 15.234687407;
        double r17787987 = r17787986 + r17787954;
        double r17787988 = r17787954 * r17787987;
        double r17787989 = r17787985 + r17787988;
        double r17787990 = r17787954 * r17787989;
        double r17787991 = r17787984 + r17787990;
        double r17787992 = r17787991 * r17787954;
        double r17787993 = r17787983 + r17787992;
        double r17787994 = r17787982 / r17787993;
        double r17787995 = r17787957 * r17787994;
        double r17787996 = r17787968 + r17787995;
        double r17787997 = r17787971 ? r17787996 : r17787969;
        double r17787998 = r17787956 ? r17787969 : r17787997;
        return r17787998;
}

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

Original28.6
Target1.0
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.4707468883041915e+53 or 3.7272833098172985e+62 < z

    1. Initial program 60.5

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity60.5

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771\right)}}\]

    4. Applied times-frac59.1

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}}\]

    5. Simplified59.1

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]

    6. Taylor expanded around inf 7.2

      \[\leadsto x + \color{blue}{\left(\left(\frac{t \cdot y}{{z}^{2}} + 3.13060547623 \cdot y\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    7. Simplified0.7

      \[\leadsto x + \color{blue}{\left(\frac{y}{z} \cdot \frac{t}{z} + \left(y \cdot 3.13060547623 - 36.527041698806414 \cdot \frac{y}{z}\right)\right)}\]

    if -1.4707468883041915e+53 < z < 3.7272833098172985e+62

    1. Initial program 3.0

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity3.0

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771\right)}}\]

    4. Applied times-frac1.4

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}}\]

    5. Simplified1.4

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.4707468883041915 \cdot 10^{+53}:\\ \;\;\;\;\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + \frac{t}{z} \cdot \frac{y}{z}\right) + x\\ \mathbf{elif}\;z \le 3.7272833098172985 \cdot 10^{+62}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot \left(a + z \cdot \left(z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right) + t\right)\right)}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + \frac{t}{z} \cdot \frac{y}{z}\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(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))) (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))))