Average Error: 20.0 → 0.2
Time: 59.6s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -123702675580259303424:\\ \;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\ \mathbf{elif}\;z \le 0.02992000358306671353725292306080518756062:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) + 0.2791953179185249767080279070796677842736}{3.350343815022303939343828460550867021084 + \left(6.012459259764103336465268512256443500519 + z\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}
↓
\begin{array}{l}
\mathbf{if}\;z \le -123702675580259303424:\\
\;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\

\mathbf{elif}\;z \le 0.02992000358306671353725292306080518756062:\\
\;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) + 0.2791953179185249767080279070796677842736}{3.350343815022303939343828460550867021084 + \left(6.012459259764103336465268512256443500519 + z\right) \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\

\end{array}
double f(double x, double y, double z) {
        double r18007923 = x;
        double r18007924 = y;
        double r18007925 = z;
        double r18007926 = 0.0692910599291889;
        double r18007927 = r18007925 * r18007926;
        double r18007928 = 0.4917317610505968;
        double r18007929 = r18007927 + r18007928;
        double r18007930 = r18007929 * r18007925;
        double r18007931 = 0.279195317918525;
        double r18007932 = r18007930 + r18007931;
        double r18007933 = r18007924 * r18007932;
        double r18007934 = 6.012459259764103;
        double r18007935 = r18007925 + r18007934;
        double r18007936 = r18007935 * r18007925;
        double r18007937 = 3.350343815022304;
        double r18007938 = r18007936 + r18007937;
        double r18007939 = r18007933 / r18007938;
        double r18007940 = r18007923 + r18007939;
        return r18007940;
}
↓
double f(double x, double y, double z) {
        double r18007941 = z;
        double r18007942 = -1.237026755802593e+20;
        bool r18007943 = r18007941 <= r18007942;
        double r18007944 = 0.0692910599291889;
        double r18007945 = y;
        double r18007946 = r18007944 * r18007945;
        double r18007947 = r18007945 / r18007941;
        double r18007948 = 0.07512208616047561;
        double r18007949 = r18007947 * r18007948;
        double r18007950 = r18007946 + r18007949;
        double r18007951 = x;
        double r18007952 = r18007950 + r18007951;
        double r18007953 = 0.029920003583066714;
        bool r18007954 = r18007941 <= r18007953;
        double r18007955 = r18007941 * r18007944;
        double r18007956 = 0.4917317610505968;
        double r18007957 = r18007955 + r18007956;
        double r18007958 = r18007941 * r18007957;
        double r18007959 = 0.279195317918525;
        double r18007960 = r18007958 + r18007959;
        double r18007961 = 3.350343815022304;
        double r18007962 = 6.012459259764103;
        double r18007963 = r18007962 + r18007941;
        double r18007964 = r18007963 * r18007941;
        double r18007965 = r18007961 + r18007964;
        double r18007966 = r18007960 / r18007965;
        double r18007967 = r18007945 * r18007966;
        double r18007968 = r18007951 + r18007967;
        double r18007969 = r18007954 ? r18007968 : r18007952;
        double r18007970 = r18007943 ? r18007952 : r18007969;
        return r18007970;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original20.0
Target0.2
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.6524566747248172760009765625:\\ \;\;\;\;\left(\frac{0.07512208616047560960637952121032867580652}{z} + 0.06929105992918889456166908757950295694172\right) \cdot y - \left(\frac{0.4046220386999212492717958866705885156989 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 657611897278737678336:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047560960637952121032867580652}{z} + 0.06929105992918889456166908757950295694172\right) \cdot y - \left(\frac{0.4046220386999212492717958866705885156989 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.237026755802593e+20 or 0.029920003583066714 < z

    1. Initial program 41.4

      \[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]

    2. Taylor expanded around inf 0.3

      \[\leadsto \color{blue}{x + \left(0.07512208616047560960637952121032867580652 \cdot \frac{y}{z} + 0.06929105992918889456166908757950295694172 \cdot y\right)}\]

    if -1.237026755802593e+20 < z < 0.029920003583066714

    1. Initial program 0.2

      \[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity0.2

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\color{blue}{1 \cdot \left(\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084\right)}}\]

    4. Applied times-frac0.1

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}}\]

    5. Simplified0.1

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -123702675580259303424:\\ \;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\ \mathbf{elif}\;z \le 0.02992000358306671353725292306080518756062:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) + 0.2791953179185249767080279070796677842736}{3.350343815022303939343828460550867021084 + \left(6.012459259764103336465268512256443500519 + z\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(0.06929105992918889456166908757950295694172 \cdot y + \frac{y}{z} \cdot 0.07512208616047560960637952121032867580652\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (if (< z -8120153.652456675) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x)) (if (< z 6.576118972787377e+20) (+ x (* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1.0 (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))