Average Error: 20.5 → 0.1
Time: 1.0m
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -56036322.86183178424835205078125 \lor \neg \left(z \le 109403654706355.234375\right):\\ \;\;\;\;\left(\left(0.06929105992918889456166908757950295694172 \cdot y + 0.07512208616047560960637952121032867580652 \cdot \frac{y}{z}\right) - \frac{y}{z \cdot z} \cdot 0.4046220386999212492717958866705885156989\right) + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.2791953179185249767080279070796677842736 + \left(z \cdot 0.4917317610505967939715787906607147306204 + \left(0.06929105992918889456166908757950295694172 \cdot z\right) \cdot z\right)}{3.350343815022303939343828460550867021084 + \left(z + 6.012459259764103336465268512256443500519\right) \cdot z} + x\\ \end{array}\]
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 -56036322.86183178424835205078125 \lor \neg \left(z \le 109403654706355.234375\right):\\
\;\;\;\;\left(\left(0.06929105992918889456166908757950295694172 \cdot y + 0.07512208616047560960637952121032867580652 \cdot \frac{y}{z}\right) - \frac{y}{z \cdot z} \cdot 0.4046220386999212492717958866705885156989\right) + x\\

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

\end{array}
double f(double x, double y, double z) {
        double r287026 = x;
        double r287027 = y;
        double r287028 = z;
        double r287029 = 0.0692910599291889;
        double r287030 = r287028 * r287029;
        double r287031 = 0.4917317610505968;
        double r287032 = r287030 + r287031;
        double r287033 = r287032 * r287028;
        double r287034 = 0.279195317918525;
        double r287035 = r287033 + r287034;
        double r287036 = r287027 * r287035;
        double r287037 = 6.012459259764103;
        double r287038 = r287028 + r287037;
        double r287039 = r287038 * r287028;
        double r287040 = 3.350343815022304;
        double r287041 = r287039 + r287040;
        double r287042 = r287036 / r287041;
        double r287043 = r287026 + r287042;
        return r287043;
}
↓
double f(double x, double y, double z) {
        double r287044 = z;
        double r287045 = -56036322.861831784;
        bool r287046 = r287044 <= r287045;
        double r287047 = 109403654706355.23;
        bool r287048 = r287044 <= r287047;
        double r287049 = !r287048;
        bool r287050 = r287046 || r287049;
        double r287051 = 0.0692910599291889;
        double r287052 = y;
        double r287053 = r287051 * r287052;
        double r287054 = 0.07512208616047561;
        double r287055 = r287052 / r287044;
        double r287056 = r287054 * r287055;
        double r287057 = r287053 + r287056;
        double r287058 = r287044 * r287044;
        double r287059 = r287052 / r287058;
        double r287060 = 0.40462203869992125;
        double r287061 = r287059 * r287060;
        double r287062 = r287057 - r287061;
        double r287063 = x;
        double r287064 = r287062 + r287063;
        double r287065 = 0.279195317918525;
        double r287066 = 0.4917317610505968;
        double r287067 = r287044 * r287066;
        double r287068 = r287051 * r287044;
        double r287069 = r287068 * r287044;
        double r287070 = r287067 + r287069;
        double r287071 = r287065 + r287070;
        double r287072 = 3.350343815022304;
        double r287073 = 6.012459259764103;
        double r287074 = r287044 + r287073;
        double r287075 = r287074 * r287044;
        double r287076 = r287072 + r287075;
        double r287077 = r287071 / r287076;
        double r287078 = r287052 * r287077;
        double r287079 = r287078 + r287063;
        double r287080 = r287050 ? r287064 : r287079;
        return r287080;
}

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

Original20.5
Target0.2
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.6524566747248172760009765625:\\ \;\;\;\;\left(\frac{0.07512208616047560960637952121032867580652}{z} + 0.06929105992918889456166908757950295694172\right) \cdot y - \left(\frac{0.4046220386999212492717958866705885156989 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 657611897278737678336:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047560960637952121032867580652}{z} + 0.06929105992918889456166908757950295694172\right) \cdot y - \left(\frac{0.4046220386999212492717958866705885156989 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -56036322.861831784 or 109403654706355.23 < z

    1. Initial program 41.7

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

    2. Simplified33.7

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

    3. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{\left(\left(0.06929105992918889456166908757950295694172 \cdot y + 0.07512208616047560960637952121032867580652 \cdot \frac{y}{z}\right) - 0.4046220386999212492717958866705885156989 \cdot \frac{y}{{z}^{2}}\right)} + x\]

    4. Simplified0.0

      \[\leadsto \color{blue}{\left(\left(0.07512208616047560960637952121032867580652 \cdot \frac{y}{z} + y \cdot 0.06929105992918889456166908757950295694172\right) - \frac{y}{z \cdot z} \cdot 0.4046220386999212492717958866705885156989\right)} + x\]

    if -56036322.861831784 < z < 109403654706355.23

    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. Simplified0.1

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

    3. Taylor expanded around 0 0.1

      \[\leadsto \frac{\color{blue}{\left(0.4917317610505967939715787906607147306204 \cdot z + 0.06929105992918889456166908757950295694172 \cdot {z}^{2}\right)} + 0.2791953179185249767080279070796677842736}{z \cdot \left(z + 6.012459259764103336465268512256443500519\right) + 3.350343815022303939343828460550867021084} \cdot y + x\]

    4. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -56036322.86183178424835205078125 \lor \neg \left(z \le 109403654706355.234375\right):\\ \;\;\;\;\left(\left(0.06929105992918889456166908757950295694172 \cdot y + 0.07512208616047560960637952121032867580652 \cdot \frac{y}{z}\right) - \frac{y}{z \cdot z} \cdot 0.4046220386999212492717958866705885156989\right) + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.2791953179185249767080279070796677842736 + \left(z \cdot 0.4917317610505967939715787906607147306204 + \left(0.06929105992918889456166908757950295694172 \cdot z\right) \cdot z\right)}{3.350343815022303939343828460550867021084 + \left(z + 6.012459259764103336465268512256443500519\right) \cdot z} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(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))))