Average Error: 20.3 → 0.1
Time: 57.7s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -130759109844861825942922027073536 \lor \neg \left(z \le 17117062.4619325213134288787841796875\right):\\ \;\;\;\;x + \left(\left(0.07512208616047560960637952121032867580652 \cdot \frac{y}{z} + 0.06929105992918889456166908757950295694172 \cdot y\right) - 0.4046220386999212492717958866705885156989 \cdot \frac{y}{{z}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \end{array}\]
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 -130759109844861825942922027073536 \lor \neg \left(z \le 17117062.4619325213134288787841796875\right):\\
\;\;\;\;x + \left(\left(0.07512208616047560960637952121032867580652 \cdot \frac{y}{z} + 0.06929105992918889456166908757950295694172 \cdot y\right) - 0.4046220386999212492717958866705885156989 \cdot \frac{y}{{z}^{2}}\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r280698 = x;
        double r280699 = y;
        double r280700 = z;
        double r280701 = 0.0692910599291889;
        double r280702 = r280700 * r280701;
        double r280703 = 0.4917317610505968;
        double r280704 = r280702 + r280703;
        double r280705 = r280704 * r280700;
        double r280706 = 0.279195317918525;
        double r280707 = r280705 + r280706;
        double r280708 = r280699 * r280707;
        double r280709 = 6.012459259764103;
        double r280710 = r280700 + r280709;
        double r280711 = r280710 * r280700;
        double r280712 = 3.350343815022304;
        double r280713 = r280711 + r280712;
        double r280714 = r280708 / r280713;
        double r280715 = r280698 + r280714;
        return r280715;
}
↓
double f(double x, double y, double z) {
        double r280716 = z;
        double r280717 = -1.3075910984486183e+32;
        bool r280718 = r280716 <= r280717;
        double r280719 = 17117062.46193252;
        bool r280720 = r280716 <= r280719;
        double r280721 = !r280720;
        bool r280722 = r280718 || r280721;
        double r280723 = x;
        double r280724 = 0.07512208616047561;
        double r280725 = y;
        double r280726 = r280725 / r280716;
        double r280727 = r280724 * r280726;
        double r280728 = 0.0692910599291889;
        double r280729 = r280728 * r280725;
        double r280730 = r280727 + r280729;
        double r280731 = 0.40462203869992125;
        double r280732 = 2.0;
        double r280733 = pow(r280716, r280732);
        double r280734 = r280725 / r280733;
        double r280735 = r280731 * r280734;
        double r280736 = r280730 - r280735;
        double r280737 = r280723 + r280736;
        double r280738 = r280716 * r280728;
        double r280739 = 0.4917317610505968;
        double r280740 = r280738 + r280739;
        double r280741 = r280740 * r280716;
        double r280742 = 0.279195317918525;
        double r280743 = r280741 + r280742;
        double r280744 = 6.012459259764103;
        double r280745 = r280716 + r280744;
        double r280746 = r280745 * r280716;
        double r280747 = 3.350343815022304;
        double r280748 = r280746 + r280747;
        double r280749 = r280743 / r280748;
        double r280750 = r280725 * r280749;
        double r280751 = r280723 + r280750;
        double r280752 = r280722 ? r280737 : r280751;
        return r280752;
}

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

Original20.3
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 < -1.3075910984486183e+32 or 17117062.46193252 < z

    1. Initial program 43.5

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

    2. Taylor expanded around inf 0.0

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

    if -1.3075910984486183e+32 < z < 17117062.46193252

    1. Initial program 0.4

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

    3. Applied *-un-lft-identity0.4

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

    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 simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -130759109844861825942922027073536 \lor \neg \left(z \le 17117062.4619325213134288787841796875\right):\\ \;\;\;\;x + \left(\left(0.07512208616047560960637952121032867580652 \cdot \frac{y}{z} + 0.06929105992918889456166908757950295694172 \cdot y\right) - 0.4046220386999212492717958866705885156989 \cdot \frac{y}{{z}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \end{array}\]

Reproduce

herbie shell --seed 2019305 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (if (< z -8120153.6524566747) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291888946) y) (- (/ (* 0.404622038699921249 y) (* z z)) x)) (if (< z 657611897278737680000) (+ x (* (* y (+ (* (+ (* z 0.0692910599291888946) 0.49173176105059679) z) 0.279195317918524977)) (/ 1 (+ (* (+ z 6.0124592597641033) z) 3.35034381502230394)))) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291888946) y) (- (/ (* 0.404622038699921249 y) (* z z)) x))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291888946) 0.49173176105059679) z) 0.279195317918524977)) (+ (* (+ z 6.0124592597641033) z) 3.35034381502230394))))