Average Error: 19.5 → 0.1
Time: 15.1s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.06929105992918889456166908757950295694172 + 0.4917317610505967939715787906607147306204\right) \cdot z + 0.2791953179185249767080279070796677842736\right)}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.322930273593699682446565286533521790133 \cdot 10^{154} \lor \neg \left(z \le 603361.98387782205827534198760986328125\right):\\ \;\;\;\;x + y \cdot \left(\left(0.06929105992918889456166908757950295694172 - 0.4046220386999212492717958866705885156989 \cdot \frac{1}{{z}^{2}}\right) + \frac{0.07512208616047560960637952121032867580652}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(0.4917317610505967939715787906607147306204 \cdot z + 0.06929105992918889456166908757950295694172 \cdot {z}^{2}\right) + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \end{array}\]
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 -1.322930273593699682446565286533521790133 \cdot 10^{154} \lor \neg \left(z \le 603361.98387782205827534198760986328125\right):\\
\;\;\;\;x + y \cdot \left(\left(0.06929105992918889456166908757950295694172 - 0.4046220386999212492717958866705885156989 \cdot \frac{1}{{z}^{2}}\right) + \frac{0.07512208616047560960637952121032867580652}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{\left(0.4917317610505967939715787906607147306204 \cdot z + 0.06929105992918889456166908757950295694172 \cdot {z}^{2}\right) + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\

\end{array}
double f(double x, double y, double z) {
        double r231733 = x;
        double r231734 = y;
        double r231735 = z;
        double r231736 = 0.0692910599291889;
        double r231737 = r231735 * r231736;
        double r231738 = 0.4917317610505968;
        double r231739 = r231737 + r231738;
        double r231740 = r231739 * r231735;
        double r231741 = 0.279195317918525;
        double r231742 = r231740 + r231741;
        double r231743 = r231734 * r231742;
        double r231744 = 6.012459259764103;
        double r231745 = r231735 + r231744;
        double r231746 = r231745 * r231735;
        double r231747 = 3.350343815022304;
        double r231748 = r231746 + r231747;
        double r231749 = r231743 / r231748;
        double r231750 = r231733 + r231749;
        return r231750;
}
↓
double f(double x, double y, double z) {
        double r231751 = z;
        double r231752 = -1.3229302735936997e+154;
        bool r231753 = r231751 <= r231752;
        double r231754 = 603361.9838778221;
        bool r231755 = r231751 <= r231754;
        double r231756 = !r231755;
        bool r231757 = r231753 || r231756;
        double r231758 = x;
        double r231759 = y;
        double r231760 = 0.0692910599291889;
        double r231761 = 0.40462203869992125;
        double r231762 = 1.0;
        double r231763 = 2.0;
        double r231764 = pow(r231751, r231763);
        double r231765 = r231762 / r231764;
        double r231766 = r231761 * r231765;
        double r231767 = r231760 - r231766;
        double r231768 = 0.07512208616047561;
        double r231769 = r231768 / r231751;
        double r231770 = r231767 + r231769;
        double r231771 = r231759 * r231770;
        double r231772 = r231758 + r231771;
        double r231773 = 0.4917317610505968;
        double r231774 = r231773 * r231751;
        double r231775 = r231760 * r231764;
        double r231776 = r231774 + r231775;
        double r231777 = 0.279195317918525;
        double r231778 = r231776 + r231777;
        double r231779 = 6.012459259764103;
        double r231780 = r231751 + r231779;
        double r231781 = r231780 * r231751;
        double r231782 = 3.350343815022304;
        double r231783 = r231781 + r231782;
        double r231784 = r231778 / r231783;
        double r231785 = r231759 * r231784;
        double r231786 = r231758 + r231785;
        double r231787 = r231757 ? r231772 : r231786;
        return r231787;
}

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

Original19.5
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 < -1.3229302735936997e+154 or 603361.9838778221 < z

    1. Initial program 47.6

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

    3. Applied *-un-lft-identity47.6

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

    4. Applied times-frac41.6

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

    5. Simplified41.6

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

    6. Taylor expanded around 0 41.6

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

    7. Taylor expanded around inf 0.0

      \[\leadsto x + y \cdot \color{blue}{\left(\left(0.07512208616047560960637952121032867580652 \cdot \frac{1}{z} + 0.06929105992918889456166908757950295694172\right) - 0.4046220386999212492717958866705885156989 \cdot \frac{1}{{z}^{2}}\right)}\]

    8. Simplified0.0

      \[\leadsto x + y \cdot \color{blue}{\left(\left(0.06929105992918889456166908757950295694172 - 0.4046220386999212492717958866705885156989 \cdot \frac{1}{{z}^{2}}\right) + \frac{0.07512208616047560960637952121032867580652}{z}\right)}\]

    if -1.3229302735936997e+154 < z < 603361.9838778221

    1. Initial program 2.8

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

    3. Applied *-un-lft-identity2.8

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

    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

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

    6. Taylor expanded around 0 0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.322930273593699682446565286533521790133 \cdot 10^{154} \lor \neg \left(z \le 603361.98387782205827534198760986328125\right):\\ \;\;\;\;x + y \cdot \left(\left(0.06929105992918889456166908757950295694172 - 0.4046220386999212492717958866705885156989 \cdot \frac{1}{{z}^{2}}\right) + \frac{0.07512208616047560960637952121032867580652}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(0.4917317610505967939715787906607147306204 \cdot z + 0.06929105992918889456166908757950295694172 \cdot {z}^{2}\right) + 0.2791953179185249767080279070796677842736}{\left(z + 6.012459259764103336465268512256443500519\right) \cdot z + 3.350343815022303939343828460550867021084}\\ \end{array}\]

Reproduce

herbie shell --seed 2019291 
(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))))