Average Error: 20.3 → 0.1
Time: 5.9s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.43506150379586229 \cdot 10^{32} \lor \neg \left(z \le 882330.325948550249\right):\\ \;\;\;\;x + y \cdot \frac{1}{\left(14.431876219268938 - 15.646356830292035 \cdot \frac{1}{z}\right) + \frac{\frac{101.23733352003816}{z}}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]
x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.43506150379586229 \cdot 10^{32} \lor \neg \left(z \le 882330.325948550249\right):\\
\;\;\;\;x + y \cdot \frac{1}{\left(14.431876219268938 - 15.646356830292035 \cdot \frac{1}{z}\right) + \frac{\frac{101.23733352003816}{z}}{z}}\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\

\end{array}
double f(double x, double y, double z) {
        double r263777 = x;
        double r263778 = y;
        double r263779 = z;
        double r263780 = 0.0692910599291889;
        double r263781 = r263779 * r263780;
        double r263782 = 0.4917317610505968;
        double r263783 = r263781 + r263782;
        double r263784 = r263783 * r263779;
        double r263785 = 0.279195317918525;
        double r263786 = r263784 + r263785;
        double r263787 = r263778 * r263786;
        double r263788 = 6.012459259764103;
        double r263789 = r263779 + r263788;
        double r263790 = r263789 * r263779;
        double r263791 = 3.350343815022304;
        double r263792 = r263790 + r263791;
        double r263793 = r263787 / r263792;
        double r263794 = r263777 + r263793;
        return r263794;
}
↓
double f(double x, double y, double z) {
        double r263795 = z;
        double r263796 = -1.4350615037958623e+32;
        bool r263797 = r263795 <= r263796;
        double r263798 = 882330.3259485502;
        bool r263799 = r263795 <= r263798;
        double r263800 = !r263799;
        bool r263801 = r263797 || r263800;
        double r263802 = x;
        double r263803 = y;
        double r263804 = 1.0;
        double r263805 = 14.431876219268938;
        double r263806 = 15.646356830292035;
        double r263807 = r263804 / r263795;
        double r263808 = r263806 * r263807;
        double r263809 = r263805 - r263808;
        double r263810 = 101.23733352003816;
        double r263811 = r263810 / r263795;
        double r263812 = r263811 / r263795;
        double r263813 = r263809 + r263812;
        double r263814 = r263804 / r263813;
        double r263815 = r263803 * r263814;
        double r263816 = r263802 + r263815;
        double r263817 = 0.0692910599291889;
        double r263818 = r263795 * r263817;
        double r263819 = 0.4917317610505968;
        double r263820 = r263818 + r263819;
        double r263821 = r263820 * r263795;
        double r263822 = 0.279195317918525;
        double r263823 = r263821 + r263822;
        double r263824 = 6.012459259764103;
        double r263825 = r263795 + r263824;
        double r263826 = r263825 * r263795;
        double r263827 = 3.350343815022304;
        double r263828 = r263826 + r263827;
        double r263829 = r263823 / r263828;
        double r263830 = r263803 * r263829;
        double r263831 = r263802 + r263830;
        double r263832 = r263801 ? r263816 : r263831;
        return r263832;
}

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
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.6524566747:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291888946\right) \cdot y - \left(\frac{0.404622038699921249 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 657611897278737680000:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)\right) \cdot \frac{1}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291888946\right) \cdot y - \left(\frac{0.404622038699921249 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.4350615037958623e+32 or 882330.3259485502 < z

    1. Initial program 43.4

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity43.4

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\color{blue}{1 \cdot \left(\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394\right)}}\]

    4. Applied times-frac34.4

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}}\]

    5. Simplified34.4

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
    6. Using strategy rm

    7. Applied clear-num34.4

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}}}\]

    8. Taylor expanded around inf 0.0

      \[\leadsto x + y \cdot \frac{1}{\color{blue}{\left(101.23733352003816 \cdot \frac{1}{{z}^{2}} + 14.431876219268938\right) - 15.646356830292035 \cdot \frac{1}{z}}}\]

    9. Simplified0.0

      \[\leadsto x + y \cdot \frac{1}{\color{blue}{\left(14.431876219268938 - 15.646356830292035 \cdot \frac{1}{z}\right) + \frac{\frac{101.23733352003816}{z}}{z}}}\]

    if -1.4350615037958623e+32 < z < 882330.3259485502

    1. Initial program 0.2

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
    2. Using strategy rm

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

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977\right)}{\color{blue}{1 \cdot \left(\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394\right)}}\]

    4. Applied times-frac0.1

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}}\]

    5. Simplified0.1

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.43506150379586229 \cdot 10^{32} \lor \neg \left(z \le 882330.325948550249\right):\\ \;\;\;\;x + y \cdot \frac{1}{\left(14.431876219268938 - 15.646356830292035 \cdot \frac{1}{z}\right) + \frac{\frac{101.23733352003816}{z}}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(z \cdot 0.0692910599291888946 + 0.49173176105059679\right) \cdot z + 0.279195317918524977}{\left(z + 6.0124592597641033\right) \cdot z + 3.35034381502230394}\\ \end{array}\]

Reproduce

herbie shell --seed 2020035 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (if (< z -8120153.652456675) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x)) (if (< z 657611897278737680000) (+ x (* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1 (+ (* (+ 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))))