Average Error: 19.3 → 0.1
Time: 22.3s
Precision: 64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -249743896261902.22:\\ \;\;\;\;\left(0.0692910599291889 \cdot y + \frac{y}{z} \cdot 0.07512208616047561\right) + x\\ \mathbf{elif}\;z \le 732680732.9997194:\\ \;\;\;\;\frac{y \cdot \left(0.279195317918525 + \left(z \cdot 0.4917317610505968 + z \cdot \left(z \cdot 0.0692910599291889\right)\right)\right)}{3.350343815022304 + \left(6.012459259764103 + z\right) \cdot z} + x\\ \mathbf{else}:\\ \;\;\;\;\left(0.0692910599291889 \cdot y + \frac{y}{z} \cdot 0.07512208616047561\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}
↓
\begin{array}{l}
\mathbf{if}\;z \le -249743896261902.22:\\
\;\;\;\;\left(0.0692910599291889 \cdot y + \frac{y}{z} \cdot 0.07512208616047561\right) + x\\

\mathbf{elif}\;z \le 732680732.9997194:\\
\;\;\;\;\frac{y \cdot \left(0.279195317918525 + \left(z \cdot 0.4917317610505968 + z \cdot \left(z \cdot 0.0692910599291889\right)\right)\right)}{3.350343815022304 + \left(6.012459259764103 + z\right) \cdot z} + x\\

\mathbf{else}:\\
\;\;\;\;\left(0.0692910599291889 \cdot y + \frac{y}{z} \cdot 0.07512208616047561\right) + x\\

\end{array}
double f(double x, double y, double z) {
        double r22493697 = x;
        double r22493698 = y;
        double r22493699 = z;
        double r22493700 = 0.0692910599291889;
        double r22493701 = r22493699 * r22493700;
        double r22493702 = 0.4917317610505968;
        double r22493703 = r22493701 + r22493702;
        double r22493704 = r22493703 * r22493699;
        double r22493705 = 0.279195317918525;
        double r22493706 = r22493704 + r22493705;
        double r22493707 = r22493698 * r22493706;
        double r22493708 = 6.012459259764103;
        double r22493709 = r22493699 + r22493708;
        double r22493710 = r22493709 * r22493699;
        double r22493711 = 3.350343815022304;
        double r22493712 = r22493710 + r22493711;
        double r22493713 = r22493707 / r22493712;
        double r22493714 = r22493697 + r22493713;
        return r22493714;
}
↓
double f(double x, double y, double z) {
        double r22493715 = z;
        double r22493716 = -249743896261902.22;
        bool r22493717 = r22493715 <= r22493716;
        double r22493718 = 0.0692910599291889;
        double r22493719 = y;
        double r22493720 = r22493718 * r22493719;
        double r22493721 = r22493719 / r22493715;
        double r22493722 = 0.07512208616047561;
        double r22493723 = r22493721 * r22493722;
        double r22493724 = r22493720 + r22493723;
        double r22493725 = x;
        double r22493726 = r22493724 + r22493725;
        double r22493727 = 732680732.9997194;
        bool r22493728 = r22493715 <= r22493727;
        double r22493729 = 0.279195317918525;
        double r22493730 = 0.4917317610505968;
        double r22493731 = r22493715 * r22493730;
        double r22493732 = r22493715 * r22493718;
        double r22493733 = r22493715 * r22493732;
        double r22493734 = r22493731 + r22493733;
        double r22493735 = r22493729 + r22493734;
        double r22493736 = r22493719 * r22493735;
        double r22493737 = 3.350343815022304;
        double r22493738 = 6.012459259764103;
        double r22493739 = r22493738 + r22493715;
        double r22493740 = r22493739 * r22493715;
        double r22493741 = r22493737 + r22493740;
        double r22493742 = r22493736 / r22493741;
        double r22493743 = r22493742 + r22493725;
        double r22493744 = r22493728 ? r22493743 : r22493726;
        double r22493745 = r22493717 ? r22493726 : r22493744;
        return r22493745;
}

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

Original19.3
Target0.1
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;z \lt -8120153.652456675:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z \lt 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -249743896261902.22 or 732680732.9997194 < z

    1. Initial program 40.0

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]

    2. Taylor expanded around 0 40.1

      \[\leadsto x + \frac{y \cdot \left(\color{blue}{\left(0.4917317610505968 \cdot z + 0.0692910599291889 \cdot {z}^{2}\right)} + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]

    3. Simplified40.0

      \[\leadsto x + \frac{y \cdot \left(\color{blue}{\left(z \cdot \left(z \cdot 0.0692910599291889\right) + z \cdot 0.4917317610505968\right)} + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]

    4. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{x + \left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291889 \cdot y\right)}\]

    if -249743896261902.22 < z < 732680732.9997194

    1. Initial program 0.2

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]

    2. Taylor expanded around 0 0.2

      \[\leadsto x + \frac{y \cdot \left(\color{blue}{\left(0.4917317610505968 \cdot z + 0.0692910599291889 \cdot {z}^{2}\right)} + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]

    3. Simplified0.2

      \[\leadsto x + \frac{y \cdot \left(\color{blue}{\left(z \cdot \left(z \cdot 0.0692910599291889\right) + z \cdot 0.4917317610505968\right)} + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -249743896261902.22:\\ \;\;\;\;\left(0.0692910599291889 \cdot y + \frac{y}{z} \cdot 0.07512208616047561\right) + x\\ \mathbf{elif}\;z \le 732680732.9997194:\\ \;\;\;\;\frac{y \cdot \left(0.279195317918525 + \left(z \cdot 0.4917317610505968 + z \cdot \left(z \cdot 0.0692910599291889\right)\right)\right)}{3.350343815022304 + \left(6.012459259764103 + z\right) \cdot z} + x\\ \mathbf{else}:\\ \;\;\;\;\left(0.0692910599291889 \cdot y + \frac{y}{z} \cdot 0.07512208616047561\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(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 (+ (* (+ 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))))