Average Error: 30.1 → 4.5
Time: 16.5s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.39389244567685115 \cdot 10^{38} \lor \neg \left(z \le 1751680100761613370000\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.39389244567685115 \cdot 10^{38} \lor \neg \left(z \le 1751680100761613370000\right):\\
\;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r458717 = x;
        double r458718 = y;
        double r458719 = z;
        double r458720 = 3.13060547623;
        double r458721 = r458719 * r458720;
        double r458722 = 11.1667541262;
        double r458723 = r458721 + r458722;
        double r458724 = r458723 * r458719;
        double r458725 = t;
        double r458726 = r458724 + r458725;
        double r458727 = r458726 * r458719;
        double r458728 = a;
        double r458729 = r458727 + r458728;
        double r458730 = r458729 * r458719;
        double r458731 = b;
        double r458732 = r458730 + r458731;
        double r458733 = r458718 * r458732;
        double r458734 = 15.234687407;
        double r458735 = r458719 + r458734;
        double r458736 = r458735 * r458719;
        double r458737 = 31.4690115749;
        double r458738 = r458736 + r458737;
        double r458739 = r458738 * r458719;
        double r458740 = 11.9400905721;
        double r458741 = r458739 + r458740;
        double r458742 = r458741 * r458719;
        double r458743 = 0.607771387771;
        double r458744 = r458742 + r458743;
        double r458745 = r458733 / r458744;
        double r458746 = r458717 + r458745;
        return r458746;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r458747 = z;
        double r458748 = -3.393892445676851e+38;
        bool r458749 = r458747 <= r458748;
        double r458750 = 1.7516801007616134e+21;
        bool r458751 = r458747 <= r458750;
        double r458752 = !r458751;
        bool r458753 = r458749 || r458752;
        double r458754 = x;
        double r458755 = 3.13060547623;
        double r458756 = y;
        double r458757 = r458755 * r458756;
        double r458758 = t;
        double r458759 = r458758 * r458756;
        double r458760 = 2.0;
        double r458761 = pow(r458747, r458760);
        double r458762 = r458759 / r458761;
        double r458763 = r458757 + r458762;
        double r458764 = 36.527041698806414;
        double r458765 = r458756 / r458747;
        double r458766 = r458764 * r458765;
        double r458767 = r458763 - r458766;
        double r458768 = r458754 + r458767;
        double r458769 = 15.234687407;
        double r458770 = r458747 + r458769;
        double r458771 = r458770 * r458747;
        double r458772 = 31.4690115749;
        double r458773 = r458771 + r458772;
        double r458774 = r458773 * r458747;
        double r458775 = 11.9400905721;
        double r458776 = r458774 + r458775;
        double r458777 = r458776 * r458747;
        double r458778 = 0.607771387771;
        double r458779 = r458777 + r458778;
        double r458780 = r458747 * r458755;
        double r458781 = 11.1667541262;
        double r458782 = r458780 + r458781;
        double r458783 = r458782 * r458747;
        double r458784 = r458783 + r458758;
        double r458785 = r458784 * r458747;
        double r458786 = a;
        double r458787 = r458785 + r458786;
        double r458788 = r458787 * r458747;
        double r458789 = b;
        double r458790 = r458788 + r458789;
        double r458791 = r458779 / r458790;
        double r458792 = r458756 / r458791;
        double r458793 = r458754 + r458792;
        double r458794 = r458753 ? r458768 : r458793;
        return r458794;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original30.1
Target0.9
Herbie4.5
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.393892445676851e+38 or 1.7516801007616134e+21 < z

    1. Initial program 59.3

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]

    2. Taylor expanded around inf 8.5

      \[\leadsto x + \color{blue}{\left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    if -3.393892445676851e+38 < z < 1.7516801007616134e+21

    1. Initial program 1.2

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
    2. Using strategy rm

    3. Applied associate-/l*0.6

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.39389244567685115 \cdot 10^{38} \lor \neg \left(z \le 1751680100761613370000\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1))) (if (< z 7.066965436914287e+59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771) (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))