Average Error: 29.0 → 4.9
Time: 7.0s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
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 -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\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 r436751 = x;
        double r436752 = y;
        double r436753 = z;
        double r436754 = 3.13060547623;
        double r436755 = r436753 * r436754;
        double r436756 = 11.1667541262;
        double r436757 = r436755 + r436756;
        double r436758 = r436757 * r436753;
        double r436759 = t;
        double r436760 = r436758 + r436759;
        double r436761 = r436760 * r436753;
        double r436762 = a;
        double r436763 = r436761 + r436762;
        double r436764 = r436763 * r436753;
        double r436765 = b;
        double r436766 = r436764 + r436765;
        double r436767 = r436752 * r436766;
        double r436768 = 15.234687407;
        double r436769 = r436753 + r436768;
        double r436770 = r436769 * r436753;
        double r436771 = 31.4690115749;
        double r436772 = r436770 + r436771;
        double r436773 = r436772 * r436753;
        double r436774 = 11.9400905721;
        double r436775 = r436773 + r436774;
        double r436776 = r436775 * r436753;
        double r436777 = 0.607771387771;
        double r436778 = r436776 + r436777;
        double r436779 = r436767 / r436778;
        double r436780 = r436751 + r436779;
        return r436780;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r436781 = z;
        double r436782 = -1.7407917578078988e+36;
        bool r436783 = r436781 <= r436782;
        double r436784 = 10094.050046646438;
        bool r436785 = r436781 <= r436784;
        double r436786 = !r436785;
        bool r436787 = r436783 || r436786;
        double r436788 = x;
        double r436789 = 3.13060547623;
        double r436790 = y;
        double r436791 = r436789 * r436790;
        double r436792 = t;
        double r436793 = r436792 * r436790;
        double r436794 = 2.0;
        double r436795 = pow(r436781, r436794);
        double r436796 = r436793 / r436795;
        double r436797 = r436791 + r436796;
        double r436798 = 36.527041698806414;
        double r436799 = r436790 / r436781;
        double r436800 = r436798 * r436799;
        double r436801 = r436797 - r436800;
        double r436802 = r436788 + r436801;
        double r436803 = 15.234687407;
        double r436804 = r436781 + r436803;
        double r436805 = r436804 * r436781;
        double r436806 = 31.4690115749;
        double r436807 = r436805 + r436806;
        double r436808 = r436807 * r436781;
        double r436809 = 11.9400905721;
        double r436810 = r436808 + r436809;
        double r436811 = r436810 * r436781;
        double r436812 = 0.607771387771;
        double r436813 = r436811 + r436812;
        double r436814 = r436781 * r436789;
        double r436815 = 11.1667541262;
        double r436816 = r436814 + r436815;
        double r436817 = r436816 * r436781;
        double r436818 = r436817 + r436792;
        double r436819 = r436818 * r436781;
        double r436820 = a;
        double r436821 = r436819 + r436820;
        double r436822 = r436821 * r436781;
        double r436823 = b;
        double r436824 = r436822 + r436823;
        double r436825 = r436813 / r436824;
        double r436826 = r436790 / r436825;
        double r436827 = r436788 + r436826;
        double r436828 = r436787 ? r436802 : r436827;
        return r436828;
}

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

Original29.0
Target1.1
Herbie4.9
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.7407917578078988e+36 or 10094.050046646438 < z

    1. Initial program 57.3

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

    2. Taylor expanded around inf 9.3

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

    if -1.7407917578078988e+36 < z < 10094.050046646438

    1. Initial program 0.7

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

    3. Applied associate-/l*0.4

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

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))))