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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.7503197233736622 \cdot 10^{25} \lor \neg \left(z \le 14972530473052320000\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

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 -1.7503197233736622 \cdot 10^{25} \lor \neg \left(z \le 14972530473052320000\right):\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\

\mathbf{else}:\\
\;\;\;\;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}\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r330735 = x;
        double r330736 = y;
        double r330737 = z;
        double r330738 = 3.13060547623;
        double r330739 = r330737 * r330738;
        double r330740 = 11.1667541262;
        double r330741 = r330739 + r330740;
        double r330742 = r330741 * r330737;
        double r330743 = t;
        double r330744 = r330742 + r330743;
        double r330745 = r330744 * r330737;
        double r330746 = a;
        double r330747 = r330745 + r330746;
        double r330748 = r330747 * r330737;
        double r330749 = b;
        double r330750 = r330748 + r330749;
        double r330751 = r330736 * r330750;
        double r330752 = 15.234687407;
        double r330753 = r330737 + r330752;
        double r330754 = r330753 * r330737;
        double r330755 = 31.4690115749;
        double r330756 = r330754 + r330755;
        double r330757 = r330756 * r330737;
        double r330758 = 11.9400905721;
        double r330759 = r330757 + r330758;
        double r330760 = r330759 * r330737;
        double r330761 = 0.607771387771;
        double r330762 = r330760 + r330761;
        double r330763 = r330751 / r330762;
        double r330764 = r330735 + r330763;
        return r330764;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r330765 = z;
        double r330766 = -1.7503197233736622e+25;
        bool r330767 = r330765 <= r330766;
        double r330768 = 1.497253047305232e+19;
        bool r330769 = r330765 <= r330768;
        double r330770 = !r330769;
        bool r330771 = r330767 || r330770;
        double r330772 = y;
        double r330773 = 3.13060547623;
        double r330774 = t;
        double r330775 = 2.0;
        double r330776 = pow(r330765, r330775);
        double r330777 = r330774 / r330776;
        double r330778 = r330773 + r330777;
        double r330779 = x;
        double r330780 = fma(r330772, r330778, r330779);
        double r330781 = r330765 * r330773;
        double r330782 = 11.1667541262;
        double r330783 = r330781 + r330782;
        double r330784 = r330783 * r330765;
        double r330785 = r330784 + r330774;
        double r330786 = r330785 * r330765;
        double r330787 = a;
        double r330788 = r330786 + r330787;
        double r330789 = r330788 * r330765;
        double r330790 = b;
        double r330791 = r330789 + r330790;
        double r330792 = r330772 * r330791;
        double r330793 = 15.234687407;
        double r330794 = r330765 + r330793;
        double r330795 = r330794 * r330765;
        double r330796 = 31.4690115749;
        double r330797 = r330795 + r330796;
        double r330798 = r330797 * r330765;
        double r330799 = 11.9400905721;
        double r330800 = r330798 + r330799;
        double r330801 = r330800 * r330765;
        double r330802 = 0.607771387771;
        double r330803 = r330801 + r330802;
        double r330804 = r330792 / r330803;
        double r330805 = r330779 + r330804;
        double r330806 = r330771 ? r330780 : r330805;
        return r330806;
}

Original	30.1
Target	0.9
Herbie	1.1

Derivation

Split input into 2 regimes
if z < -1.7503197233736622e+25 or 1.497253047305232e+19 < z
1. Initial program 58.6
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified56.3
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 8.7
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified1.7
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)}\]
if -1.7503197233736622e+25 < z < 1.497253047305232e+19
1. Initial program 0.6
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
Recombined 2 regimes into one program.
Final simplification1.1
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.7503197233736622 \cdot 10^{25} \lor \neg \left(z \le 14972530473052320000\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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))))

Error

Target

Derivation

`if z < -1.7503197233736622e+25 or 1.497253047305232e+19 < z`

`if -1.7503197233736622e+25 < z < 1.497253047305232e+19`

Reproduce