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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -5.7622742072428377 \cdot 10^{61} \lor \neg \left(z \le 4.1810546146577023 \cdot 10^{44}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + t \cdot \frac{1}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

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 -5.7622742072428377 \cdot 10^{61} \lor \neg \left(z \le 4.1810546146577023 \cdot 10^{44}\right):\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + t \cdot \frac{1}{{z}^{2}}, x\right)\\

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

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r1834 = x;
        double r1835 = y;
        double r1836 = z;
        double r1837 = 3.13060547623;
        double r1838 = r1836 * r1837;
        double r1839 = 11.1667541262;
        double r1840 = r1838 + r1839;
        double r1841 = r1840 * r1836;
        double r1842 = t;
        double r1843 = r1841 + r1842;
        double r1844 = r1843 * r1836;
        double r1845 = a;
        double r1846 = r1844 + r1845;
        double r1847 = r1846 * r1836;
        double r1848 = b;
        double r1849 = r1847 + r1848;
        double r1850 = r1835 * r1849;
        double r1851 = 15.234687407;
        double r1852 = r1836 + r1851;
        double r1853 = r1852 * r1836;
        double r1854 = 31.4690115749;
        double r1855 = r1853 + r1854;
        double r1856 = r1855 * r1836;
        double r1857 = 11.9400905721;
        double r1858 = r1856 + r1857;
        double r1859 = r1858 * r1836;
        double r1860 = 0.607771387771;
        double r1861 = r1859 + r1860;
        double r1862 = r1850 / r1861;
        double r1863 = r1834 + r1862;
        return r1863;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r1864 = z;
        double r1865 = -5.762274207242838e+61;
        bool r1866 = r1864 <= r1865;
        double r1867 = 4.181054614657702e+44;
        bool r1868 = r1864 <= r1867;
        double r1869 = !r1868;
        bool r1870 = r1866 || r1869;
        double r1871 = y;
        double r1872 = 3.13060547623;
        double r1873 = t;
        double r1874 = 1.0;
        double r1875 = 2.0;
        double r1876 = pow(r1864, r1875);
        double r1877 = r1874 / r1876;
        double r1878 = r1873 * r1877;
        double r1879 = r1872 + r1878;
        double r1880 = x;
        double r1881 = fma(r1871, r1879, r1880);
        double r1882 = 15.234687407;
        double r1883 = r1864 + r1882;
        double r1884 = 31.4690115749;
        double r1885 = fma(r1883, r1864, r1884);
        double r1886 = 11.9400905721;
        double r1887 = fma(r1885, r1864, r1886);
        double r1888 = 0.607771387771;
        double r1889 = fma(r1887, r1864, r1888);
        double r1890 = r1871 / r1889;
        double r1891 = 11.1667541262;
        double r1892 = fma(r1864, r1872, r1891);
        double r1893 = fma(r1892, r1864, r1873);
        double r1894 = a;
        double r1895 = fma(r1893, r1864, r1894);
        double r1896 = b;
        double r1897 = fma(r1895, r1864, r1896);
        double r1898 = fma(r1890, r1897, r1880);
        double r1899 = r1870 ? r1881 : r1898;
        return r1899;
}

Original	29.3
Target	0.9
Herbie	1.1

Derivation

Split input into 2 regimes
if z < -5.762274207242838e+61 or 4.181054614657702e+44 < z
1. Initial program 61.8
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified60.3
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 8.4
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified0.8
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)}\]
5. Using strategy rm
6. Applied div-inv0.8
  \[\leadsto \mathsf{fma}\left(y, 3.13060547622999996 + \color{blue}{t \cdot \frac{1}{{z}^{2}}}, x\right)\]
if -5.762274207242838e+61 < z < 4.181054614657702e+44
1. Initial program 2.6
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified1.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
Recombined 2 regimes into one program.
Final simplification1.1
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.7622742072428377 \cdot 10^{61} \lor \neg \left(z \le 4.1810546146577023 \cdot 10^{44}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + t \cdot \frac{1}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 +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 < -5.762274207242838e+61 or 4.181054614657702e+44 < z`

`if -5.762274207242838e+61 < z < 4.181054614657702e+44`

Reproduce