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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -5.7622742072428377 \cdot 10^{61} \lor \neg \left(z \le 6.5875831388733411 \cdot 10^{55}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

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 -5.7622742072428377 \cdot 10^{61} \lor \neg \left(z \le 6.5875831388733411 \cdot 10^{55}\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 r1833 = x;
        double r1834 = y;
        double r1835 = z;
        double r1836 = 3.13060547623;
        double r1837 = r1835 * r1836;
        double r1838 = 11.1667541262;
        double r1839 = r1837 + r1838;
        double r1840 = r1839 * r1835;
        double r1841 = t;
        double r1842 = r1840 + r1841;
        double r1843 = r1842 * r1835;
        double r1844 = a;
        double r1845 = r1843 + r1844;
        double r1846 = r1845 * r1835;
        double r1847 = b;
        double r1848 = r1846 + r1847;
        double r1849 = r1834 * r1848;
        double r1850 = 15.234687407;
        double r1851 = r1835 + r1850;
        double r1852 = r1851 * r1835;
        double r1853 = 31.4690115749;
        double r1854 = r1852 + r1853;
        double r1855 = r1854 * r1835;
        double r1856 = 11.9400905721;
        double r1857 = r1855 + r1856;
        double r1858 = r1857 * r1835;
        double r1859 = 0.607771387771;
        double r1860 = r1858 + r1859;
        double r1861 = r1849 / r1860;
        double r1862 = r1833 + r1861;
        return r1862;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r1863 = z;
        double r1864 = -5.762274207242838e+61;
        bool r1865 = r1863 <= r1864;
        double r1866 = 6.587583138873341e+55;
        bool r1867 = r1863 <= r1866;
        double r1868 = !r1867;
        bool r1869 = r1865 || r1868;
        double r1870 = x;
        double r1871 = 3.13060547623;
        double r1872 = y;
        double r1873 = r1871 * r1872;
        double r1874 = t;
        double r1875 = r1874 * r1872;
        double r1876 = 2.0;
        double r1877 = pow(r1863, r1876);
        double r1878 = r1875 / r1877;
        double r1879 = r1873 + r1878;
        double r1880 = 36.527041698806414;
        double r1881 = r1872 / r1863;
        double r1882 = r1880 * r1881;
        double r1883 = r1879 - r1882;
        double r1884 = r1870 + r1883;
        double r1885 = 15.234687407;
        double r1886 = r1863 + r1885;
        double r1887 = r1886 * r1863;
        double r1888 = 31.4690115749;
        double r1889 = r1887 + r1888;
        double r1890 = r1889 * r1863;
        double r1891 = 11.9400905721;
        double r1892 = r1890 + r1891;
        double r1893 = r1892 * r1863;
        double r1894 = 0.607771387771;
        double r1895 = r1893 + r1894;
        double r1896 = r1863 * r1871;
        double r1897 = 11.1667541262;
        double r1898 = r1896 + r1897;
        double r1899 = r1898 * r1863;
        double r1900 = r1899 + r1874;
        double r1901 = r1900 * r1863;
        double r1902 = a;
        double r1903 = r1901 + r1902;
        double r1904 = r1903 * r1863;
        double r1905 = b;
        double r1906 = r1904 + r1905;
        double r1907 = r1895 / r1906;
        double r1908 = r1872 / r1907;
        double r1909 = r1870 + r1908;
        double r1910 = r1869 ? r1884 : r1909;
        return r1910;
}

Original	29.3
Target	0.9
Herbie	4.4

Derivation

Split input into 2 regimes
if z < -5.762274207242838e+61 or 6.587583138873341e+55 < z
1. Initial program 62.3
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Taylor expanded around inf 8.3
  \[\leadsto x + \color{blue}{\left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]
if -5.762274207242838e+61 < z < 6.587583138873341e+55
1. Initial program 3.0
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Using strategy rm
3. Applied associate-/l*1.2
  \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]
Recombined 2 regimes into one program.
Final simplification4.4
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.7622742072428377 \cdot 10^{61} \lor \neg \left(z \le 6.5875831388733411 \cdot 10^{55}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(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

Try it out

Target

Derivation

`if z < -5.762274207242838e+61 or 6.587583138873341e+55 < z`

`if -5.762274207242838e+61 < z < 6.587583138873341e+55`

Reproduce

In
Out