Average Error: 28.0 → 28.2
Time: 36.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2421880 = x;
        double r2421881 = y;
        double r2421882 = r2421880 * r2421881;
        double r2421883 = z;
        double r2421884 = r2421882 + r2421883;
        double r2421885 = r2421884 * r2421881;
        double r2421886 = 27464.7644705;
        double r2421887 = r2421885 + r2421886;
        double r2421888 = r2421887 * r2421881;
        double r2421889 = 230661.510616;
        double r2421890 = r2421888 + r2421889;
        double r2421891 = r2421890 * r2421881;
        double r2421892 = t;
        double r2421893 = r2421891 + r2421892;
        double r2421894 = a;
        double r2421895 = r2421881 + r2421894;
        double r2421896 = r2421895 * r2421881;
        double r2421897 = b;
        double r2421898 = r2421896 + r2421897;
        double r2421899 = r2421898 * r2421881;
        double r2421900 = c;
        double r2421901 = r2421899 + r2421900;
        double r2421902 = r2421901 * r2421881;
        double r2421903 = i;
        double r2421904 = r2421902 + r2421903;
        double r2421905 = r2421893 / r2421904;
        return r2421905;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2421906 = 1.0;
        double r2421907 = y;
        double r2421908 = a;
        double r2421909 = r2421907 + r2421908;
        double r2421910 = b;
        double r2421911 = fma(r2421909, r2421907, r2421910);
        double r2421912 = c;
        double r2421913 = fma(r2421907, r2421911, r2421912);
        double r2421914 = i;
        double r2421915 = fma(r2421913, r2421907, r2421914);
        double r2421916 = x;
        double r2421917 = z;
        double r2421918 = fma(r2421907, r2421916, r2421917);
        double r2421919 = 27464.7644705;
        double r2421920 = fma(r2421907, r2421918, r2421919);
        double r2421921 = 230661.510616;
        double r2421922 = fma(r2421907, r2421920, r2421921);
        double r2421923 = t;
        double r2421924 = fma(r2421907, r2421922, r2421923);
        double r2421925 = r2421915 / r2421924;
        double r2421926 = r2421906 / r2421925;
        return r2421926;
}

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

Bits error versus c

Bits error versus i

Derivation

  1. Initial program 28.0

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified28.0

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}}\]
  3. Using strategy rm

  4. Applied clear-num28.2

    \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}}\]

  5. Final simplification28.2

    \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))