Average Error: 27.9 → 28.1
Time: 35.7s
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 r2422868 = x;
        double r2422869 = y;
        double r2422870 = r2422868 * r2422869;
        double r2422871 = z;
        double r2422872 = r2422870 + r2422871;
        double r2422873 = r2422872 * r2422869;
        double r2422874 = 27464.7644705;
        double r2422875 = r2422873 + r2422874;
        double r2422876 = r2422875 * r2422869;
        double r2422877 = 230661.510616;
        double r2422878 = r2422876 + r2422877;
        double r2422879 = r2422878 * r2422869;
        double r2422880 = t;
        double r2422881 = r2422879 + r2422880;
        double r2422882 = a;
        double r2422883 = r2422869 + r2422882;
        double r2422884 = r2422883 * r2422869;
        double r2422885 = b;
        double r2422886 = r2422884 + r2422885;
        double r2422887 = r2422886 * r2422869;
        double r2422888 = c;
        double r2422889 = r2422887 + r2422888;
        double r2422890 = r2422889 * r2422869;
        double r2422891 = i;
        double r2422892 = r2422890 + r2422891;
        double r2422893 = r2422881 / r2422892;
        return r2422893;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2422894 = 1.0;
        double r2422895 = y;
        double r2422896 = a;
        double r2422897 = r2422895 + r2422896;
        double r2422898 = b;
        double r2422899 = fma(r2422897, r2422895, r2422898);
        double r2422900 = c;
        double r2422901 = fma(r2422895, r2422899, r2422900);
        double r2422902 = i;
        double r2422903 = fma(r2422901, r2422895, r2422902);
        double r2422904 = x;
        double r2422905 = z;
        double r2422906 = fma(r2422895, r2422904, r2422905);
        double r2422907 = 27464.7644705;
        double r2422908 = fma(r2422895, r2422906, r2422907);
        double r2422909 = 230661.510616;
        double r2422910 = fma(r2422895, r2422908, r2422909);
        double r2422911 = t;
        double r2422912 = fma(r2422895, r2422910, r2422911);
        double r2422913 = r2422903 / r2422912;
        double r2422914 = r2422894 / r2422913;
        return r2422914;
}

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 27.9

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

  2. Simplified27.9

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

  4. Applied clear-num28.1

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

  5. Final simplification28.1

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

Reproduce

herbie shell --seed 2019158 +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)))