Average Error: 29.3 → 29.3
Time: 20.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r87908 = x;
        double r87909 = y;
        double r87910 = r87908 * r87909;
        double r87911 = z;
        double r87912 = r87910 + r87911;
        double r87913 = r87912 * r87909;
        double r87914 = 27464.7644705;
        double r87915 = r87913 + r87914;
        double r87916 = r87915 * r87909;
        double r87917 = 230661.510616;
        double r87918 = r87916 + r87917;
        double r87919 = r87918 * r87909;
        double r87920 = t;
        double r87921 = r87919 + r87920;
        double r87922 = a;
        double r87923 = r87909 + r87922;
        double r87924 = r87923 * r87909;
        double r87925 = b;
        double r87926 = r87924 + r87925;
        double r87927 = r87926 * r87909;
        double r87928 = c;
        double r87929 = r87927 + r87928;
        double r87930 = r87929 * r87909;
        double r87931 = i;
        double r87932 = r87930 + r87931;
        double r87933 = r87921 / r87932;
        return r87933;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r87934 = x;
        double r87935 = y;
        double r87936 = z;
        double r87937 = fma(r87934, r87935, r87936);
        double r87938 = 27464.7644705;
        double r87939 = fma(r87937, r87935, r87938);
        double r87940 = 230661.510616;
        double r87941 = fma(r87939, r87935, r87940);
        double r87942 = t;
        double r87943 = fma(r87941, r87935, r87942);
        double r87944 = a;
        double r87945 = r87935 + r87944;
        double r87946 = b;
        double r87947 = fma(r87945, r87935, r87946);
        double r87948 = c;
        double r87949 = fma(r87947, r87935, r87948);
        double r87950 = i;
        double r87951 = fma(r87949, r87935, r87950);
        double r87952 = r87943 / r87951;
        return r87952;
}

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 29.3

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified29.3

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}}\]

  3. Final simplification29.3

    \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))