Average Error: 28.9 → 28.9
Time: 38.1s
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 r70888 = x;
        double r70889 = y;
        double r70890 = r70888 * r70889;
        double r70891 = z;
        double r70892 = r70890 + r70891;
        double r70893 = r70892 * r70889;
        double r70894 = 27464.7644705;
        double r70895 = r70893 + r70894;
        double r70896 = r70895 * r70889;
        double r70897 = 230661.510616;
        double r70898 = r70896 + r70897;
        double r70899 = r70898 * r70889;
        double r70900 = t;
        double r70901 = r70899 + r70900;
        double r70902 = a;
        double r70903 = r70889 + r70902;
        double r70904 = r70903 * r70889;
        double r70905 = b;
        double r70906 = r70904 + r70905;
        double r70907 = r70906 * r70889;
        double r70908 = c;
        double r70909 = r70907 + r70908;
        double r70910 = r70909 * r70889;
        double r70911 = i;
        double r70912 = r70910 + r70911;
        double r70913 = r70901 / r70912;
        return r70913;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70914 = x;
        double r70915 = y;
        double r70916 = z;
        double r70917 = fma(r70914, r70915, r70916);
        double r70918 = 27464.7644705;
        double r70919 = fma(r70917, r70915, r70918);
        double r70920 = 230661.510616;
        double r70921 = fma(r70919, r70915, r70920);
        double r70922 = t;
        double r70923 = fma(r70921, r70915, r70922);
        double r70924 = a;
        double r70925 = r70915 + r70924;
        double r70926 = b;
        double r70927 = fma(r70925, r70915, r70926);
        double r70928 = c;
        double r70929 = fma(r70927, r70915, r70928);
        double r70930 = i;
        double r70931 = fma(r70929, r70915, r70930);
        double r70932 = r70923 / r70931;
        return r70932;
}

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 28.9

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

  2. Simplified28.9

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

  3. Final simplification28.9

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

Reproduce

herbie shell --seed 2019322 +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)))