Average Error: 28.7 → 28.7
Time: 23.9s
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 r62873 = x;
        double r62874 = y;
        double r62875 = r62873 * r62874;
        double r62876 = z;
        double r62877 = r62875 + r62876;
        double r62878 = r62877 * r62874;
        double r62879 = 27464.7644705;
        double r62880 = r62878 + r62879;
        double r62881 = r62880 * r62874;
        double r62882 = 230661.510616;
        double r62883 = r62881 + r62882;
        double r62884 = r62883 * r62874;
        double r62885 = t;
        double r62886 = r62884 + r62885;
        double r62887 = a;
        double r62888 = r62874 + r62887;
        double r62889 = r62888 * r62874;
        double r62890 = b;
        double r62891 = r62889 + r62890;
        double r62892 = r62891 * r62874;
        double r62893 = c;
        double r62894 = r62892 + r62893;
        double r62895 = r62894 * r62874;
        double r62896 = i;
        double r62897 = r62895 + r62896;
        double r62898 = r62886 / r62897;
        return r62898;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62899 = x;
        double r62900 = y;
        double r62901 = z;
        double r62902 = fma(r62899, r62900, r62901);
        double r62903 = 27464.7644705;
        double r62904 = fma(r62902, r62900, r62903);
        double r62905 = 230661.510616;
        double r62906 = fma(r62904, r62900, r62905);
        double r62907 = t;
        double r62908 = fma(r62906, r62900, r62907);
        double r62909 = a;
        double r62910 = r62900 + r62909;
        double r62911 = b;
        double r62912 = fma(r62910, r62900, r62911);
        double r62913 = c;
        double r62914 = fma(r62912, r62900, r62913);
        double r62915 = i;
        double r62916 = fma(r62914, r62900, r62915);
        double r62917 = r62908 / r62916;
        return r62917;
}

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 28.7

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

  2. Simplified28.7

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

  3. Final simplification28.7

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

Reproduce

herbie shell --seed 2019208 +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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))