Average Error: 0.0 → 0.0
Time: 7.6s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r44891 = x;
        double r44892 = y;
        double r44893 = r44891 * r44892;
        double r44894 = z;
        double r44895 = t;
        double r44896 = r44894 * r44895;
        double r44897 = r44893 + r44896;
        double r44898 = a;
        double r44899 = b;
        double r44900 = r44898 * r44899;
        double r44901 = r44897 + r44900;
        double r44902 = c;
        double r44903 = i;
        double r44904 = r44902 * r44903;
        double r44905 = r44901 + r44904;
        return r44905;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r44906 = c;
        double r44907 = i;
        double r44908 = a;
        double r44909 = b;
        double r44910 = x;
        double r44911 = y;
        double r44912 = z;
        double r44913 = t;
        double r44914 = r44912 * r44913;
        double r44915 = fma(r44910, r44911, r44914);
        double r44916 = fma(r44908, r44909, r44915);
        double r44917 = fma(r44906, r44907, r44916);
        return r44917;
}

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 0.0

    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))