Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, \mathsf{fma}\left(c, i, b \cdot a\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r854671 = x;
        double r854672 = y;
        double r854673 = r854671 * r854672;
        double r854674 = z;
        double r854675 = t;
        double r854676 = r854674 * r854675;
        double r854677 = r854673 + r854676;
        double r854678 = a;
        double r854679 = b;
        double r854680 = r854678 * r854679;
        double r854681 = r854677 + r854680;
        double r854682 = c;
        double r854683 = i;
        double r854684 = r854682 * r854683;
        double r854685 = r854681 + r854684;
        return r854685;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r854686 = z;
        double r854687 = t;
        double r854688 = x;
        double r854689 = y;
        double r854690 = c;
        double r854691 = i;
        double r854692 = b;
        double r854693 = a;
        double r854694 = r854692 * r854693;
        double r854695 = fma(r854690, r854691, r854694);
        double r854696 = fma(r854688, r854689, r854695);
        double r854697 = fma(r854686, r854687, r854696);
        return r854697;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))