Average Error: 0.0 → 0.0
Time: 20.4s
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 r4167864 = x;
        double r4167865 = y;
        double r4167866 = r4167864 * r4167865;
        double r4167867 = z;
        double r4167868 = t;
        double r4167869 = r4167867 * r4167868;
        double r4167870 = r4167866 + r4167869;
        double r4167871 = a;
        double r4167872 = b;
        double r4167873 = r4167871 * r4167872;
        double r4167874 = r4167870 + r4167873;
        double r4167875 = c;
        double r4167876 = i;
        double r4167877 = r4167875 * r4167876;
        double r4167878 = r4167874 + r4167877;
        return r4167878;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4167879 = z;
        double r4167880 = t;
        double r4167881 = x;
        double r4167882 = y;
        double r4167883 = c;
        double r4167884 = i;
        double r4167885 = b;
        double r4167886 = a;
        double r4167887 = r4167885 * r4167886;
        double r4167888 = fma(r4167883, r4167884, r4167887);
        double r4167889 = fma(r4167881, r4167882, r4167888);
        double r4167890 = fma(r4167879, r4167880, r4167889);
        return r4167890;
}

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 2019172 +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)))