Average Error: 0.0 → 0.0
Time: 10.6s
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 r2375852 = x;
        double r2375853 = y;
        double r2375854 = r2375852 * r2375853;
        double r2375855 = z;
        double r2375856 = t;
        double r2375857 = r2375855 * r2375856;
        double r2375858 = r2375854 + r2375857;
        double r2375859 = a;
        double r2375860 = b;
        double r2375861 = r2375859 * r2375860;
        double r2375862 = r2375858 + r2375861;
        double r2375863 = c;
        double r2375864 = i;
        double r2375865 = r2375863 * r2375864;
        double r2375866 = r2375862 + r2375865;
        return r2375866;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2375867 = z;
        double r2375868 = t;
        double r2375869 = x;
        double r2375870 = y;
        double r2375871 = c;
        double r2375872 = i;
        double r2375873 = b;
        double r2375874 = a;
        double r2375875 = r2375873 * r2375874;
        double r2375876 = fma(r2375871, r2375872, r2375875);
        double r2375877 = fma(r2375869, r2375870, r2375876);
        double r2375878 = fma(r2375867, r2375868, r2375877);
        return r2375878;
}

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 2019164 +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)))