Average Error: 0.0 → 0.0
Time: 15.8s
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 r6286863 = x;
        double r6286864 = y;
        double r6286865 = r6286863 * r6286864;
        double r6286866 = z;
        double r6286867 = t;
        double r6286868 = r6286866 * r6286867;
        double r6286869 = r6286865 + r6286868;
        double r6286870 = a;
        double r6286871 = b;
        double r6286872 = r6286870 * r6286871;
        double r6286873 = r6286869 + r6286872;
        double r6286874 = c;
        double r6286875 = i;
        double r6286876 = r6286874 * r6286875;
        double r6286877 = r6286873 + r6286876;
        return r6286877;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r6286878 = z;
        double r6286879 = t;
        double r6286880 = x;
        double r6286881 = y;
        double r6286882 = c;
        double r6286883 = i;
        double r6286884 = b;
        double r6286885 = a;
        double r6286886 = r6286884 * r6286885;
        double r6286887 = fma(r6286882, r6286883, r6286886);
        double r6286888 = fma(r6286880, r6286881, r6286887);
        double r6286889 = fma(r6286878, r6286879, r6286888);
        return r6286889;
}

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 2019162 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))