Average Error: 0.0 → 0.0
Time: 10.7s
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 r4165980 = x;
        double r4165981 = y;
        double r4165982 = r4165980 * r4165981;
        double r4165983 = z;
        double r4165984 = t;
        double r4165985 = r4165983 * r4165984;
        double r4165986 = r4165982 + r4165985;
        double r4165987 = a;
        double r4165988 = b;
        double r4165989 = r4165987 * r4165988;
        double r4165990 = r4165986 + r4165989;
        double r4165991 = c;
        double r4165992 = i;
        double r4165993 = r4165991 * r4165992;
        double r4165994 = r4165990 + r4165993;
        return r4165994;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4165995 = z;
        double r4165996 = t;
        double r4165997 = x;
        double r4165998 = y;
        double r4165999 = c;
        double r4166000 = i;
        double r4166001 = b;
        double r4166002 = a;
        double r4166003 = r4166001 * r4166002;
        double r4166004 = fma(r4165999, r4166000, r4166003);
        double r4166005 = fma(r4165997, r4165998, r4166004);
        double r4166006 = fma(r4165995, r4165996, r4166005);
        return r4166006;
}

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 2019169 +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)))