Average Error: 0.0 → 0.0
Time: 15.1s
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 r2395809 = x;
        double r2395810 = y;
        double r2395811 = r2395809 * r2395810;
        double r2395812 = z;
        double r2395813 = t;
        double r2395814 = r2395812 * r2395813;
        double r2395815 = r2395811 + r2395814;
        double r2395816 = a;
        double r2395817 = b;
        double r2395818 = r2395816 * r2395817;
        double r2395819 = r2395815 + r2395818;
        double r2395820 = c;
        double r2395821 = i;
        double r2395822 = r2395820 * r2395821;
        double r2395823 = r2395819 + r2395822;
        return r2395823;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2395824 = z;
        double r2395825 = t;
        double r2395826 = x;
        double r2395827 = y;
        double r2395828 = c;
        double r2395829 = i;
        double r2395830 = b;
        double r2395831 = a;
        double r2395832 = r2395830 * r2395831;
        double r2395833 = fma(r2395828, r2395829, r2395832);
        double r2395834 = fma(r2395826, r2395827, r2395833);
        double r2395835 = fma(r2395824, r2395825, r2395834);
        return r2395835;
}

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 2019149 +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)))