Average Error: 0.0 → 0.0
Time: 16.0s
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 r1289728 = x;
        double r1289729 = y;
        double r1289730 = r1289728 * r1289729;
        double r1289731 = z;
        double r1289732 = t;
        double r1289733 = r1289731 * r1289732;
        double r1289734 = r1289730 + r1289733;
        double r1289735 = a;
        double r1289736 = b;
        double r1289737 = r1289735 * r1289736;
        double r1289738 = r1289734 + r1289737;
        double r1289739 = c;
        double r1289740 = i;
        double r1289741 = r1289739 * r1289740;
        double r1289742 = r1289738 + r1289741;
        return r1289742;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1289743 = z;
        double r1289744 = t;
        double r1289745 = x;
        double r1289746 = y;
        double r1289747 = c;
        double r1289748 = i;
        double r1289749 = b;
        double r1289750 = a;
        double r1289751 = r1289749 * r1289750;
        double r1289752 = fma(r1289747, r1289748, r1289751);
        double r1289753 = fma(r1289745, r1289746, r1289752);
        double r1289754 = fma(r1289743, r1289744, r1289753);
        return r1289754;
}

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 2019154 +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)))