Average Error: 0.0 → 0.0
Time: 21.3s
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 r5251718 = x;
        double r5251719 = y;
        double r5251720 = r5251718 * r5251719;
        double r5251721 = z;
        double r5251722 = t;
        double r5251723 = r5251721 * r5251722;
        double r5251724 = r5251720 + r5251723;
        double r5251725 = a;
        double r5251726 = b;
        double r5251727 = r5251725 * r5251726;
        double r5251728 = r5251724 + r5251727;
        double r5251729 = c;
        double r5251730 = i;
        double r5251731 = r5251729 * r5251730;
        double r5251732 = r5251728 + r5251731;
        return r5251732;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r5251733 = z;
        double r5251734 = t;
        double r5251735 = x;
        double r5251736 = y;
        double r5251737 = c;
        double r5251738 = i;
        double r5251739 = b;
        double r5251740 = a;
        double r5251741 = r5251739 * r5251740;
        double r5251742 = fma(r5251737, r5251738, r5251741);
        double r5251743 = fma(r5251735, r5251736, r5251742);
        double r5251744 = fma(r5251733, r5251734, r5251743);
        return r5251744;
}

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 2019172 +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)))