Average Error: 0.0 → 0.0
Time: 5.2s
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 r1739608 = x;
        double r1739609 = y;
        double r1739610 = r1739608 * r1739609;
        double r1739611 = z;
        double r1739612 = t;
        double r1739613 = r1739611 * r1739612;
        double r1739614 = r1739610 + r1739613;
        double r1739615 = a;
        double r1739616 = b;
        double r1739617 = r1739615 * r1739616;
        double r1739618 = r1739614 + r1739617;
        double r1739619 = c;
        double r1739620 = i;
        double r1739621 = r1739619 * r1739620;
        double r1739622 = r1739618 + r1739621;
        return r1739622;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1739623 = z;
        double r1739624 = t;
        double r1739625 = x;
        double r1739626 = y;
        double r1739627 = c;
        double r1739628 = i;
        double r1739629 = b;
        double r1739630 = a;
        double r1739631 = r1739629 * r1739630;
        double r1739632 = fma(r1739627, r1739628, r1739631);
        double r1739633 = fma(r1739625, r1739626, r1739632);
        double r1739634 = fma(r1739623, r1739624, r1739633);
        return r1739634;
}

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 2019139 +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)))