Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(i, c, \mathsf{fma}\left(b, a, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(i, c, \mathsf{fma}\left(b, a, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r141530 = x;
        double r141531 = y;
        double r141532 = r141530 * r141531;
        double r141533 = z;
        double r141534 = t;
        double r141535 = r141533 * r141534;
        double r141536 = r141532 + r141535;
        double r141537 = a;
        double r141538 = b;
        double r141539 = r141537 * r141538;
        double r141540 = r141536 + r141539;
        double r141541 = c;
        double r141542 = i;
        double r141543 = r141541 * r141542;
        double r141544 = r141540 + r141543;
        return r141544;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r141545 = i;
        double r141546 = c;
        double r141547 = b;
        double r141548 = a;
        double r141549 = x;
        double r141550 = y;
        double r141551 = z;
        double r141552 = t;
        double r141553 = r141551 * r141552;
        double r141554 = fma(r141549, r141550, r141553);
        double r141555 = fma(r141547, r141548, r141554);
        double r141556 = fma(r141545, r141546, r141555);
        return r141556;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(i, c, \mathsf{fma}\left(b, a, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(i, c, \mathsf{fma}\left(b, a, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\]

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))