Average Error: 0.0 → 0.0
Time: 638.0ms
Precision: 64
\[x \cdot y + z \cdot t\]
↓
\[\mathsf{fma}\left(x, y, z \cdot t\right)\]
x \cdot y + z \cdot t
↓
\mathsf{fma}\left(x, y, z \cdot t\right)
double f(double x, double y, double z, double t) {
        double r111742 = x;
        double r111743 = y;
        double r111744 = r111742 * r111743;
        double r111745 = z;
        double r111746 = t;
        double r111747 = r111745 * r111746;
        double r111748 = r111744 + r111747;
        return r111748;
}
↓
double f(double x, double y, double z, double t) {
        double r111749 = x;
        double r111750 = y;
        double r111751 = z;
        double r111752 = t;
        double r111753 = r111751 * r111752;
        double r111754 = fma(r111749, r111750, r111753);
        return r111754;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Initial program 0.0

    \[x \cdot y + z \cdot t\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))