Average Error: 0.0 → 0.0
Time: 1.7s
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 r148936 = x;
        double r148937 = y;
        double r148938 = r148936 * r148937;
        double r148939 = z;
        double r148940 = t;
        double r148941 = r148939 * r148940;
        double r148942 = r148938 + r148941;
        return r148942;
}
↓
double f(double x, double y, double z, double t) {
        double r148943 = x;
        double r148944 = y;
        double r148945 = z;
        double r148946 = t;
        double r148947 = r148945 * r148946;
        double r148948 = fma(r148943, r148944, r148947);
        return r148948;
}

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 2020047 +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)))