Average Error: 0.0 → 0.0
Time: 671.0ms
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 r130082 = x;
        double r130083 = y;
        double r130084 = r130082 * r130083;
        double r130085 = z;
        double r130086 = t;
        double r130087 = r130085 * r130086;
        double r130088 = r130084 + r130087;
        return r130088;
}
↓
double f(double x, double y, double z, double t) {
        double r130089 = x;
        double r130090 = y;
        double r130091 = z;
        double r130092 = t;
        double r130093 = r130091 * r130092;
        double r130094 = fma(r130089, r130090, r130093);
        return r130094;
}

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 2020025 +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)))