Average Error: 0.0 → 0.0
Time: 3.7s
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 r80378 = x;
        double r80379 = y;
        double r80380 = r80378 * r80379;
        double r80381 = z;
        double r80382 = t;
        double r80383 = r80381 * r80382;
        double r80384 = r80380 + r80383;
        return r80384;
}
↓
double f(double x, double y, double z, double t) {
        double r80385 = x;
        double r80386 = y;
        double r80387 = z;
        double r80388 = t;
        double r80389 = r80387 * r80388;
        double r80390 = fma(r80385, r80386, r80389);
        return r80390;
}

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 2019322 +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)))