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 r125523 = x;
        double r125524 = y;
        double r125525 = r125523 * r125524;
        double r125526 = z;
        double r125527 = t;
        double r125528 = r125526 * r125527;
        double r125529 = r125525 + r125528;
        return r125529;
}
↓
double f(double x, double y, double z, double t) {
        double r125530 = x;
        double r125531 = y;
        double r125532 = z;
        double r125533 = t;
        double r125534 = r125532 * r125533;
        double r125535 = fma(r125530, r125531, r125534);
        return r125535;
}

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 2019323 +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)))