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 r111296 = x;
        double r111297 = y;
        double r111298 = r111296 * r111297;
        double r111299 = z;
        double r111300 = t;
        double r111301 = r111299 * r111300;
        double r111302 = r111298 + r111301;
        return r111302;
}
↓
double f(double x, double y, double z, double t) {
        double r111303 = x;
        double r111304 = y;
        double r111305 = z;
        double r111306 = t;
        double r111307 = r111305 * r111306;
        double r111308 = fma(r111303, r111304, r111307);
        return r111308;
}

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 2020046 +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)))