Average Error: 0.0 → 0.0
Time: 682.0ms
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 r105089 = x;
        double r105090 = y;
        double r105091 = r105089 * r105090;
        double r105092 = z;
        double r105093 = t;
        double r105094 = r105092 * r105093;
        double r105095 = r105091 + r105094;
        return r105095;
}
↓
double f(double x, double y, double z, double t) {
        double r105096 = x;
        double r105097 = y;
        double r105098 = z;
        double r105099 = t;
        double r105100 = r105098 * r105099;
        double r105101 = fma(r105096, r105097, r105100);
        return r105101;
}

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 2020001 +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)))