Average Error: 0.0 → 0.0
Time: 1.4s
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 r4588149 = x;
        double r4588150 = y;
        double r4588151 = r4588149 * r4588150;
        double r4588152 = z;
        double r4588153 = t;
        double r4588154 = r4588152 * r4588153;
        double r4588155 = r4588151 + r4588154;
        return r4588155;
}
↓
double f(double x, double y, double z, double t) {
        double r4588156 = x;
        double r4588157 = y;
        double r4588158 = z;
        double r4588159 = t;
        double r4588160 = r4588158 * r4588159;
        double r4588161 = fma(r4588156, r4588157, r4588160);
        return r4588161;
}

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 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))