Average Error: 0.0 → 0.0
Time: 8.1s
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 r118025 = x;
        double r118026 = y;
        double r118027 = r118025 * r118026;
        double r118028 = z;
        double r118029 = t;
        double r118030 = r118028 * r118029;
        double r118031 = r118027 + r118030;
        return r118031;
}
↓
double f(double x, double y, double z, double t) {
        double r118032 = x;
        double r118033 = y;
        double r118034 = z;
        double r118035 = t;
        double r118036 = r118034 * r118035;
        double r118037 = fma(r118032, r118033, r118036);
        return r118037;
}

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 2019303 +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)))