Average Error: 0.0 → 0.0
Time: 1.1s
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 r60961 = x;
        double r60962 = y;
        double r60963 = r60961 * r60962;
        double r60964 = z;
        double r60965 = t;
        double r60966 = r60964 * r60965;
        double r60967 = r60963 + r60966;
        return r60967;
}
↓
double f(double x, double y, double z, double t) {
        double r60968 = x;
        double r60969 = y;
        double r60970 = z;
        double r60971 = t;
        double r60972 = r60970 * r60971;
        double r60973 = fma(r60968, r60969, r60972);
        return r60973;
}

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 2019326 +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)))