Average Error: 0.0 → 0.0
Time: 1.8s
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 r69946 = x;
        double r69947 = y;
        double r69948 = r69946 * r69947;
        double r69949 = z;
        double r69950 = t;
        double r69951 = r69949 * r69950;
        double r69952 = r69948 + r69951;
        return r69952;
}
↓
double f(double x, double y, double z, double t) {
        double r69953 = x;
        double r69954 = y;
        double r69955 = z;
        double r69956 = t;
        double r69957 = r69955 * r69956;
        double r69958 = fma(r69953, r69954, r69957);
        return r69958;
}

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 2019199 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))