Average Error: 0.0 → 0.0
Time: 715.0ms
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 r92387 = x;
        double r92388 = y;
        double r92389 = r92387 * r92388;
        double r92390 = z;
        double r92391 = t;
        double r92392 = r92390 * r92391;
        double r92393 = r92389 + r92392;
        return r92393;
}
↓
double f(double x, double y, double z, double t) {
        double r92394 = x;
        double r92395 = y;
        double r92396 = z;
        double r92397 = t;
        double r92398 = r92396 * r92397;
        double r92399 = fma(r92394, r92395, r92398);
        return r92399;
}

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)))