Average Error: 0.0 → 0.0
Time: 686.0ms
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 r109553 = x;
        double r109554 = y;
        double r109555 = r109553 * r109554;
        double r109556 = z;
        double r109557 = t;
        double r109558 = r109556 * r109557;
        double r109559 = r109555 + r109558;
        return r109559;
}
↓
double f(double x, double y, double z, double t) {
        double r109560 = x;
        double r109561 = y;
        double r109562 = z;
        double r109563 = t;
        double r109564 = r109562 * r109563;
        double r109565 = fma(r109560, r109561, r109564);
        return r109565;
}

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)))