Average Error: 0.0 → 0.0
Time: 608.0ms
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 r118000 = x;
        double r118001 = y;
        double r118002 = r118000 * r118001;
        double r118003 = z;
        double r118004 = t;
        double r118005 = r118003 * r118004;
        double r118006 = r118002 + r118005;
        return r118006;
}
↓
double f(double x, double y, double z, double t) {
        double r118007 = x;
        double r118008 = y;
        double r118009 = z;
        double r118010 = t;
        double r118011 = r118009 * r118010;
        double r118012 = fma(r118007, r118008, r118011);
        return r118012;
}

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 2020065 +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)))