Average Error: 0.0 → 0.0
Time: 12.3s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(z + x, y, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(z + x, y, x\right)
double f(double x, double y, double z) {
        double r89616 = x;
        double r89617 = y;
        double r89618 = z;
        double r89619 = r89618 + r89616;
        double r89620 = r89617 * r89619;
        double r89621 = r89616 + r89620;
        return r89621;
}
↓
double f(double x, double y, double z) {
        double r89622 = z;
        double r89623 = x;
        double r89624 = r89622 + r89623;
        double r89625 = y;
        double r89626 = fma(r89624, r89625, r89623);
        return r89626;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x + y \cdot \left(z + x\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(z + x, y, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z + x, y, x\right)\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))