Average Error: 0.0 → 0.0
Time: 11.4s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(y, x + z, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(y, x + z, x\right)
double f(double x, double y, double z) {
        double r6550467 = x;
        double r6550468 = y;
        double r6550469 = z;
        double r6550470 = r6550469 + r6550467;
        double r6550471 = r6550468 * r6550470;
        double r6550472 = r6550467 + r6550471;
        return r6550472;
}
↓
double f(double x, double y, double z) {
        double r6550473 = y;
        double r6550474 = x;
        double r6550475 = z;
        double r6550476 = r6550474 + r6550475;
        double r6550477 = fma(r6550473, r6550476, r6550474);
        return r6550477;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))