Average Error: 0.0 → 0.0
Time: 7.7s
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 r124985 = x;
        double r124986 = y;
        double r124987 = z;
        double r124988 = r124987 + r124985;
        double r124989 = r124986 * r124988;
        double r124990 = r124985 + r124989;
        return r124990;
}
↓
double f(double x, double y, double z) {
        double r124991 = z;
        double r124992 = x;
        double r124993 = r124991 + r124992;
        double r124994 = y;
        double r124995 = fma(r124993, r124994, r124992);
        return r124995;
}

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 2019323 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))