Average Error: 0.0 → 0.0
Time: 5.1s
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 r73532 = x;
        double r73533 = y;
        double r73534 = z;
        double r73535 = r73534 + r73532;
        double r73536 = r73533 * r73535;
        double r73537 = r73532 + r73536;
        return r73537;
}
↓
double f(double x, double y, double z) {
        double r73538 = z;
        double r73539 = x;
        double r73540 = r73538 + r73539;
        double r73541 = y;
        double r73542 = fma(r73540, r73541, r73539);
        return r73542;
}

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 2019198 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))