Average Error: 0.0 → 0.0
Time: 2.6s
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 r70094 = x;
        double r70095 = y;
        double r70096 = z;
        double r70097 = r70096 + r70094;
        double r70098 = r70095 * r70097;
        double r70099 = r70094 + r70098;
        return r70099;
}
↓
double f(double x, double y, double z) {
        double r70100 = y;
        double r70101 = x;
        double r70102 = z;
        double r70103 = r70101 + r70102;
        double r70104 = fma(r70100, r70103, r70101);
        return r70104;
}

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 2019194 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))