Average Error: 0.0 → 0.0
Time: 3.8s
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 r83164 = x;
        double r83165 = y;
        double r83166 = z;
        double r83167 = r83166 + r83164;
        double r83168 = r83165 * r83167;
        double r83169 = r83164 + r83168;
        return r83169;
}
↓
double f(double x, double y, double z) {
        double r83170 = y;
        double r83171 = x;
        double r83172 = z;
        double r83173 = r83171 + r83172;
        double r83174 = fma(r83170, r83173, r83171);
        return r83174;
}

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 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))