Average Error: 0.0 → 0.0
Time: 8.0s
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 r102319 = x;
        double r102320 = y;
        double r102321 = z;
        double r102322 = r102321 + r102319;
        double r102323 = r102320 * r102322;
        double r102324 = r102319 + r102323;
        return r102324;
}
↓
double f(double x, double y, double z) {
        double r102325 = y;
        double r102326 = x;
        double r102327 = z;
        double r102328 = r102326 + r102327;
        double r102329 = fma(r102325, r102328, r102326);
        return r102329;
}

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 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))