Average Error: 0.0 → 0.0
Time: 687.0ms
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(y, z + x, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(y, z + x, x\right)
double f(double x, double y, double z) {
        double r80262 = x;
        double r80263 = y;
        double r80264 = z;
        double r80265 = r80264 + r80262;
        double r80266 = r80263 * r80265;
        double r80267 = r80262 + r80266;
        return r80267;
}
↓
double f(double x, double y, double z) {
        double r80268 = y;
        double r80269 = z;
        double r80270 = x;
        double r80271 = r80269 + r80270;
        double r80272 = fma(r80268, r80271, r80270);
        return r80272;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, z + x, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, z + x, x\right)\]

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))