Average Error: 0.0 → 0.0
Time: 4.4s
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 r79840 = x;
        double r79841 = y;
        double r79842 = z;
        double r79843 = r79842 + r79840;
        double r79844 = r79841 * r79843;
        double r79845 = r79840 + r79844;
        return r79845;
}
↓
double f(double x, double y, double z) {
        double r79846 = z;
        double r79847 = x;
        double r79848 = r79846 + r79847;
        double r79849 = y;
        double r79850 = fma(r79848, r79849, r79847);
        return r79850;
}

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 2019322 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))