Average Error: 0.0 → 0.0
Time: 709.0ms
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 r92791 = x;
        double r92792 = y;
        double r92793 = z;
        double r92794 = r92793 + r92791;
        double r92795 = r92792 * r92794;
        double r92796 = r92791 + r92795;
        return r92796;
}
↓
double f(double x, double y, double z) {
        double r92797 = y;
        double r92798 = z;
        double r92799 = x;
        double r92800 = r92798 + r92799;
        double r92801 = fma(r92797, r92800, r92799);
        return r92801;
}

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 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))