Average Error: 0.0 → 0.0
Time: 2.9s
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 r93809 = x;
        double r93810 = y;
        double r93811 = z;
        double r93812 = r93811 + r93809;
        double r93813 = r93810 * r93812;
        double r93814 = r93809 + r93813;
        return r93814;
}
↓
double f(double x, double y, double z) {
        double r93815 = y;
        double r93816 = x;
        double r93817 = z;
        double r93818 = r93816 + r93817;
        double r93819 = fma(r93815, r93818, r93816);
        return r93819;
}

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 2019196 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))