Average Error: 0.0 → 0.0
Time: 3.9s
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 r12545130 = x;
        double r12545131 = y;
        double r12545132 = z;
        double r12545133 = r12545132 + r12545130;
        double r12545134 = r12545131 * r12545133;
        double r12545135 = r12545130 + r12545134;
        return r12545135;
}
↓
double f(double x, double y, double z) {
        double r12545136 = y;
        double r12545137 = z;
        double r12545138 = x;
        double r12545139 = r12545137 + r12545138;
        double r12545140 = fma(r12545136, r12545139, r12545138);
        return r12545140;
}

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 2019173 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))