Average Error: 0.0 → 0.0
Time: 7.3s
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 r111827 = x;
        double r111828 = y;
        double r111829 = z;
        double r111830 = r111829 + r111827;
        double r111831 = r111828 * r111830;
        double r111832 = r111827 + r111831;
        return r111832;
}
↓
double f(double x, double y, double z) {
        double r111833 = z;
        double r111834 = x;
        double r111835 = r111833 + r111834;
        double r111836 = y;
        double r111837 = fma(r111835, r111836, r111834);
        return r111837;
}

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 2019235 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))