Average Error: 0.0 → 0.0
Time: 5.6s
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 r93871 = x;
        double r93872 = y;
        double r93873 = z;
        double r93874 = r93873 + r93871;
        double r93875 = r93872 * r93874;
        double r93876 = r93871 + r93875;
        return r93876;
}
↓
double f(double x, double y, double z) {
        double r93877 = z;
        double r93878 = x;
        double r93879 = r93877 + r93878;
        double r93880 = y;
        double r93881 = fma(r93879, r93880, r93878);
        return r93881;
}

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 2019209 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))