Average Error: 0.0 → 0.0
Time: 7.7s
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 r92899 = x;
        double r92900 = y;
        double r92901 = z;
        double r92902 = r92901 + r92899;
        double r92903 = r92900 * r92902;
        double r92904 = r92899 + r92903;
        return r92904;
}
↓
double f(double x, double y, double z) {
        double r92905 = z;
        double r92906 = x;
        double r92907 = r92905 + r92906;
        double r92908 = y;
        double r92909 = fma(r92907, r92908, r92906);
        return r92909;
}

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 2019323 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))