Average Error: 0.0 → 0.0
Time: 8.7s
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 r67912 = x;
        double r67913 = y;
        double r67914 = z;
        double r67915 = r67914 + r67912;
        double r67916 = r67913 * r67915;
        double r67917 = r67912 + r67916;
        return r67917;
}
↓
double f(double x, double y, double z) {
        double r67918 = z;
        double r67919 = x;
        double r67920 = r67918 + r67919;
        double r67921 = y;
        double r67922 = fma(r67920, r67921, r67919);
        return r67922;
}

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))))