Average Error: 0.0 → 0.0
Time: 7.4s
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 r69730 = x;
        double r69731 = y;
        double r69732 = z;
        double r69733 = r69732 + r69730;
        double r69734 = r69731 * r69733;
        double r69735 = r69730 + r69734;
        return r69735;
}
↓
double f(double x, double y, double z) {
        double r69736 = z;
        double r69737 = x;
        double r69738 = r69736 + r69737;
        double r69739 = y;
        double r69740 = fma(r69738, r69739, r69737);
        return r69740;
}

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 2019212 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))