Average Error: 0.0 → 0.0
Time: 938.0ms
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[\mathsf{fma}\left(y, z + x, x\right)\]
x + y \cdot \left(z + x\right)
↓
\mathsf{fma}\left(y, z + x, x\right)
double f(double x, double y, double z) {
        double r121644 = x;
        double r121645 = y;
        double r121646 = z;
        double r121647 = r121646 + r121644;
        double r121648 = r121645 * r121647;
        double r121649 = r121644 + r121648;
        return r121649;
}
↓
double f(double x, double y, double z) {
        double r121650 = y;
        double r121651 = z;
        double r121652 = x;
        double r121653 = r121651 + r121652;
        double r121654 = fma(r121650, r121653, r121652);
        return r121654;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, z + x, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, z + x, x\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))