Average Error: 0.0 → 0.0
Time: 751.0ms
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 r87563 = x;
        double r87564 = y;
        double r87565 = z;
        double r87566 = r87565 + r87563;
        double r87567 = r87564 * r87566;
        double r87568 = r87563 + r87567;
        return r87568;
}
↓
double f(double x, double y, double z) {
        double r87569 = y;
        double r87570 = z;
        double r87571 = x;
        double r87572 = r87570 + r87571;
        double r87573 = fma(r87569, r87572, r87571);
        return r87573;
}

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 2019352 +o rules:numerics
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))