Average Error: 17.8 → 0.0
Time: 2.0s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[\mathsf{fma}\left(y, x - z, 0\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
\mathsf{fma}\left(y, x - z, 0\right)
double f(double x, double y, double z) {
        double r536687 = x;
        double r536688 = y;
        double r536689 = r536687 * r536688;
        double r536690 = r536688 * r536688;
        double r536691 = r536689 + r536690;
        double r536692 = z;
        double r536693 = r536688 * r536692;
        double r536694 = r536691 - r536693;
        double r536695 = r536694 - r536690;
        return r536695;
}
↓
double f(double x, double y, double z) {
        double r536696 = y;
        double r536697 = x;
        double r536698 = z;
        double r536699 = r536697 - r536698;
        double r536700 = 0.0;
        double r536701 = fma(r536696, r536699, r536700);
        return r536701;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original17.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.8

    \[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x - z, 0\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x - z, 0\right)\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (- (- (+ (* x y) (* y y)) (* y z)) (* y y)))