Average Error: 17.9 → 0.0
Time: 1.1s
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 r514746 = x;
        double r514747 = y;
        double r514748 = r514746 * r514747;
        double r514749 = r514747 * r514747;
        double r514750 = r514748 + r514749;
        double r514751 = z;
        double r514752 = r514747 * r514751;
        double r514753 = r514750 - r514752;
        double r514754 = r514753 - r514749;
        return r514754;
}
↓
double f(double x, double y, double z) {
        double r514755 = y;
        double r514756 = x;
        double r514757 = z;
        double r514758 = r514756 - r514757;
        double r514759 = 0.0;
        double r514760 = fma(r514755, r514758, r514759);
        return r514760;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original17.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.9

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

  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 2020046 +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)))