Average Error: 17.9 → 0.0
Time: 2.7s
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 r506702 = x;
        double r506703 = y;
        double r506704 = r506702 * r506703;
        double r506705 = r506703 * r506703;
        double r506706 = r506704 + r506705;
        double r506707 = z;
        double r506708 = r506703 * r506707;
        double r506709 = r506706 - r506708;
        double r506710 = r506709 - r506705;
        return r506710;
}
↓
double f(double x, double y, double z) {
        double r506711 = y;
        double r506712 = x;
        double r506713 = z;
        double r506714 = r506712 - r506713;
        double r506715 = 0.0;
        double r506716 = fma(r506711, r506714, r506715);
        return r506716;
}

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 2020001 +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)))