Average Error: 12.9 → 0.0
Time: 24.4s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot x - y \cdot z\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot x - y \cdot z
double f(double x, double y, double z) {
        double r408860 = x;
        double r408861 = y;
        double r408862 = r408860 * r408861;
        double r408863 = r408861 * r408861;
        double r408864 = r408862 - r408863;
        double r408865 = r408864 + r408863;
        double r408866 = z;
        double r408867 = r408861 * r408866;
        double r408868 = r408865 - r408867;
        return r408868;
}
↓
double f(double x, double y, double z) {
        double r408869 = y;
        double r408870 = x;
        double r408871 = r408869 * r408870;
        double r408872 = z;
        double r408873 = r408869 * r408872;
        double r408874 = r408871 - r408873;
        return r408874;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original12.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.9

    \[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
  2. Using strategy rm

  3. Applied associate-+l-8.0

    \[\leadsto \color{blue}{\left(x \cdot y - \left(y \cdot y - y \cdot y\right)\right)} - y \cdot z\]

  4. Simplified0.0

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

  5. Final simplification0.0

    \[\leadsto y \cdot x - y \cdot z\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

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

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