Average Error: 13.2 → 0.0
Time: 11.3s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r324747 = x;
        double r324748 = y;
        double r324749 = r324747 * r324748;
        double r324750 = r324748 * r324748;
        double r324751 = r324749 - r324750;
        double r324752 = r324751 + r324750;
        double r324753 = z;
        double r324754 = r324748 * r324753;
        double r324755 = r324752 - r324754;
        return r324755;
}
↓
double f(double x, double y, double z) {
        double r324756 = x;
        double r324757 = z;
        double r324758 = r324756 - r324757;
        double r324759 = y;
        double r324760 = r324758 * r324759;
        return r324760;
}

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

Original13.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.2

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019235 
(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)))