Average Error: 12.9 → 0.0
Time: 1.9s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r483785 = x;
        double r483786 = y;
        double r483787 = r483785 * r483786;
        double r483788 = r483786 * r483786;
        double r483789 = r483787 - r483788;
        double r483790 = r483789 + r483788;
        double r483791 = z;
        double r483792 = r483786 * r483791;
        double r483793 = r483790 - r483792;
        return r483793;
}
↓
double f(double x, double y, double z) {
        double r483794 = y;
        double r483795 = x;
        double r483796 = z;
        double r483797 = r483795 - r483796;
        double r483798 = r483794 * r483797;
        return r483798;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020035 +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)))