Average Error: 13.2 → 0.0
Time: 3.3s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot x + y \cdot \left(-z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot x + y \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r669658 = x;
        double r669659 = y;
        double r669660 = r669658 * r669659;
        double r669661 = r669659 * r669659;
        double r669662 = r669660 - r669661;
        double r669663 = r669662 + r669661;
        double r669664 = z;
        double r669665 = r669659 * r669664;
        double r669666 = r669663 - r669665;
        return r669666;
}
↓
double f(double x, double y, double z) {
        double r669667 = y;
        double r669668 = x;
        double r669669 = r669667 * r669668;
        double r669670 = z;
        double r669671 = -r669670;
        double r669672 = r669667 * r669671;
        double r669673 = r669669 + r669672;
        return r669673;
}

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

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019362 
(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)))