Average Error: 17.9 → 0.0
Time: 1.3s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot x + y \cdot \left(-z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot x + y \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r486764 = x;
        double r486765 = y;
        double r486766 = r486764 * r486765;
        double r486767 = z;
        double r486768 = r486765 * r486767;
        double r486769 = r486766 - r486768;
        double r486770 = r486765 * r486765;
        double r486771 = r486769 - r486770;
        double r486772 = r486771 + r486770;
        return r486772;
}
↓
double f(double x, double y, double z) {
        double r486773 = y;
        double r486774 = x;
        double r486775 = r486773 * r486774;
        double r486776 = z;
        double r486777 = -r486776;
        double r486778 = r486773 * r486777;
        double r486779 = r486775 + r486778;
        return r486779;
}

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

Original17.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.9

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

  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 2019354 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

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

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