Average Error: 17.5 → 0.0
Time: 33.4s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[x \cdot y + \left(-z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
x \cdot y + \left(-z\right) \cdot y
double f(double x, double y, double z) {
        double r660684 = x;
        double r660685 = y;
        double r660686 = r660684 * r660685;
        double r660687 = z;
        double r660688 = r660685 * r660687;
        double r660689 = r660686 - r660688;
        double r660690 = r660685 * r660685;
        double r660691 = r660689 - r660690;
        double r660692 = r660691 + r660690;
        return r660692;
}
↓
double f(double x, double y, double z) {
        double r660693 = x;
        double r660694 = y;
        double r660695 = r660693 * r660694;
        double r660696 = z;
        double r660697 = -r660696;
        double r660698 = r660697 * r660694;
        double r660699 = r660695 + r660698;
        return r660699;
}

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

Original17.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.5

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

  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. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(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)))