Average Error: 12.4 → 0.0
Time: 6.8s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(-z\right) \cdot y + y \cdot x\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(-z\right) \cdot y + y \cdot x
double f(double x, double y, double z) {
        double r27356727 = x;
        double r27356728 = y;
        double r27356729 = r27356727 * r27356728;
        double r27356730 = r27356728 * r27356728;
        double r27356731 = r27356729 - r27356730;
        double r27356732 = r27356731 + r27356730;
        double r27356733 = z;
        double r27356734 = r27356728 * r27356733;
        double r27356735 = r27356732 - r27356734;
        return r27356735;
}
↓
double f(double x, double y, double z) {
        double r27356736 = z;
        double r27356737 = -r27356736;
        double r27356738 = y;
        double r27356739 = r27356737 * r27356738;
        double r27356740 = x;
        double r27356741 = r27356738 * r27356740;
        double r27356742 = r27356739 + r27356741;
        return r27356742;
}

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

Original12.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.4

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

  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

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"

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

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