Average Error: 12.5 → 0.0
Time: 3.0s
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 r491709 = x;
        double r491710 = y;
        double r491711 = r491709 * r491710;
        double r491712 = r491710 * r491710;
        double r491713 = r491711 - r491712;
        double r491714 = r491713 + r491712;
        double r491715 = z;
        double r491716 = r491710 * r491715;
        double r491717 = r491714 - r491716;
        return r491717;
}
↓
double f(double x, double y, double z) {
        double r491718 = y;
        double r491719 = x;
        double r491720 = z;
        double r491721 = r491719 - r491720;
        double r491722 = r491718 * r491721;
        return r491722;
}

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

Original12.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.5

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

  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 2020056 
(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)))