Average Error: 12.6 → 0.0
Time: 3.7s
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 r365710 = x;
        double r365711 = y;
        double r365712 = r365710 * r365711;
        double r365713 = r365711 * r365711;
        double r365714 = r365712 - r365713;
        double r365715 = r365714 + r365713;
        double r365716 = z;
        double r365717 = r365711 * r365716;
        double r365718 = r365715 - r365717;
        return r365718;
}
↓
double f(double x, double y, double z) {
        double r365719 = y;
        double r365720 = x;
        double r365721 = z;
        double r365722 = r365720 - r365721;
        double r365723 = r365719 * r365722;
        return r365723;
}

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

Original12.6
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.6

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

  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 2019304 
(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)))