Average Error: 12.9 → 0.0
Time: 1.3s
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 r640621 = x;
        double r640622 = y;
        double r640623 = r640621 * r640622;
        double r640624 = r640622 * r640622;
        double r640625 = r640623 - r640624;
        double r640626 = r640625 + r640624;
        double r640627 = z;
        double r640628 = r640622 * r640627;
        double r640629 = r640626 - r640628;
        return r640629;
}
↓
double f(double x, double y, double z) {
        double r640630 = y;
        double r640631 = x;
        double r640632 = z;
        double r640633 = r640631 - r640632;
        double r640634 = r640630 * r640633;
        return r640634;
}

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

Original12.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.9

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

  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 2019353 
(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)))