Average Error: 12.9 → 0.0
Time: 12.7s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r784441 = x;
        double r784442 = y;
        double r784443 = r784441 * r784442;
        double r784444 = r784442 * r784442;
        double r784445 = r784443 - r784444;
        double r784446 = r784445 + r784444;
        double r784447 = z;
        double r784448 = r784442 * r784447;
        double r784449 = r784446 - r784448;
        return r784449;
}
↓
double f(double x, double y, double z) {
        double r784450 = x;
        double r784451 = z;
        double r784452 = r784450 - r784451;
        double r784453 = y;
        double r784454 = r784452 * r784453;
        return r784454;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 
(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)))