Average Error: 17.4 → 0.0
Time: 4.8s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r368614 = x;
        double r368615 = y;
        double r368616 = r368614 * r368615;
        double r368617 = z;
        double r368618 = r368615 * r368617;
        double r368619 = r368616 - r368618;
        double r368620 = r368615 * r368615;
        double r368621 = r368619 - r368620;
        double r368622 = r368621 + r368620;
        return r368622;
}
↓
double f(double x, double y, double z) {
        double r368623 = y;
        double r368624 = x;
        double r368625 = z;
        double r368626 = r368624 - r368625;
        double r368627 = r368623 * r368626;
        return r368627;
}

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

Original17.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.4

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

  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 2019303 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

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

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