Average Error: 12.9 → 0.0
Time: 22.7s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[x \cdot y - y \cdot z\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
x \cdot y - y \cdot z
double f(double x, double y, double z) {
        double r355647 = x;
        double r355648 = y;
        double r355649 = r355647 * r355648;
        double r355650 = r355648 * r355648;
        double r355651 = r355649 - r355650;
        double r355652 = r355651 + r355650;
        double r355653 = z;
        double r355654 = r355648 * r355653;
        double r355655 = r355652 - r355654;
        return r355655;
}
↓
double f(double x, double y, double z) {
        double r355656 = x;
        double r355657 = y;
        double r355658 = r355656 * r355657;
        double r355659 = z;
        double r355660 = r355657 * r355659;
        double r355661 = r355658 - r355660;
        return r355661;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{x \cdot y} - y \cdot z\]

  3. Final simplification0.0

    \[\leadsto x \cdot y - y \cdot z\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(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)))