Average Error: 13.4 → 0.0
Time: 29.2s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot x - y \cdot z\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot x - y \cdot z
double f(double x, double y, double z) {
        double r298782 = x;
        double r298783 = y;
        double r298784 = r298782 * r298783;
        double r298785 = r298783 * r298783;
        double r298786 = r298784 - r298785;
        double r298787 = r298786 + r298785;
        double r298788 = z;
        double r298789 = r298783 * r298788;
        double r298790 = r298787 - r298789;
        return r298790;
}
↓
double f(double x, double y, double z) {
        double r298791 = y;
        double r298792 = x;
        double r298793 = r298791 * r298792;
        double r298794 = z;
        double r298795 = r298791 * r298794;
        double r298796 = r298793 - r298795;
        return r298796;
}

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

Original13.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.4

    \[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
  2. Using strategy rm

  3. Applied associate-+l-8.3

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

  4. Simplified0.0

    \[\leadsto \left(x \cdot y - \color{blue}{0}\right) - y \cdot z\]

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 +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)))