Average Error: 13.3 → 0.0
Time: 14.8s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(-z\right) \cdot y + y \cdot x\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(-z\right) \cdot y + y \cdot x
double f(double x, double y, double z) {
        double r21418816 = x;
        double r21418817 = y;
        double r21418818 = r21418816 * r21418817;
        double r21418819 = r21418817 * r21418817;
        double r21418820 = r21418818 - r21418819;
        double r21418821 = r21418820 + r21418819;
        double r21418822 = z;
        double r21418823 = r21418817 * r21418822;
        double r21418824 = r21418821 - r21418823;
        return r21418824;
}
↓
double f(double x, double y, double z) {
        double r21418825 = z;
        double r21418826 = -r21418825;
        double r21418827 = y;
        double r21418828 = r21418826 * r21418827;
        double r21418829 = x;
        double r21418830 = r21418827 * r21418829;
        double r21418831 = r21418828 + r21418830;
        return r21418831;
}

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

Original13.3
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.3

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

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"

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

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