Average Error: 13.4 → 0.0
Time: 9.6s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[x \cdot y + \left(-z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
x \cdot y + \left(-z\right) \cdot y
double f(double x, double y, double z) {
        double r593676 = x;
        double r593677 = y;
        double r593678 = r593676 * r593677;
        double r593679 = r593677 * r593677;
        double r593680 = r593678 - r593679;
        double r593681 = r593680 + r593679;
        double r593682 = z;
        double r593683 = r593677 * r593682;
        double r593684 = r593681 - r593683;
        return r593684;
}
↓
double f(double x, double y, double z) {
        double r593685 = x;
        double r593686 = y;
        double r593687 = r593685 * r593686;
        double r593688 = z;
        double r593689 = -r593688;
        double r593690 = r593689 * r593686;
        double r593691 = r593687 + r593690;
        return r593691;
}

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. 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. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(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)))