Average Error: 12.9 → 0.0
Time: 3.2s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot x + y \cdot \left(-z\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot x + y \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r450712 = x;
        double r450713 = y;
        double r450714 = r450712 * r450713;
        double r450715 = r450713 * r450713;
        double r450716 = r450714 - r450715;
        double r450717 = r450716 + r450715;
        double r450718 = z;
        double r450719 = r450713 * r450718;
        double r450720 = r450717 - r450719;
        return r450720;
}
↓
double f(double x, double y, double z) {
        double r450721 = y;
        double r450722 = x;
        double r450723 = r450721 * r450722;
        double r450724 = z;
        double r450725 = -r450724;
        double r450726 = r450721 * r450725;
        double r450727 = r450723 + r450726;
        return r450727;
}

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. 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

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

Reproduce

herbie shell --seed 2019322 
(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)))