Average Error: 17.5 → 0.0
Time: 18.4s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[x \cdot y + \left(-z\right) \cdot y\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
x \cdot y + \left(-z\right) \cdot y
double f(double x, double y, double z) {
        double r489812 = x;
        double r489813 = y;
        double r489814 = r489812 * r489813;
        double r489815 = r489813 * r489813;
        double r489816 = r489814 + r489815;
        double r489817 = z;
        double r489818 = r489813 * r489817;
        double r489819 = r489816 - r489818;
        double r489820 = r489819 - r489815;
        return r489820;
}
↓
double f(double x, double y, double z) {
        double r489821 = x;
        double r489822 = y;
        double r489823 = r489821 * r489822;
        double r489824 = z;
        double r489825 = -r489824;
        double r489826 = r489825 * r489822;
        double r489827 = r489823 + r489826;
        return r489827;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

Enter valid numbers for all inputs

Target

Original17.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.5

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

  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 2020045 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

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

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