Average Error: 17.1 → 0.0
Time: 2.0s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double code(double x, double y, double z) {
	return ((((x * y) - (y * z)) - (y * y)) + (y * y));
}
↓
double code(double x, double y, double z) {
	return (y * (x - z));
}

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

Original17.1
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.1

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

  2. Simplified0.0

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

  4. Applied add-sqr-sqrt31.4

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

  5. Applied associate-*r*31.4

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

  7. Applied associate-*l*31.4

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

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

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