Average Error: 17.7 → 0.0
Time: 2.4s
Precision: binary64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y \]
↓
\[y \cdot x - y \cdot z \]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot x - y \cdot z

(FPCore (x y z)
 :precision binary64
 (+ (- (- (* x y) (* y z)) (* y y)) (* y y)))
↓
(FPCore (x y z) :precision binary64 (- (* y x) (* y z)))
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) - (y * z);
}

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

Original17.7
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y \]

Derivation

  1. Initial program 17.7

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

  2. Simplified0.0

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

  4. Applied sub-neg_binary640.0

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

  5. Applied distribute-rgt-in_binary640.0

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

  6. Simplified0.0

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

  8. Applied neg-sub0_binary640.0

    \[\leadsto x \cdot y + \color{blue}{\left(0 - z \cdot y\right)} \]

  9. Applied associate-+r-_binary640.0

    \[\leadsto \color{blue}{\left(x \cdot y + 0\right) - z \cdot y} \]

  10. Simplified0.0

    \[\leadsto \color{blue}{y \cdot x} - z \cdot y \]

  11. Final simplification0.0

    \[\leadsto y \cdot x - y \cdot z \]

Reproduce

herbie shell --seed 2021204 
(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)))