Average Error: 12.6 → 0.0
Time: 2.7s
Precision: binary64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot x - y \cdot z\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot x - y \cdot z
(FPCore (x y z)
 :precision binary64
 (- (+ (- (* x y) (* y y)) (* y y)) (* y z)))
↓
(FPCore (x y z) :precision binary64 (- (* y x) (* y z)))
double code(double x, double y, double z) {
	return (((x * y) - (y * y)) + (y * y)) - (y * z);
}
↓
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

Original12.6
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.6

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

  2. Simplified0.0

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

  4. Applied sub-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

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020233 
(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)))