Average Error: 0.0 → 0.0
Time: 2.0s
Precision: binary64
\[2 \cdot \left(x \cdot x - x \cdot y\right)\]
↓
\[2 \cdot \left(x \cdot x\right) + y \cdot \left(x \cdot -2\right)\]
2 \cdot \left(x \cdot x - x \cdot y\right)
↓
2 \cdot \left(x \cdot x\right) + y \cdot \left(x \cdot -2\right)
(FPCore (x y) :precision binary64 (* 2.0 (- (* x x) (* x y))))
↓
(FPCore (x y) :precision binary64 (+ (* 2.0 (* x x)) (* y (* x -2.0))))
double code(double x, double y) {
	return 2.0 * ((x * x) - (x * y));
}
↓
double code(double x, double y) {
	return (2.0 * (x * x)) + (y * (x * -2.0));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(x \cdot 2\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x - x \cdot y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(x - y\right)\right)}\]
  3. Using strategy rm

  4. Applied sub-neg_binary640.0

    \[\leadsto 2 \cdot \left(x \cdot \color{blue}{\left(x + \left(-y\right)\right)}\right)\]

  5. Applied distribute-rgt-in_binary640.0

    \[\leadsto 2 \cdot \color{blue}{\left(x \cdot x + \left(-y\right) \cdot x\right)}\]

  6. Applied distribute-rgt-in_binary640.0

    \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot 2 + \left(\left(-y\right) \cdot x\right) \cdot 2}\]

  7. Simplified0.0

    \[\leadsto \color{blue}{2 \cdot \left(x \cdot x\right)} + \left(\left(-y\right) \cdot x\right) \cdot 2\]

  8. Simplified0.0

    \[\leadsto 2 \cdot \left(x \cdot x\right) + \color{blue}{y \cdot \left(x \cdot -2\right)}\]

  9. Final simplification0.0

    \[\leadsto 2 \cdot \left(x \cdot x\right) + y \cdot \left(x \cdot -2\right)\]

Reproduce

herbie shell --seed 2020232 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (* (* x 2.0) (- x y))

  (* 2.0 (- (* x x) (* x y))))