Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[2 \cdot \left(x \cdot x - x \cdot y\right)\]
↓
\[\left(x \cdot 2\right) \cdot x + \left(x \cdot 2\right) \cdot \left(-y\right)\]
2 \cdot \left(x \cdot x - x \cdot y\right)
↓
\left(x \cdot 2\right) \cdot x + \left(x \cdot 2\right) \cdot \left(-y\right)
double code(double x, double y) {
	return (2.0 * ((x * x) - (x * y)));
}
↓
double code(double x, double y) {
	return (((x * 2.0) * x) + ((x * 2.0) * -y));
}

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. Using strategy rm

  3. Applied distribute-lft-out--0.0

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

  4. Applied associate-*r*0.0

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

  5. Simplified0.0

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

  7. Applied sub-neg0.0

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

  8. Applied distribute-lft-in0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (* (* x 2) (- x y))

  (* 2 (- (* x x) (* x y))))