Average Error: 0.0 → 0.0
Time: 1.8s
Precision: binary64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot \left(x + \left(y + y\right)\right) + y \cdot y\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot \left(x + \left(y + y\right)\right) + y \cdot y
(FPCore (x y) :precision binary64 (* (+ x y) (+ x y)))
↓
(FPCore (x y) :precision binary64 (+ (* x (+ x (+ y y))) (* y y)))
double code(double x, double y) {
	return ((double) (((double) (x + y)) * ((double) (x + y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (x * ((double) (x + ((double) (y + y)))))) + ((double) (y * 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
\[x \cdot x + \left(y \cdot y + 2 \cdot \left(y \cdot x\right)\right)\]

Derivation

  1. Initial program Error: 0.0 bits

    \[\left(x + y\right) \cdot \left(x + y\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-inError: 0.0 bits

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

  4. SimplifiedError: 0.0 bits

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

  5. SimplifiedError: 0.0 bits

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

  7. Applied distribute-lft-inError: 0.0 bits

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

  8. Applied associate-+r+Error: 0.0 bits

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

  9. SimplifiedError: 0.0 bits

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

  10. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"
  :precision binary64

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

  (* (+ x y) (+ x y)))