Average Error: 0.0 → 0.0
Time: 2.9s
Precision: binary64
\[[x, y]=\mathsf{sort}([x, y])\]
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[y \cdot \left(y + x \cdot 2\right) + x \cdot x\]
\left(x + y\right) \cdot \left(x + y\right)
↓
y \cdot \left(y + x \cdot 2\right) + x \cdot x
(FPCore (x y) :precision binary64 (* (+ x y) (+ x y)))
↓
(FPCore (x y) :precision binary64 (+ (* y (+ y (* x 2.0))) (* x x)))
double code(double x, double y) {
	return (x + y) * (x + y);
}
↓
double code(double x, double y) {
	return (y * (y + (x * 2.0))) + (x * x);
}

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 0.0

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

  3. Applied distribute-rgt-in_binary64_160550.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  7. Applied distribute-rgt-in_binary64_160550.0

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

  8. Taylor expanded around 0 0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2021043 
(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)))