Average Error: 0.0 → 0.0
Time: 4.0s
Precision: binary64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot x + y \cdot \left(y + x \cdot 2\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot x + y \cdot \left(y + x \cdot 2\right)
(FPCore (x y) :precision binary64 (* (+ x y) (+ x y)))
↓
(FPCore (x y) :precision binary64 (+ (* x x) (* y (+ y (* x 2.0)))))
double code(double x, double y) {
	return (x + y) * (x + y);
}
↓
double code(double x, double y) {
	return (x * x) + (y * (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
\[x \cdot x + \left(y \cdot y + 2 \cdot \left(y \cdot x\right)\right)\]

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_140090.0

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

  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 add-cbrt-cube_binary64_1409521.4

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x \cdot \left(y + x\right)\right) \cdot \left(x \cdot \left(y + x\right)\right)\right) \cdot \left(x \cdot \left(y + x\right)\right)}} + y \cdot \left(y + x\right)\]

  8. Simplified21.4

    \[\leadsto \sqrt[3]{\color{blue}{{\left(x \cdot \left(y + x\right)\right)}^{3}}} + y \cdot \left(y + x\right)\]

  9. Taylor expanded around 0 0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2021098 
(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)))