Average Error: 0.0 → 0.0
Time: 4.8s
Precision: binary64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot x + y \cdot \left(2 \cdot x + y\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot x + y \cdot \left(2 \cdot x + y\right)
double code(double x, double y) {
	return ((double) (((double) (x + y)) * ((double) (x + y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (x * x)) + ((double) (y * ((double) (((double) (2.0 * x)) + 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 0.0

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020182 
(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)))