Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot \left(y \cdot 2 + x\right) + {y}^{2}\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot \left(y \cdot 2 + x\right) + {y}^{2}
double code(double x, double y) {
	return ((x + y) * (x + y));
}
↓
double code(double x, double y) {
	return ((x * ((y * 2.0) + x)) + pow(y, 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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020078 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"
  :precision binary64

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

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