Average Error: 0.0 → 0.0
Time: 1.6s
Precision: binary64
\[\left(x + y\right) \cdot \left(x + y\right) \]
↓
\[\left(x + y\right) \cdot \left(x + y\right) \]
\left(x + y\right) \cdot \left(x + y\right)
↓
\left(x + y\right) \cdot \left(x + y\right)

(FPCore (x y) :precision binary64 (* (+ x y) (+ x y)))
↓
(FPCore (x y) :precision binary64 (* (+ x y) (+ x y)))
double code(double x, double y) {
	return (x + y) * (x + y);
}
↓
double code(double x, double y) {
	return (x + y) * (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. Applied *-un-lft-identity_binary640.0

    \[\leadsto \left(x + y\right) \cdot \color{blue}{\left(1 \cdot \left(x + y\right)\right)} \]

  3. Applied *-un-lft-identity_binary640.0

    \[\leadsto \color{blue}{\left(1 \cdot \left(x + y\right)\right)} \cdot \left(1 \cdot \left(x + y\right)\right) \]

  4. Applied swap-sqr_binary640.0

    \[\leadsto \color{blue}{\left(1 \cdot 1\right) \cdot \left(\left(x + y\right) \cdot \left(x + y\right)\right)} \]

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2021307 
(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)))