Average Error: 0.0 → 0.0
Time: 1.8s
Precision: binary64
\[\left(x + y\right) \cdot \left(x + y\right) \]
↓
\[2 \cdot \left(y \cdot x\right) + \left({y}^{2} + {x}^{2}\right) \]
\left(x + y\right) \cdot \left(x + y\right)
↓
2 \cdot \left(y \cdot x\right) + \left({y}^{2} + {x}^{2}\right)

(FPCore (x y) :precision binary64 (* (+ x y) (+ x y)))
↓
(FPCore (x y)
 :precision binary64
 (+ (* 2.0 (* y x)) (+ (pow y 2.0) (pow x 2.0))))
double code(double x, double y) {
	return (x + y) * (x + y);
}
↓
double code(double x, double y) {
	return (2.0 * (y * x)) + (pow(y, 2.0) + pow(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. Taylor expanded around 0 0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021204 
(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)))