Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[{\left(x + y\right)}^{2}\]
\left(x + y\right) \cdot \left(x + y\right)
↓
{\left(x + y\right)}^{2}
(FPCore (x y) :precision binary64 (* (+ x y) (+ x y)))
↓
(FPCore (x y) :precision binary64 (pow (+ x y) 2.0))
double code(double x, double y) {
	return (x + y) * (x + y);
}
↓
double code(double x, double y) {
	return pow((x + 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. Using strategy rm

  3. Applied pow2_binary640.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020273 
(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)))