Average Error: 0.1 → 0.1
Time: 3.0s
Precision: binary64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y \]
↓
\[y \cdot y + \left(y \cdot y + \left(y \cdot y + x \cdot x\right)\right) \]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
y \cdot y + \left(y \cdot y + \left(y \cdot y + x \cdot x\right)\right)

(FPCore (x y) :precision binary64 (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
↓
(FPCore (x y) :precision binary64 (+ (* y y) (+ (* y y) (+ (* y y) (* x x)))))
double code(double x, double y) {
	return (((x * x) + (y * y)) + (y * y)) + (y * y);
}
↓
double code(double x, double y) {
	return (y * y) + ((y * y) + ((y * y) + (x * x)));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[x \cdot x + y \cdot \left(y + \left(y + y\right)\right) \]

Derivation

  1. Initial program 0.1

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

  2. Applied +-commutative_binary640.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2022081 
(FPCore (x y)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, E"
  :precision binary64

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

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