Average Error: 0.1 → 0.1
Time: 3.9s
Precision: binary64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[\left({x}^{2} + 2 \cdot {y}^{2}\right) + y \cdot y\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
\left({x}^{2} + 2 \cdot {y}^{2}\right) + y \cdot y
(FPCore (x y) :precision binary64 (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
↓
(FPCore (x y)
 :precision binary64
 (+ (+ (pow x 2.0) (* 2.0 (pow y 2.0))) (* y y)))
double code(double x, double y) {
	return (((x * x) + (y * y)) + (y * y)) + (y * y);
}
↓
double code(double x, double y) {
	return (pow(x, 2.0) + (2.0 * pow(y, 2.0))) + (y * 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

Original0.1
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. Taylor expanded around 0 0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2021015 
(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)))