Average Error: 0.1 → 0.1
Time: 2.4s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[\left(3 \cdot y\right) \cdot y + {x}^{2}\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
\left(3 \cdot y\right) \cdot y + {x}^{2}
double code(double x, double y) {
	return ((((x * x) + (y * y)) + (y * y)) + (y * y));
}
↓
double code(double x, double y) {
	return (((3.0 * y) * y) + 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

Original0.1
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. Using strategy rm

  3. Applied +-commutative0.1

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

  4. Applied associate-+l+0.1

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

  5. Applied associate-+l+0.1

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

  6. Simplified0.1

    \[\leadsto y \cdot y + \color{blue}{\left({x}^{2} + y \cdot \left(y + y\right)\right)}\]
  7. Using strategy rm

  8. Applied +-commutative0.1

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

  9. Applied associate-+r+0.1

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

  10. Simplified0.1

    \[\leadsto \color{blue}{\left(3 \cdot y\right) \cdot y} + {x}^{2}\]

  11. Final simplification0.1

    \[\leadsto \left(3 \cdot y\right) \cdot y + {x}^{2}\]

Reproduce

herbie shell --seed 2020078 
(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)))