Average Error: 0.1 → 0.1
Time: 2.9s
Precision: binary64
Cost: 576
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[x \cdot x + y \cdot \left(y \cdot 3\right)\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
x \cdot x + y \cdot \left(y \cdot 3\right)
(FPCore (x y) :precision binary64 (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
↓
(FPCore (x y) :precision binary64 (+ (* x x) (* y (* y 3.0))))
double code(double x, double y) {
	return (((x * x) + (y * y)) + (y * y)) + (y * y);
}
↓
double code(double x, double y) {
	return (x * x) + (y * (y * 3.0));
}

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

Alternatives

Alternative 1
Error0.1
Cost576
\[x \cdot x + 3 \cdot \left(y \cdot y\right)\]
Alternative 2
Error12.2
Cost648
\[\begin{array}{l} \mathbf{if}\;y \leq -5.8943467104242605 \cdot 10^{-58} \lor \neg \left(y \leq 1.1442197627234586 \cdot 10^{-39}\right):\\ \;\;\;\;y \cdot \left(y \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array}\]
Alternative 3
Error27.9
Cost192
\[x \cdot x\]
Alternative 4
Error55.1
Cost64
\[0\]
Alternative 5
Error60.7
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto x \cdot x + y \cdot \left(y \cdot 3\right)\]

Reproduce

herbie shell --seed 2021044 
(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)))