Average Error: 0.0 → 0.0
Time: 3.4s
Precision: binary64
Cost: 576
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[y \cdot y + x \cdot \left(x + 2\right)\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
y \cdot y + x \cdot \left(x + 2\right)
(FPCore (x y) :precision binary64 (+ (+ (* x 2.0) (* x x)) (* y y)))
↓
(FPCore (x y) :precision binary64 (+ (* y y) (* x (+ x 2.0))))
double code(double x, double y) {
	return ((x * 2.0) + (x * x)) + (y * y);
}
↓
double code(double x, double y) {
	return (y * y) + (x * (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

Original0.0
Target0.0
Herbie0.0
\[y \cdot y + \left(2 \cdot x + x \cdot x\right)\]

Alternatives

Alternative 1
Error1.3
Cost776
\[\begin{array}{l} \mathbf{if}\;x \leq -1.9879762122458797 \lor \neg \left(x \leq 2.024813580233853\right):\\ \;\;\;\;y \cdot y + x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y + \left(x + x\right)\\ \end{array}\]
Alternative 2
Error4.1
Cost776
\[\begin{array}{l} \mathbf{if}\;y \leq -5.8943467104242605 \cdot 10^{-58} \lor \neg \left(y \leq 9.712121151576375 \cdot 10^{-87}\right):\\ \;\;\;\;y \cdot y + x \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \end{array}\]
Alternative 3
Error9.6
Cost648
\[\begin{array}{l} \mathbf{if}\;y \leq -6.719132278111369 \cdot 10^{-33} \lor \neg \left(y \leq 3.083384684452112 \cdot 10^{-39}\right):\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \end{array}\]
Alternative 4
Error25.3
Cost520
\[\begin{array}{l} \mathbf{if}\;x \leq -1.4114105871689388 \cdot 10^{+19} \lor \neg \left(x \leq 2.3354152405871072 \cdot 10^{+27}\right):\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array}\]
Alternative 5
Error37.6
Cost192
\[y \cdot y\]
Alternative 6
Error60.9
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

    \[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]

  2. Simplified0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"
  :precision binary64

  :herbie-target
  (+ (* y y) (+ (* 2.0 x) (* x x)))

  (+ (+ (* x 2.0) (* x x)) (* y y)))