Average Error: 0.0 → 0.0
Time: 7.2s
Precision: binary64
Cost: 704
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[y \cdot y + \left(x \cdot 2 + x \cdot x\right)\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
y \cdot y + \left(x \cdot 2 + x \cdot x\right)
(FPCore (x y) :precision binary64 (+ (+ (* x 2.0) (* x x)) (* y y)))
↓
(FPCore (x y) :precision binary64 (+ (* y y) (+ (* x 2.0) (* x x))))
double code(double x, double y) {
	return ((x * 2.0) + (x * x)) + (y * y);
}
↓
double code(double x, double y) {
	return (y * y) + ((x * 2.0) + (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

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

Alternatives

Alternative 1
Error1.4
Cost21056
\[\sqrt[3]{x \cdot \left(x + 2\right) + y \cdot y} \cdot \left(\sqrt[3]{x \cdot \left(x + 2\right) + y \cdot y} \cdot \sqrt[3]{x \cdot \left(x + 2\right) + y \cdot y}\right)\]
Alternative 2
Error40.7
Cost20992
\[\frac{{\left(x \cdot \left(x + 2\right)\right)}^{3} + {y}^{6}}{{y}^{4} + \left(x \cdot \left(x + 2\right)\right) \cdot \left(x \cdot \left(x + 2\right) - y \cdot y\right)}\]
Alternative 3
Error29.4
Cost14656
\[\frac{{\left(x \cdot \left(x + 2\right)\right)}^{2}}{x \cdot \left(x + 2\right) - y \cdot y} - \frac{{y}^{4}}{x \cdot \left(x + 2\right) - y \cdot y}\]
Alternative 4
Error12.6
Cost8448
\[\left(x \cdot \left(x + 2\right)\right) \cdot \frac{1}{1 - \frac{y \cdot y}{x \cdot \left(x + 2\right)}} - \frac{{y}^{4}}{x \cdot \left(x + 2\right) - y \cdot y}\]
Alternative 5
Error12.6
Cost8320
\[\frac{x \cdot \left(x + 2\right)}{1 - \frac{y \cdot y}{x \cdot \left(x + 2\right)}} - \frac{{y}^{4}}{x \cdot \left(x + 2\right) - y \cdot y}\]
Alternative 6
Error29.4
Cost7936
\[\frac{x \cdot \left(x \cdot \left(\left(x + 2\right) \cdot \left(x + 2\right)\right)\right) - {y}^{4}}{x \cdot \left(x + 2\right) - y \cdot y}\]
Alternative 7
Error49.5
Cost7232
\[\frac{-{y}^{4}}{x \cdot \left(x + 2\right) - y \cdot y}\]
Alternative 8
Error0.0
Cost576
\[x \cdot \left(x + 2\right) + y \cdot y\]
Alternative 9
Error20.9
Cost448
\[y \cdot y + x \cdot x\]
Alternative 10
Error18.0
Cost448
\[y \cdot y + \left(x + x\right)\]
Alternative 11
Error24.3
Cost320
\[x \cdot \left(x + 2\right)\]
Alternative 12
Error44.6
Cost192
\[x \cdot x\]
Alternative 13
Error38.0
Cost192
\[y \cdot y\]
Alternative 14
Error60.9
Cost64
\[1\]
Alternative 15
Error61.9
Cost64
\[0\]
Alternative 16
Error62.6
Cost64
\[-1\]

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021042 
(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)))