Average Error: 0.0 → 0.0
Time: 1.3s
Precision: binary64
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[x \cdot \left(x + 2\right) + y \cdot y\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
x \cdot \left(x + 2\right) + y \cdot y
(FPCore (x y) :precision binary64 (+ (+ (* x 2.0) (* x x)) (* y y)))
↓
(FPCore (x y) :precision binary64 (+ (* x (+ x 2.0)) (* y y)))
double code(double x, double y) {
	return ((double) (((double) (((double) (x * 2.0)) + ((double) (x * x)))) + ((double) (y * y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (x * ((double) (x + 2.0)))) + ((double) (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

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

Derivation

  1. Initial program Error: 0.0 bits

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

  2. SimplifiedError: 0.0 bits

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

  3. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020204 
(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)))