Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y\]
↓
\[y \cdot y + x \cdot \left(2 + x\right)\]
\left(x \cdot 2 + x \cdot x\right) + y \cdot y
↓
y \cdot y + x \cdot \left(2 + x\right)
double f(double x, double y) {
        double r518897 = x;
        double r518898 = 2.0;
        double r518899 = r518897 * r518898;
        double r518900 = r518897 * r518897;
        double r518901 = r518899 + r518900;
        double r518902 = y;
        double r518903 = r518902 * r518902;
        double r518904 = r518901 + r518903;
        return r518904;
}
↓
double f(double x, double y) {
        double r518905 = y;
        double r518906 = r518905 * r518905;
        double r518907 = x;
        double r518908 = 2.0;
        double r518909 = r518908 + r518907;
        double r518910 = r518907 * r518909;
        double r518911 = r518906 + r518910;
        return r518911;
}

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 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"
  :precision binary64

  :herbie-target
  (+ (* y y) (+ (* 2 x) (* x x)))

  (+ (+ (* x 2) (* x x)) (* y y)))