Average Error: 0.0 → 0.0
Time: 3.1s
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 r328863 = x;
        double r328864 = 2.0;
        double r328865 = r328863 * r328864;
        double r328866 = r328863 * r328863;
        double r328867 = r328865 + r328866;
        double r328868 = y;
        double r328869 = r328868 * r328868;
        double r328870 = r328867 + r328869;
        return r328870;
}
↓
double f(double x, double y) {
        double r328871 = y;
        double r328872 = r328871 * r328871;
        double r328873 = x;
        double r328874 = 2.0;
        double r328875 = r328874 + r328873;
        double r328876 = r328873 * r328875;
        double r328877 = r328872 + r328876;
        return r328877;
}

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 2019326 
(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)))