Average Error: 0.0 → 0.0
Time: 8.0s
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 r307843 = x;
        double r307844 = 2.0;
        double r307845 = r307843 * r307844;
        double r307846 = r307843 * r307843;
        double r307847 = r307845 + r307846;
        double r307848 = y;
        double r307849 = r307848 * r307848;
        double r307850 = r307847 + r307849;
        return r307850;
}
↓
double f(double x, double y) {
        double r307851 = y;
        double r307852 = r307851 * r307851;
        double r307853 = x;
        double r307854 = 2.0;
        double r307855 = r307854 + r307853;
        double r307856 = r307853 * r307855;
        double r307857 = r307852 + r307856;
        return r307857;
}

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 2019322 
(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)))