Average Error: 0.0 → 0.0
Time: 2.1s
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 r451047 = x;
        double r451048 = 2.0;
        double r451049 = r451047 * r451048;
        double r451050 = r451047 * r451047;
        double r451051 = r451049 + r451050;
        double r451052 = y;
        double r451053 = r451052 * r451052;
        double r451054 = r451051 + r451053;
        return r451054;
}
↓
double f(double x, double y) {
        double r451055 = y;
        double r451056 = r451055 * r451055;
        double r451057 = x;
        double r451058 = 2.0;
        double r451059 = r451058 + r451057;
        double r451060 = r451057 * r451059;
        double r451061 = r451056 + r451060;
        return r451061;
}

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 2020081 
(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)))