Average Error: 0.0 → 0.0
Time: 6.5s
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 r283869 = x;
        double r283870 = 2.0;
        double r283871 = r283869 * r283870;
        double r283872 = r283869 * r283869;
        double r283873 = r283871 + r283872;
        double r283874 = y;
        double r283875 = r283874 * r283874;
        double r283876 = r283873 + r283875;
        return r283876;
}
↓
double f(double x, double y) {
        double r283877 = y;
        double r283878 = r283877 * r283877;
        double r283879 = x;
        double r283880 = 2.0;
        double r283881 = r283880 + r283879;
        double r283882 = r283879 * r283881;
        double r283883 = r283878 + r283882;
        return r283883;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

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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 2019304 
(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)))