Average Error: 0.0 → 0.0
Time: 1.1s
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 r418830 = x;
        double r418831 = 2.0;
        double r418832 = r418830 * r418831;
        double r418833 = r418830 * r418830;
        double r418834 = r418832 + r418833;
        double r418835 = y;
        double r418836 = r418835 * r418835;
        double r418837 = r418834 + r418836;
        return r418837;
}
↓
double f(double x, double y) {
        double r418838 = y;
        double r418839 = r418838 * r418838;
        double r418840 = x;
        double r418841 = 2.0;
        double r418842 = r418841 + r418840;
        double r418843 = r418840 * r418842;
        double r418844 = r418839 + r418843;
        return r418844;
}

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 2020001 
(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)))