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 r279825 = x;
        double r279826 = 2.0;
        double r279827 = r279825 * r279826;
        double r279828 = r279825 * r279825;
        double r279829 = r279827 + r279828;
        double r279830 = y;
        double r279831 = r279830 * r279830;
        double r279832 = r279829 + r279831;
        return r279832;
}
↓
double f(double x, double y) {
        double r279833 = y;
        double r279834 = r279833 * r279833;
        double r279835 = x;
        double r279836 = 2.0;
        double r279837 = r279836 + r279835;
        double r279838 = r279835 * r279837;
        double r279839 = r279834 + r279838;
        return r279839;
}

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)))