Average Error: 0.0 → 0.0
Time: 8.2s
Precision: 64
\[\left(x \cdot y + x\right) + y\]
↓
\[\left(y + x \cdot y\right) + x\]
\left(x \cdot y + x\right) + y
↓
\left(y + x \cdot y\right) + x
double f(double x, double y) {
        double r4478894 = x;
        double r4478895 = y;
        double r4478896 = r4478894 * r4478895;
        double r4478897 = r4478896 + r4478894;
        double r4478898 = r4478897 + r4478895;
        return r4478898;
}
↓
double f(double x, double y) {
        double r4478899 = y;
        double r4478900 = x;
        double r4478901 = r4478900 * r4478899;
        double r4478902 = r4478899 + r4478901;
        double r4478903 = r4478902 + r4478900;
        return r4478903;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(x \cdot y + x\right) + y\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{x + \left(y + x \cdot y\right)}\]

  3. Final simplification0.0

    \[\leadsto \left(y + x \cdot y\right) + x\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y)
  :name "Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B"
  (+ (+ (* x y) x) y))