Average Error: 0.1 → 0.1
Time: 39.6s
Precision: 64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[1 \cdot x + \left(-x \cdot y\right) \cdot x\]
x \cdot \left(1 - x \cdot y\right)
↓
1 \cdot x + \left(-x \cdot y\right) \cdot x
double f(double x, double y) {
        double r56896 = x;
        double r56897 = 1.0;
        double r56898 = y;
        double r56899 = r56896 * r56898;
        double r56900 = r56897 - r56899;
        double r56901 = r56896 * r56900;
        return r56901;
}
↓
double f(double x, double y) {
        double r56902 = 1.0;
        double r56903 = x;
        double r56904 = r56902 * r56903;
        double r56905 = y;
        double r56906 = r56903 * r56905;
        double r56907 = -r56906;
        double r56908 = r56907 * r56903;
        double r56909 = r56904 + r56908;
        return r56909;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \left(1 - x \cdot y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.1

    \[\leadsto x \cdot \color{blue}{\left(1 + \left(-x \cdot y\right)\right)}\]

  4. Applied distribute-rgt-in0.1

    \[\leadsto \color{blue}{1 \cdot x + \left(-x \cdot y\right) \cdot x}\]

  5. Final simplification0.1

    \[\leadsto 1 \cdot x + \left(-x \cdot y\right) \cdot x\]

Reproduce

herbie shell --seed 2019202 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  (* x (- 1 (* x y))))