Average Error: 0.1 → 0.1
Time: 17.8s
Precision: 64
\[x \cdot \left(1.0 - x \cdot y\right)\]
↓
\[x \cdot 1.0 + \left(-y \cdot x\right) \cdot x\]
x \cdot \left(1.0 - x \cdot y\right)
↓
x \cdot 1.0 + \left(-y \cdot x\right) \cdot x
double f(double x, double y) {
        double r3623053 = x;
        double r3623054 = 1.0;
        double r3623055 = y;
        double r3623056 = r3623053 * r3623055;
        double r3623057 = r3623054 - r3623056;
        double r3623058 = r3623053 * r3623057;
        return r3623058;
}
↓
double f(double x, double y) {
        double r3623059 = x;
        double r3623060 = 1.0;
        double r3623061 = r3623059 * r3623060;
        double r3623062 = y;
        double r3623063 = r3623062 * r3623059;
        double r3623064 = -r3623063;
        double r3623065 = r3623064 * r3623059;
        double r3623066 = r3623061 + r3623065;
        return r3623066;
}

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

    \[x \cdot \left(1.0 - x \cdot y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.1

    \[\leadsto x \cdot \color{blue}{\left(1.0 + \left(-x \cdot y\right)\right)}\]

  4. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{x \cdot 1.0 + x \cdot \left(-x \cdot y\right)}\]

  5. Final simplification0.1

    \[\leadsto x \cdot 1.0 + \left(-y \cdot x\right) \cdot x\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  (* x (- 1.0 (* x y))))