Average Error: 0.0 → 0.0
Time: 887.0ms
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)
double f(double x) {
        double r43682 = x;
        double r43683 = 1.0;
        double r43684 = 0.5;
        double r43685 = r43682 * r43684;
        double r43686 = r43683 - r43685;
        double r43687 = r43682 * r43686;
        return r43687;
}
↓
double f(double x) {
        double r43688 = x;
        double r43689 = 1.0;
        double r43690 = r43688 * r43689;
        double r43691 = 0.5;
        double r43692 = r43688 * r43691;
        double r43693 = -r43692;
        double r43694 = r43688 * r43693;
        double r43695 = r43690 + r43694;
        return r43695;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot \left(1 - x \cdot 0.5\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto x \cdot \color{blue}{\left(1 + \left(-x \cdot 0.5\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)}\]

  5. Final simplification0.0

    \[\leadsto x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)\]

Reproduce

herbie shell --seed 2019347 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))