Average Error: 0.0 → 0.0
Time: 978.0ms
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 r42693 = x;
        double r42694 = 1.0;
        double r42695 = 0.5;
        double r42696 = r42693 * r42695;
        double r42697 = r42694 - r42696;
        double r42698 = r42693 * r42697;
        return r42698;
}
↓
double f(double x) {
        double r42699 = x;
        double r42700 = 1.0;
        double r42701 = r42699 * r42700;
        double r42702 = 0.5;
        double r42703 = r42699 * r42702;
        double r42704 = -r42703;
        double r42705 = r42699 * r42704;
        double r42706 = r42701 + r42705;
        return r42706;
}

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 2020081 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))