Average Error: 0.0 → 0.0
Time: 908.0ms
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 r40695 = x;
        double r40696 = 1.0;
        double r40697 = 0.5;
        double r40698 = r40695 * r40697;
        double r40699 = r40696 - r40698;
        double r40700 = r40695 * r40699;
        return r40700;
}
↓
double f(double x) {
        double r40701 = x;
        double r40702 = 1.0;
        double r40703 = r40701 * r40702;
        double r40704 = 0.5;
        double r40705 = r40701 * r40704;
        double r40706 = -r40705;
        double r40707 = r40701 * r40706;
        double r40708 = r40703 + r40707;
        return r40708;
}

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 2020021 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))