Average Error: 0.0 → 0.0
Time: 820.0ms
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 r50819 = x;
        double r50820 = 1.0;
        double r50821 = 0.5;
        double r50822 = r50819 * r50821;
        double r50823 = r50820 - r50822;
        double r50824 = r50819 * r50823;
        return r50824;
}
↓
double f(double x) {
        double r50825 = x;
        double r50826 = 1.0;
        double r50827 = r50825 * r50826;
        double r50828 = 0.5;
        double r50829 = r50825 * r50828;
        double r50830 = -r50829;
        double r50831 = r50825 * r50830;
        double r50832 = r50827 + r50831;
        return r50832;
}

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 2020060 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))