Average Error: 0.0 → 0.0
Time: 746.0ms
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 r33659 = x;
        double r33660 = 1.0;
        double r33661 = 0.5;
        double r33662 = r33659 * r33661;
        double r33663 = r33660 - r33662;
        double r33664 = r33659 * r33663;
        return r33664;
}
↓
double f(double x) {
        double r33665 = x;
        double r33666 = 1.0;
        double r33667 = r33665 * r33666;
        double r33668 = 0.5;
        double r33669 = r33665 * r33668;
        double r33670 = -r33669;
        double r33671 = r33665 * r33670;
        double r33672 = r33667 + r33671;
        return r33672;
}

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 2020083 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))