Average Error: 0.0 → 0.0
Time: 864.0ms
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 r46792 = x;
        double r46793 = 1.0;
        double r46794 = 0.5;
        double r46795 = r46792 * r46794;
        double r46796 = r46793 - r46795;
        double r46797 = r46792 * r46796;
        return r46797;
}
↓
double f(double x) {
        double r46798 = x;
        double r46799 = 1.0;
        double r46800 = r46798 * r46799;
        double r46801 = 0.5;
        double r46802 = r46798 * r46801;
        double r46803 = -r46802;
        double r46804 = r46798 * r46803;
        double r46805 = r46800 + r46804;
        return r46805;
}

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 2020018 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))