Average Error: 0.0 → 0.0
Time: 905.0ms
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 r46725 = x;
        double r46726 = 1.0;
        double r46727 = 0.5;
        double r46728 = r46725 * r46727;
        double r46729 = r46726 - r46728;
        double r46730 = r46725 * r46729;
        return r46730;
}
↓
double f(double x) {
        double r46731 = x;
        double r46732 = 1.0;
        double r46733 = r46731 * r46732;
        double r46734 = 0.5;
        double r46735 = r46731 * r46734;
        double r46736 = -r46735;
        double r46737 = r46731 * r46736;
        double r46738 = r46733 + r46737;
        return r46738;
}

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 2020001 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))