Average Error: 0.0 → 0.0
Time: 1.0s
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 r47572 = x;
        double r47573 = 1.0;
        double r47574 = 0.5;
        double r47575 = r47572 * r47574;
        double r47576 = r47573 - r47575;
        double r47577 = r47572 * r47576;
        return r47577;
}
↓
double f(double x) {
        double r47578 = x;
        double r47579 = 1.0;
        double r47580 = r47578 * r47579;
        double r47581 = 0.5;
        double r47582 = r47578 * r47581;
        double r47583 = -r47582;
        double r47584 = r47578 * r47583;
        double r47585 = r47580 + r47584;
        return r47585;
}

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 2020034 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))