Average Error: 0.0 → 0.0
Time: 861.0ms
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 r34625 = x;
        double r34626 = 1.0;
        double r34627 = 0.5;
        double r34628 = r34625 * r34627;
        double r34629 = r34626 - r34628;
        double r34630 = r34625 * r34629;
        return r34630;
}
↓
double f(double x) {
        double r34631 = x;
        double r34632 = 1.0;
        double r34633 = r34631 * r34632;
        double r34634 = 0.5;
        double r34635 = r34631 * r34634;
        double r34636 = -r34635;
        double r34637 = r34631 * r34636;
        double r34638 = r34633 + r34637;
        return r34638;
}

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