Average Error: 0.0 → 0.0
Time: 884.0ms
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 r67005 = x;
        double r67006 = 1.0;
        double r67007 = 0.5;
        double r67008 = r67005 * r67007;
        double r67009 = r67006 - r67008;
        double r67010 = r67005 * r67009;
        return r67010;
}
↓
double f(double x) {
        double r67011 = x;
        double r67012 = 1.0;
        double r67013 = r67011 * r67012;
        double r67014 = 0.5;
        double r67015 = r67011 * r67014;
        double r67016 = -r67015;
        double r67017 = r67011 * r67016;
        double r67018 = r67013 + r67017;
        return r67018;
}

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 2020065 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))