Average Error: 0.0 → 0.0
Time: 7.1s
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[1 \cdot x + \left(-x \cdot 0.5\right) \cdot x\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
1 \cdot x + \left(-x \cdot 0.5\right) \cdot x
double f(double x) {
        double r47939 = x;
        double r47940 = 1.0;
        double r47941 = 0.5;
        double r47942 = r47939 * r47941;
        double r47943 = r47940 - r47942;
        double r47944 = r47939 * r47943;
        return r47944;
}
↓
double f(double x) {
        double r47945 = 1.0;
        double r47946 = x;
        double r47947 = r47945 * r47946;
        double r47948 = 0.5;
        double r47949 = r47946 * r47948;
        double r47950 = -r47949;
        double r47951 = r47950 * r47946;
        double r47952 = r47947 + r47951;
        return r47952;
}

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-rgt-in0.0

    \[\leadsto \color{blue}{1 \cdot x + \left(-x \cdot 0.5\right) \cdot x}\]

  5. Final simplification0.0

    \[\leadsto 1 \cdot x + \left(-x \cdot 0.5\right) \cdot x\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))