Average Error: 0.0 → 0.0
Time: 806.0ms
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 r58926 = x;
        double r58927 = 1.0;
        double r58928 = 0.5;
        double r58929 = r58926 * r58928;
        double r58930 = r58927 - r58929;
        double r58931 = r58926 * r58930;
        return r58931;
}
↓
double f(double x) {
        double r58932 = x;
        double r58933 = 1.0;
        double r58934 = r58932 * r58933;
        double r58935 = 0.5;
        double r58936 = r58932 * r58935;
        double r58937 = -r58936;
        double r58938 = r58932 * r58937;
        double r58939 = r58934 + r58938;
        return r58939;
}

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 2020046 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))