Average Error: 0.0 → 0.0
Time: 812.0ms
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 r43644 = x;
        double r43645 = 1.0;
        double r43646 = 0.5;
        double r43647 = r43644 * r43646;
        double r43648 = r43645 - r43647;
        double r43649 = r43644 * r43648;
        return r43649;
}
↓
double f(double x) {
        double r43650 = x;
        double r43651 = 1.0;
        double r43652 = r43650 * r43651;
        double r43653 = 0.5;
        double r43654 = r43650 * r43653;
        double r43655 = -r43654;
        double r43656 = r43650 * r43655;
        double r43657 = r43652 + r43656;
        return r43657;
}

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 2020049 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))