Average Error: 0.0 → 0.0
Time: 854.0ms
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 r53798 = x;
        double r53799 = 1.0;
        double r53800 = 0.5;
        double r53801 = r53798 * r53800;
        double r53802 = r53799 - r53801;
        double r53803 = r53798 * r53802;
        return r53803;
}
↓
double f(double x) {
        double r53804 = x;
        double r53805 = 1.0;
        double r53806 = r53804 * r53805;
        double r53807 = 0.5;
        double r53808 = r53804 * r53807;
        double r53809 = -r53808;
        double r53810 = r53804 * r53809;
        double r53811 = r53806 + r53810;
        return r53811;
}

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 2020057 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))