Average Error: 0.0 → 0.0
Time: 815.0ms
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 r62816 = x;
        double r62817 = 1.0;
        double r62818 = 0.5;
        double r62819 = r62816 * r62818;
        double r62820 = r62817 - r62819;
        double r62821 = r62816 * r62820;
        return r62821;
}
↓
double f(double x) {
        double r62822 = x;
        double r62823 = 1.0;
        double r62824 = r62822 * r62823;
        double r62825 = 0.5;
        double r62826 = r62822 * r62825;
        double r62827 = -r62826;
        double r62828 = r62822 * r62827;
        double r62829 = r62824 + r62828;
        return r62829;
}

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 2020060 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))