Average Error: 0.0 → 0.0
Time: 4.4s
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[1 \cdot x + \left(x \cdot 0.5\right) \cdot \left(-x\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
1 \cdot x + \left(x \cdot 0.5\right) \cdot \left(-x\right)
double f(double x) {
        double r38798 = x;
        double r38799 = 1.0;
        double r38800 = 0.5;
        double r38801 = r38798 * r38800;
        double r38802 = r38799 - r38801;
        double r38803 = r38798 * r38802;
        return r38803;
}
↓
double f(double x) {
        double r38804 = 1.0;
        double r38805 = x;
        double r38806 = r38804 * r38805;
        double r38807 = 0.5;
        double r38808 = r38805 * r38807;
        double r38809 = -r38805;
        double r38810 = r38808 * r38809;
        double r38811 = r38806 + r38810;
        return r38811;
}

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. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))