Average Error: 0.0 → 0.1
Time: 5.9s
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[x \cdot 1 + \left(-0.5 \cdot {x}^{2}\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
x \cdot 1 + \left(-0.5 \cdot {x}^{2}\right)
double f(double x) {
        double r38875 = x;
        double r38876 = 1.0;
        double r38877 = 0.5;
        double r38878 = r38875 * r38877;
        double r38879 = r38876 - r38878;
        double r38880 = r38875 * r38879;
        return r38880;
}
↓
double f(double x) {
        double r38881 = x;
        double r38882 = 1.0;
        double r38883 = r38881 * r38882;
        double r38884 = 0.5;
        double r38885 = 2.0;
        double r38886 = pow(r38881, r38885);
        double r38887 = r38884 * r38886;
        double r38888 = -r38887;
        double r38889 = r38883 + r38888;
        return r38889;
}

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. Simplified0.1

    \[\leadsto x \cdot 1 + \color{blue}{\left(-0.5 \cdot {x}^{2}\right)}\]

  6. Final simplification0.1

    \[\leadsto x \cdot 1 + \left(-0.5 \cdot {x}^{2}\right)\]

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))