Average Error: 0.0 → 0.0
Time: 833.0ms
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 r40880 = x;
        double r40881 = 1.0;
        double r40882 = 0.5;
        double r40883 = r40880 * r40882;
        double r40884 = r40881 - r40883;
        double r40885 = r40880 * r40884;
        return r40885;
}
↓
double f(double x) {
        double r40886 = x;
        double r40887 = 1.0;
        double r40888 = r40886 * r40887;
        double r40889 = 0.5;
        double r40890 = r40886 * r40889;
        double r40891 = -r40890;
        double r40892 = r40886 * r40891;
        double r40893 = r40888 + r40892;
        return r40893;
}

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 2020046 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))