Average Error: 0.0 → 0.0
Time: 904.0ms
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 r51903 = x;
        double r51904 = 1.0;
        double r51905 = 0.5;
        double r51906 = r51903 * r51905;
        double r51907 = r51904 - r51906;
        double r51908 = r51903 * r51907;
        return r51908;
}
↓
double f(double x) {
        double r51909 = x;
        double r51910 = 1.0;
        double r51911 = r51909 * r51910;
        double r51912 = 0.5;
        double r51913 = r51909 * r51912;
        double r51914 = -r51913;
        double r51915 = r51909 * r51914;
        double r51916 = r51911 + r51915;
        return r51916;
}

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 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))))