Average Error: 0.0 → 0.0
Time: 6.9s
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 r38316 = x;
        double r38317 = 1.0;
        double r38318 = 0.5;
        double r38319 = r38316 * r38318;
        double r38320 = r38317 - r38319;
        double r38321 = r38316 * r38320;
        return r38321;
}
↓
double f(double x) {
        double r38322 = x;
        double r38323 = 1.0;
        double r38324 = r38322 * r38323;
        double r38325 = 0.5;
        double r38326 = 2.0;
        double r38327 = pow(r38322, r38326);
        double r38328 = r38325 * r38327;
        double r38329 = -r38328;
        double r38330 = r38324 + r38329;
        return r38330;
}

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

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))