Average Error: 0.0 → 0.0
Time: 757.0ms
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 r57316 = x;
        double r57317 = 1.0;
        double r57318 = 0.5;
        double r57319 = r57316 * r57318;
        double r57320 = r57317 - r57319;
        double r57321 = r57316 * r57320;
        return r57321;
}
↓
double f(double x) {
        double r57322 = x;
        double r57323 = 1.0;
        double r57324 = r57322 * r57323;
        double r57325 = 0.5;
        double r57326 = r57322 * r57325;
        double r57327 = -r57326;
        double r57328 = r57322 * r57327;
        double r57329 = r57324 + r57328;
        return r57329;
}

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 2020083 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))