Average Error: 0.0 → 0.0
Time: 1.0s
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 r40320 = x;
        double r40321 = 1.0;
        double r40322 = 0.5;
        double r40323 = r40320 * r40322;
        double r40324 = r40321 - r40323;
        double r40325 = r40320 * r40324;
        return r40325;
}
↓
double f(double x) {
        double r40326 = x;
        double r40327 = 1.0;
        double r40328 = r40326 * r40327;
        double r40329 = 0.5;
        double r40330 = r40326 * r40329;
        double r40331 = -r40330;
        double r40332 = r40326 * r40331;
        double r40333 = r40328 + r40332;
        return r40333;
}

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 2020089 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))