Average Error: 0.0 → 0.0
Time: 4.6s
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 r45275 = x;
        double r45276 = 1.0;
        double r45277 = 0.5;
        double r45278 = r45275 * r45277;
        double r45279 = r45276 - r45278;
        double r45280 = r45275 * r45279;
        return r45280;
}
↓
double f(double x) {
        double r45281 = x;
        double r45282 = 1.0;
        double r45283 = r45281 * r45282;
        double r45284 = 0.5;
        double r45285 = r45281 * r45284;
        double r45286 = -r45285;
        double r45287 = r45281 * r45286;
        double r45288 = r45283 + r45287;
        return r45288;
}

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 2019209 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))