Average Error: 0.0 → 0.0
Time: 4.5s
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[1 \cdot x + \left(-0.5 \cdot \left(x \cdot x\right)\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
1 \cdot x + \left(-0.5 \cdot \left(x \cdot x\right)\right)
double f(double x) {
        double r45283 = x;
        double r45284 = 1.0;
        double r45285 = 0.5;
        double r45286 = r45283 * r45285;
        double r45287 = r45284 - r45286;
        double r45288 = r45283 * r45287;
        return r45288;
}
↓
double f(double x) {
        double r45289 = 1.0;
        double r45290 = x;
        double r45291 = r45289 * r45290;
        double r45292 = 0.5;
        double r45293 = r45290 * r45290;
        double r45294 = r45292 * r45293;
        double r45295 = -r45294;
        double r45296 = r45291 + r45295;
        return r45296;
}

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

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

  6. Simplified0.0

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

  7. Final simplification0.0

    \[\leadsto 1 \cdot x + \left(-0.5 \cdot \left(x \cdot x\right)\right)\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))