Average Error: 0.0 → 0.0
Time: 789.0ms
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 r45184 = x;
        double r45185 = 1.0;
        double r45186 = 0.5;
        double r45187 = r45184 * r45186;
        double r45188 = r45185 - r45187;
        double r45189 = r45184 * r45188;
        return r45189;
}
↓
double f(double x) {
        double r45190 = x;
        double r45191 = 1.0;
        double r45192 = r45190 * r45191;
        double r45193 = 0.5;
        double r45194 = r45190 * r45193;
        double r45195 = -r45194;
        double r45196 = r45190 * r45195;
        double r45197 = r45192 + r45196;
        return r45197;
}

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 2020036 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))