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 r34544 = x;
        double r34545 = 1.0;
        double r34546 = 0.5;
        double r34547 = r34544 * r34546;
        double r34548 = r34545 - r34547;
        double r34549 = r34544 * r34548;
        return r34549;
}
↓
double f(double x) {
        double r34550 = x;
        double r34551 = 1.0;
        double r34552 = r34550 * r34551;
        double r34553 = 0.5;
        double r34554 = r34550 * r34553;
        double r34555 = -r34554;
        double r34556 = r34550 * r34555;
        double r34557 = r34552 + r34556;
        return r34557;
}

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 2020034 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))