Average Error: 0.0 → 0.0
Time: 4.7s
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 r41976 = x;
        double r41977 = 1.0;
        double r41978 = 0.5;
        double r41979 = r41976 * r41978;
        double r41980 = r41977 - r41979;
        double r41981 = r41976 * r41980;
        return r41981;
}
↓
double f(double x) {
        double r41982 = x;
        double r41983 = 1.0;
        double r41984 = r41982 * r41983;
        double r41985 = 0.5;
        double r41986 = r41982 * r41985;
        double r41987 = -r41986;
        double r41988 = r41982 * r41987;
        double r41989 = r41984 + r41988;
        return r41989;
}

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 2019208 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))