Average Error: 0.0 → 0.0
Time: 2.7s
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[1 \cdot x + \left(0.5 \cdot x\right) \cdot \left(-x\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
1 \cdot x + \left(0.5 \cdot x\right) \cdot \left(-x\right)
double f(double x) {
        double r45980 = x;
        double r45981 = 1.0;
        double r45982 = 0.5;
        double r45983 = r45980 * r45982;
        double r45984 = r45981 - r45983;
        double r45985 = r45980 * r45984;
        return r45985;
}
↓
double f(double x) {
        double r45986 = 1.0;
        double r45987 = x;
        double r45988 = r45986 * r45987;
        double r45989 = 0.5;
        double r45990 = r45989 * r45987;
        double r45991 = -r45987;
        double r45992 = r45990 * r45991;
        double r45993 = r45988 + r45992;
        return r45993;
}

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-rgt-in0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  (* x (- 1.0 (* x 0.5))))