Average Error: 0.0 → 0.0
Time: 7.2s
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[x \cdot 1 + \left(-0.5 \cdot {x}^{2}\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
x \cdot 1 + \left(-0.5 \cdot {x}^{2}\right)
double f(double x) {
        double r34673 = x;
        double r34674 = 1.0;
        double r34675 = 0.5;
        double r34676 = r34673 * r34675;
        double r34677 = r34674 - r34676;
        double r34678 = r34673 * r34677;
        return r34678;
}
↓
double f(double x) {
        double r34679 = x;
        double r34680 = 1.0;
        double r34681 = r34679 * r34680;
        double r34682 = 0.5;
        double r34683 = 2.0;
        double r34684 = pow(r34679, r34683);
        double r34685 = r34682 * r34684;
        double r34686 = -r34685;
        double r34687 = r34681 + r34686;
        return r34687;
}

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

    \[\leadsto x \cdot 1 + \color{blue}{\left(-0.5 \cdot {x}^{2}\right)}\]

  6. Final simplification0.0

    \[\leadsto x \cdot 1 + \left(-0.5 \cdot {x}^{2}\right)\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))