Average Error: 0.0 → 0.0
Time: 7.5s
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 r49730 = x;
        double r49731 = 1.0;
        double r49732 = 0.5;
        double r49733 = r49730 * r49732;
        double r49734 = r49731 - r49733;
        double r49735 = r49730 * r49734;
        return r49735;
}
↓
double f(double x) {
        double r49736 = x;
        double r49737 = 1.0;
        double r49738 = r49736 * r49737;
        double r49739 = 0.5;
        double r49740 = 2.0;
        double r49741 = pow(r49736, r49740);
        double r49742 = r49739 * r49741;
        double r49743 = -r49742;
        double r49744 = r49738 + r49743;
        return r49744;
}

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 2019306 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))