Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[1 \cdot x + \left(-0.5 \cdot \left(x \cdot x\right)\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
1 \cdot x + \left(-0.5 \cdot \left(x \cdot x\right)\right)
double f(double x) {
        double r55646 = x;
        double r55647 = 1.0;
        double r55648 = 0.5;
        double r55649 = r55646 * r55648;
        double r55650 = r55647 - r55649;
        double r55651 = r55646 * r55650;
        return r55651;
}
↓
double f(double x) {
        double r55652 = 1.0;
        double r55653 = x;
        double r55654 = r55652 * r55653;
        double r55655 = 0.5;
        double r55656 = r55653 * r55653;
        double r55657 = r55655 * r55656;
        double r55658 = -r55657;
        double r55659 = r55654 + r55658;
        return r55659;
}

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

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))