Average Error: 0.0 → 0.0
Time: 9.0s
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 r67691 = x;
        double r67692 = 1.0;
        double r67693 = 0.5;
        double r67694 = r67691 * r67693;
        double r67695 = r67692 - r67694;
        double r67696 = r67691 * r67695;
        return r67696;
}
↓
double f(double x) {
        double r67697 = x;
        double r67698 = 1.0;
        double r67699 = r67697 * r67698;
        double r67700 = 0.5;
        double r67701 = 2.0;
        double r67702 = pow(r67697, r67701);
        double r67703 = r67700 * r67702;
        double r67704 = -r67703;
        double r67705 = r67699 + r67704;
        return r67705;
}

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 2019325 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))