Average Error: 0.0 → 0.0
Time: 855.0ms
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
x \cdot 1 + x \cdot \left(-x \cdot 0.5\right)
double f(double x) {
        double r61472 = x;
        double r61473 = 1.0;
        double r61474 = 0.5;
        double r61475 = r61472 * r61474;
        double r61476 = r61473 - r61475;
        double r61477 = r61472 * r61476;
        return r61477;
}
↓
double f(double x) {
        double r61478 = x;
        double r61479 = 1.0;
        double r61480 = r61478 * r61479;
        double r61481 = 0.5;
        double r61482 = r61478 * r61481;
        double r61483 = -r61482;
        double r61484 = r61478 * r61483;
        double r61485 = r61480 + r61484;
        return r61485;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))