Average Error: 0.0 → 0.0
Time: 941.0ms
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 r64556 = x;
        double r64557 = 1.0;
        double r64558 = 0.5;
        double r64559 = r64556 * r64558;
        double r64560 = r64557 - r64559;
        double r64561 = r64556 * r64560;
        return r64561;
}
↓
double f(double x) {
        double r64562 = x;
        double r64563 = 1.0;
        double r64564 = r64562 * r64563;
        double r64565 = 0.5;
        double r64566 = r64562 * r64565;
        double r64567 = -r64566;
        double r64568 = r64562 * r64567;
        double r64569 = r64564 + r64568;
        return r64569;
}

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 2020001 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))