Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[x \cdot 1 + \left(-0.5 \cdot x\right) \cdot x\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
x \cdot 1 + \left(-0.5 \cdot x\right) \cdot x
double f(double x) {
        double r2253837 = x;
        double r2253838 = 1.0;
        double r2253839 = 0.5;
        double r2253840 = r2253837 * r2253839;
        double r2253841 = r2253838 - r2253840;
        double r2253842 = r2253837 * r2253841;
        return r2253842;
}
↓
double f(double x) {
        double r2253843 = x;
        double r2253844 = 1.0;
        double r2253845 = r2253843 * r2253844;
        double r2253846 = 0.5;
        double r2253847 = r2253846 * r2253843;
        double r2253848 = -r2253847;
        double r2253849 = r2253848 * r2253843;
        double r2253850 = r2253845 + r2253849;
        return r2253850;
}

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

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  (* x (- 1.0 (* x 0.5))))