Average Error: 0.0 → 0.0
Time: 7.1s
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[1 \cdot x + \left(0.5 \cdot x\right) \cdot \left(-x\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
1 \cdot x + \left(0.5 \cdot x\right) \cdot \left(-x\right)
double f(double x) {
        double r2665255 = x;
        double r2665256 = 1.0;
        double r2665257 = 0.5;
        double r2665258 = r2665255 * r2665257;
        double r2665259 = r2665256 - r2665258;
        double r2665260 = r2665255 * r2665259;
        return r2665260;
}
↓
double f(double x) {
        double r2665261 = 1.0;
        double r2665262 = x;
        double r2665263 = r2665261 * r2665262;
        double r2665264 = 0.5;
        double r2665265 = r2665264 * r2665262;
        double r2665266 = -r2665262;
        double r2665267 = r2665265 * r2665266;
        double r2665268 = r2665263 + r2665267;
        return r2665268;
}

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-rgt-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  (* x (- 1.0 (* x 0.5))))