Average Error: 0.0 → 0.0
Time: 906.0ms
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 r60309 = x;
        double r60310 = 1.0;
        double r60311 = 0.5;
        double r60312 = r60309 * r60311;
        double r60313 = r60310 - r60312;
        double r60314 = r60309 * r60313;
        return r60314;
}
↓
double f(double x) {
        double r60315 = x;
        double r60316 = 1.0;
        double r60317 = r60315 * r60316;
        double r60318 = 0.5;
        double r60319 = r60315 * r60318;
        double r60320 = -r60319;
        double r60321 = r60315 * r60320;
        double r60322 = r60317 + r60321;
        return r60322;
}

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 2020002 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))