Average Error: 0.0 → 0.0
Time: 886.0ms
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 r32389 = x;
        double r32390 = 1.0;
        double r32391 = 0.5;
        double r32392 = r32389 * r32391;
        double r32393 = r32390 - r32392;
        double r32394 = r32389 * r32393;
        return r32394;
}
↓
double f(double x) {
        double r32395 = x;
        double r32396 = 1.0;
        double r32397 = r32395 * r32396;
        double r32398 = 0.5;
        double r32399 = r32395 * r32398;
        double r32400 = -r32399;
        double r32401 = r32395 * r32400;
        double r32402 = r32397 + r32401;
        return r32402;
}

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 2020021 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))