Average Error: 0.0 → 0.0
Time: 1.1s
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 r84530 = x;
        double r84531 = 1.0;
        double r84532 = 0.5;
        double r84533 = r84530 * r84532;
        double r84534 = r84531 - r84533;
        double r84535 = r84530 * r84534;
        return r84535;
}
↓
double f(double x) {
        double r84536 = x;
        double r84537 = 1.0;
        double r84538 = r84536 * r84537;
        double r84539 = 0.5;
        double r84540 = r84536 * r84539;
        double r84541 = -r84540;
        double r84542 = r84536 * r84541;
        double r84543 = r84538 + r84542;
        return r84543;
}

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 2020081 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))