Average Error: 0.0 → 0.0
Time: 844.0ms
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 r59510 = x;
        double r59511 = 1.0;
        double r59512 = 0.5;
        double r59513 = r59510 * r59512;
        double r59514 = r59511 - r59513;
        double r59515 = r59510 * r59514;
        return r59515;
}
↓
double f(double x) {
        double r59516 = x;
        double r59517 = 1.0;
        double r59518 = r59516 * r59517;
        double r59519 = 0.5;
        double r59520 = r59516 * r59519;
        double r59521 = -r59520;
        double r59522 = r59516 * r59521;
        double r59523 = r59518 + r59522;
        return r59523;
}

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 2020062 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))