Average Error: 0.0 → 0.0
Time: 869.0ms
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 r40113 = x;
        double r40114 = 1.0;
        double r40115 = 0.5;
        double r40116 = r40113 * r40115;
        double r40117 = r40114 - r40116;
        double r40118 = r40113 * r40117;
        return r40118;
}
↓
double f(double x) {
        double r40119 = x;
        double r40120 = 1.0;
        double r40121 = r40119 * r40120;
        double r40122 = 0.5;
        double r40123 = r40119 * r40122;
        double r40124 = -r40123;
        double r40125 = r40119 * r40124;
        double r40126 = r40121 + r40125;
        return r40126;
}

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 2020036 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))