Average Error: 0.0 → 0.0
Time: 860.0ms
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 r43134 = x;
        double r43135 = 1.0;
        double r43136 = 0.5;
        double r43137 = r43134 * r43136;
        double r43138 = r43135 - r43137;
        double r43139 = r43134 * r43138;
        return r43139;
}
↓
double f(double x) {
        double r43140 = x;
        double r43141 = 1.0;
        double r43142 = r43140 * r43141;
        double r43143 = 0.5;
        double r43144 = r43140 * r43143;
        double r43145 = -r43144;
        double r43146 = r43140 * r43145;
        double r43147 = r43142 + r43146;
        return r43147;
}

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))))