Average Error: 0.0 → 0.0
Time: 15.5s
Precision: 64
\[x \cdot \left(1.0 - x \cdot 0.5\right)\]
↓
\[x \cdot 1.0 + \left(-0.5 \cdot x\right) \cdot x\]
x \cdot \left(1.0 - x \cdot 0.5\right)
↓
x \cdot 1.0 + \left(-0.5 \cdot x\right) \cdot x
double f(double x) {
        double r2999782 = x;
        double r2999783 = 1.0;
        double r2999784 = 0.5;
        double r2999785 = r2999782 * r2999784;
        double r2999786 = r2999783 - r2999785;
        double r2999787 = r2999782 * r2999786;
        return r2999787;
}
↓
double f(double x) {
        double r2999788 = x;
        double r2999789 = 1.0;
        double r2999790 = r2999788 * r2999789;
        double r2999791 = 0.5;
        double r2999792 = r2999791 * r2999788;
        double r2999793 = -r2999792;
        double r2999794 = r2999793 * r2999788;
        double r2999795 = r2999790 + r2999794;
        return r2999795;
}

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

    \[x \cdot \left(1.0 - x \cdot 0.5\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto x \cdot \color{blue}{\left(1.0 + \left(-x \cdot 0.5\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{x \cdot 1.0 + x \cdot \left(-x \cdot 0.5\right)}\]

  5. Final simplification0.0

    \[\leadsto x \cdot 1.0 + \left(-0.5 \cdot x\right) \cdot x\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  (* x (- 1.0 (* x 0.5))))