Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[x \cdot \left(1 - x \cdot 0.5\right)\]
↓
\[1 \cdot x + \left(-0.5 \cdot {x}^{2}\right)\]
x \cdot \left(1 - x \cdot 0.5\right)
↓
1 \cdot x + \left(-0.5 \cdot {x}^{2}\right)
double f(double x) {
        double r52905 = x;
        double r52906 = 1.0;
        double r52907 = 0.5;
        double r52908 = r52905 * r52907;
        double r52909 = r52906 - r52908;
        double r52910 = r52905 * r52909;
        return r52910;
}
↓
double f(double x) {
        double r52911 = 1.0;
        double r52912 = x;
        double r52913 = r52911 * r52912;
        double r52914 = 0.5;
        double r52915 = 2.0;
        double r52916 = pow(r52912, r52915);
        double r52917 = r52914 * r52916;
        double r52918 = -r52917;
        double r52919 = r52913 + r52918;
        return r52919;
}

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. Simplified0.0

    \[\leadsto \color{blue}{1 \cdot x} + x \cdot \left(-x \cdot 0.5\right)\]

  6. Simplified0.0

    \[\leadsto 1 \cdot x + \color{blue}{\left(-0.5 \cdot {x}^{2}\right)}\]

  7. Final simplification0.0

    \[\leadsto 1 \cdot x + \left(-0.5 \cdot {x}^{2}\right)\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (- 1 (* x 0.5))))