Average Error: 0.0 → 0.0
Time: 15.0s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061}{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\]
↓
\[x - \frac{1}{\frac{x \cdot \left(0.99229 + 0.04481 \cdot x\right) + 1.0}{x \cdot 0.27061 + 2.30753}}\]
x - \frac{2.30753 + x \cdot 0.27061}{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}
↓
x - \frac{1}{\frac{x \cdot \left(0.99229 + 0.04481 \cdot x\right) + 1.0}{x \cdot 0.27061 + 2.30753}}
double f(double x) {
        double r4866683 = x;
        double r4866684 = 2.30753;
        double r4866685 = 0.27061;
        double r4866686 = r4866683 * r4866685;
        double r4866687 = r4866684 + r4866686;
        double r4866688 = 1.0;
        double r4866689 = 0.99229;
        double r4866690 = 0.04481;
        double r4866691 = r4866683 * r4866690;
        double r4866692 = r4866689 + r4866691;
        double r4866693 = r4866692 * r4866683;
        double r4866694 = r4866688 + r4866693;
        double r4866695 = r4866687 / r4866694;
        double r4866696 = r4866683 - r4866695;
        return r4866696;
}
↓
double f(double x) {
        double r4866697 = x;
        double r4866698 = 1.0;
        double r4866699 = 0.99229;
        double r4866700 = 0.04481;
        double r4866701 = r4866700 * r4866697;
        double r4866702 = r4866699 + r4866701;
        double r4866703 = r4866697 * r4866702;
        double r4866704 = 1.0;
        double r4866705 = r4866703 + r4866704;
        double r4866706 = 0.27061;
        double r4866707 = r4866697 * r4866706;
        double r4866708 = 2.30753;
        double r4866709 = r4866707 + r4866708;
        double r4866710 = r4866705 / r4866709;
        double r4866711 = r4866698 / r4866710;
        double r4866712 = r4866697 - r4866711;
        return r4866712;
}

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

    \[x - \frac{2.30753 + x \cdot 0.27061}{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\]
  2. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto x - \color{blue}{\frac{1}{\frac{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}{2.30753 + x \cdot 0.27061}}}\]

  4. Final simplification0.0

    \[\leadsto x - \frac{1}{\frac{x \cdot \left(0.99229 + 0.04481 \cdot x\right) + 1.0}{x \cdot 0.27061 + 2.30753}}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))