Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
double f(double x) {
        double r102617 = x;
        double r102618 = 2.30753;
        double r102619 = 0.27061;
        double r102620 = r102617 * r102619;
        double r102621 = r102618 + r102620;
        double r102622 = 1.0;
        double r102623 = 0.99229;
        double r102624 = 0.04481;
        double r102625 = r102617 * r102624;
        double r102626 = r102623 + r102625;
        double r102627 = r102626 * r102617;
        double r102628 = r102622 + r102627;
        double r102629 = r102621 / r102628;
        double r102630 = r102617 - r102629;
        return r102630;
}
↓
double f(double x) {
        double r102631 = x;
        double r102632 = 2.30753;
        double r102633 = 0.27061;
        double r102634 = r102631 * r102633;
        double r102635 = r102632 + r102634;
        double r102636 = 1.0;
        double r102637 = 1.0;
        double r102638 = 0.99229;
        double r102639 = 0.04481;
        double r102640 = r102631 * r102639;
        double r102641 = r102638 + r102640;
        double r102642 = r102641 * r102631;
        double r102643 = r102637 + r102642;
        double r102644 = r102636 / r102643;
        double r102645 = r102635 * r102644;
        double r102646 = r102631 - r102645;
        return r102646;
}

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

    \[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
  2. Using strategy rm

  3. Applied div-inv0.0

    \[\leadsto x - \color{blue}{\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}\]

  4. Final simplification0.0

    \[\leadsto x - \left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* (+ 0.99229 (* x 0.04481)) x)))))