Average Error: 0.0 → 0.0
Time: 1.9s
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 r90613 = x;
        double r90614 = 2.30753;
        double r90615 = 0.27061;
        double r90616 = r90613 * r90615;
        double r90617 = r90614 + r90616;
        double r90618 = 1.0;
        double r90619 = 0.99229;
        double r90620 = 0.04481;
        double r90621 = r90613 * r90620;
        double r90622 = r90619 + r90621;
        double r90623 = r90622 * r90613;
        double r90624 = r90618 + r90623;
        double r90625 = r90617 / r90624;
        double r90626 = r90613 - r90625;
        return r90626;
}
↓
double f(double x) {
        double r90627 = x;
        double r90628 = 2.30753;
        double r90629 = 0.27061;
        double r90630 = r90627 * r90629;
        double r90631 = r90628 + r90630;
        double r90632 = 1.0;
        double r90633 = 1.0;
        double r90634 = 0.99229;
        double r90635 = 0.04481;
        double r90636 = r90627 * r90635;
        double r90637 = r90634 + r90636;
        double r90638 = r90637 * r90627;
        double r90639 = r90633 + r90638;
        double r90640 = r90632 / r90639;
        double r90641 = r90631 * r90640;
        double r90642 = r90627 - r90641;
        return r90642;
}

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 2020062 
(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)))))