Average Error: 0.0 → 0.1
Time: 10.2s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \frac{\frac{1}{\frac{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}{2.30753 + x \cdot 0.27061000000000002}}}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \frac{\frac{1}{\frac{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}{2.30753 + x \cdot 0.27061000000000002}}}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}
double f(double x) {
        double r77617 = x;
        double r77618 = 2.30753;
        double r77619 = 0.27061;
        double r77620 = r77617 * r77619;
        double r77621 = r77618 + r77620;
        double r77622 = 1.0;
        double r77623 = 0.99229;
        double r77624 = 0.04481;
        double r77625 = r77617 * r77624;
        double r77626 = r77623 + r77625;
        double r77627 = r77626 * r77617;
        double r77628 = r77622 + r77627;
        double r77629 = r77621 / r77628;
        double r77630 = r77617 - r77629;
        return r77630;
}
↓
double f(double x) {
        double r77631 = x;
        double r77632 = 1.0;
        double r77633 = 1.0;
        double r77634 = 0.99229;
        double r77635 = 0.04481;
        double r77636 = r77631 * r77635;
        double r77637 = r77634 + r77636;
        double r77638 = r77637 * r77631;
        double r77639 = r77633 + r77638;
        double r77640 = sqrt(r77639);
        double r77641 = 2.30753;
        double r77642 = 0.27061;
        double r77643 = r77631 * r77642;
        double r77644 = r77641 + r77643;
        double r77645 = r77640 / r77644;
        double r77646 = r77632 / r77645;
        double r77647 = r77646 / r77640;
        double r77648 = r77631 - r77647;
        return r77648;
}

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 add-sqr-sqrt0.1

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

  4. Applied associate-/r*0.1

    \[\leadsto x - \color{blue}{\frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}}\]
  5. Using strategy rm

  6. Applied clear-num0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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)))))