Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \left(\frac{2.30753 + x \cdot 0.27061000000000002}{\left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)} \cdot 1\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \left(\frac{2.30753 + x \cdot 0.27061000000000002}{\left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)} \cdot 1\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)
double f(double x) {
        double r82608 = x;
        double r82609 = 2.30753;
        double r82610 = 0.27061;
        double r82611 = r82608 * r82610;
        double r82612 = r82609 + r82611;
        double r82613 = 1.0;
        double r82614 = 0.99229;
        double r82615 = 0.04481;
        double r82616 = r82608 * r82615;
        double r82617 = r82614 + r82616;
        double r82618 = r82617 * r82608;
        double r82619 = r82613 + r82618;
        double r82620 = r82612 / r82619;
        double r82621 = r82608 - r82620;
        return r82621;
}
↓
double f(double x) {
        double r82622 = x;
        double r82623 = 2.30753;
        double r82624 = 0.27061;
        double r82625 = r82622 * r82624;
        double r82626 = r82623 + r82625;
        double r82627 = 1.0;
        double r82628 = 0.99229;
        double r82629 = 0.04481;
        double r82630 = r82622 * r82629;
        double r82631 = r82628 + r82630;
        double r82632 = r82631 * r82622;
        double r82633 = r82627 + r82632;
        double r82634 = r82633 * r82626;
        double r82635 = r82626 / r82634;
        double r82636 = 1.0;
        double r82637 = r82635 * r82636;
        double r82638 = r82637 * r82626;
        double r82639 = r82622 - r82638;
        return r82639;
}

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 flip-+15.9

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

  4. Applied associate-/l/15.9

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

  6. Applied flip--15.9

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

  7. Applied associate-*r/16.0

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

  8. Applied associate-/r/16.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020049 
(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)))))