Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
double f(double x) {
        double r111622 = x;
        double r111623 = 2.30753;
        double r111624 = 0.27061;
        double r111625 = r111622 * r111624;
        double r111626 = r111623 + r111625;
        double r111627 = 1.0;
        double r111628 = 0.99229;
        double r111629 = 0.04481;
        double r111630 = r111622 * r111629;
        double r111631 = r111628 + r111630;
        double r111632 = r111631 * r111622;
        double r111633 = r111627 + r111632;
        double r111634 = r111626 / r111633;
        double r111635 = r111622 - r111634;
        return r111635;
}
↓
double f(double x) {
        double r111636 = x;
        double r111637 = 2.30753;
        double r111638 = 0.27061;
        double r111639 = r111636 * r111638;
        double r111640 = r111637 + r111639;
        double r111641 = 1.0;
        double r111642 = 0.99229;
        double r111643 = 0.04481;
        double r111644 = r111636 * r111643;
        double r111645 = r111642 + r111644;
        double r111646 = r111645 * r111636;
        double r111647 = r111641 + r111646;
        double r111648 = r111640 / r111647;
        double r111649 = r111636 - r111648;
        return r111649;
}

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

    \[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]

  2. Final simplification0.0

    \[\leadsto x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(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)))))