Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)}
double f(double x) {
        double r4675724 = x;
        double r4675725 = 2.30753;
        double r4675726 = 0.27061;
        double r4675727 = r4675724 * r4675726;
        double r4675728 = r4675725 + r4675727;
        double r4675729 = 1.0;
        double r4675730 = 0.99229;
        double r4675731 = 0.04481;
        double r4675732 = r4675724 * r4675731;
        double r4675733 = r4675730 + r4675732;
        double r4675734 = r4675733 * r4675724;
        double r4675735 = r4675729 + r4675734;
        double r4675736 = r4675728 / r4675735;
        double r4675737 = r4675724 - r4675736;
        return r4675737;
}
↓
double f(double x) {
        double r4675738 = x;
        double r4675739 = 2.30753;
        double r4675740 = 0.27061;
        double r4675741 = r4675738 * r4675740;
        double r4675742 = r4675739 + r4675741;
        double r4675743 = 1.0;
        double r4675744 = 1.0;
        double r4675745 = 0.04481;
        double r4675746 = r4675738 * r4675745;
        double r4675747 = 0.99229;
        double r4675748 = r4675746 + r4675747;
        double r4675749 = r4675738 * r4675748;
        double r4675750 = r4675744 + r4675749;
        double r4675751 = r4675743 / r4675750;
        double r4675752 = r4675742 * r4675751;
        double r4675753 = r4675738 - r4675752;
        return r4675753;
}

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. Using strategy rm

  3. Applied div-inv0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))