Average Error: 0.0 → 0.0
Time: 11.8s
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 r73758 = x;
        double r73759 = 2.30753;
        double r73760 = 0.27061;
        double r73761 = r73758 * r73760;
        double r73762 = r73759 + r73761;
        double r73763 = 1.0;
        double r73764 = 0.99229;
        double r73765 = 0.04481;
        double r73766 = r73758 * r73765;
        double r73767 = r73764 + r73766;
        double r73768 = r73767 * r73758;
        double r73769 = r73763 + r73768;
        double r73770 = r73762 / r73769;
        double r73771 = r73758 - r73770;
        return r73771;
}
↓
double f(double x) {
        double r73772 = x;
        double r73773 = 2.30753;
        double r73774 = 0.27061;
        double r73775 = r73772 * r73774;
        double r73776 = r73773 + r73775;
        double r73777 = 1.0;
        double r73778 = 0.99229;
        double r73779 = 0.04481;
        double r73780 = r73772 * r73779;
        double r73781 = r73778 + r73780;
        double r73782 = r73781 * r73772;
        double r73783 = r73777 + r73782;
        double r73784 = r73776 / r73783;
        double r73785 = r73772 - r73784;
        return r73785;
}

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 2019212 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061000000000002)) (+ 1 (* (+ 0.992290000000000005 (* x 0.044810000000000003)) x)))))