Average Error: 0.0 → 0.0
Time: 6.2s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x + 1}\]
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}{\left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x + 1}
double f(double x) {
        double r3644891 = x;
        double r3644892 = 2.30753;
        double r3644893 = 0.27061;
        double r3644894 = r3644891 * r3644893;
        double r3644895 = r3644892 + r3644894;
        double r3644896 = 1.0;
        double r3644897 = 0.99229;
        double r3644898 = 0.04481;
        double r3644899 = r3644891 * r3644898;
        double r3644900 = r3644897 + r3644899;
        double r3644901 = r3644900 * r3644891;
        double r3644902 = r3644896 + r3644901;
        double r3644903 = r3644895 / r3644902;
        double r3644904 = r3644891 - r3644903;
        return r3644904;
}
↓
double f(double x) {
        double r3644905 = x;
        double r3644906 = 2.30753;
        double r3644907 = 0.27061;
        double r3644908 = r3644905 * r3644907;
        double r3644909 = r3644906 + r3644908;
        double r3644910 = 0.04481;
        double r3644911 = r3644910 * r3644905;
        double r3644912 = 0.99229;
        double r3644913 = r3644911 + r3644912;
        double r3644914 = r3644913 * r3644905;
        double r3644915 = 1.0;
        double r3644916 = r3644914 + r3644915;
        double r3644917 = r3644909 / r3644916;
        double r3644918 = r3644905 - r3644917;
        return r3644918;
}

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

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

Reproduce

herbie shell --seed 2019171 
(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)))))