Average Error: 0.0 → 0.0
Time: 17.6s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
double f(double x) {
        double r78918 = x;
        double r78919 = 2.30753;
        double r78920 = 0.27061;
        double r78921 = r78918 * r78920;
        double r78922 = r78919 + r78921;
        double r78923 = 1.0;
        double r78924 = 0.99229;
        double r78925 = 0.04481;
        double r78926 = r78918 * r78925;
        double r78927 = r78924 + r78926;
        double r78928 = r78927 * r78918;
        double r78929 = r78923 + r78928;
        double r78930 = r78922 / r78929;
        double r78931 = r78918 - r78930;
        return r78931;
}
↓
double f(double x) {
        double r78932 = x;
        double r78933 = 2.30753;
        double r78934 = 0.27061;
        double r78935 = r78932 * r78934;
        double r78936 = r78933 + r78935;
        double r78937 = 1.0;
        double r78938 = 1.0;
        double r78939 = 0.99229;
        double r78940 = 0.04481;
        double r78941 = r78932 * r78940;
        double r78942 = r78939 + r78941;
        double r78943 = r78942 * r78932;
        double r78944 = r78938 + r78943;
        double r78945 = r78937 / r78944;
        double r78946 = r78936 * r78945;
        double r78947 = r78932 - r78946;
        return r78947;
}

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

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

Reproduce

herbie shell --seed 2019323 
(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)))))