Average Error: 0.0 → 0.0
Time: 14.0s
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 r6434062 = x;
        double r6434063 = 2.30753;
        double r6434064 = 0.27061;
        double r6434065 = r6434062 * r6434064;
        double r6434066 = r6434063 + r6434065;
        double r6434067 = 1.0;
        double r6434068 = 0.99229;
        double r6434069 = 0.04481;
        double r6434070 = r6434062 * r6434069;
        double r6434071 = r6434068 + r6434070;
        double r6434072 = r6434071 * r6434062;
        double r6434073 = r6434067 + r6434072;
        double r6434074 = r6434066 / r6434073;
        double r6434075 = r6434062 - r6434074;
        return r6434075;
}
↓
double f(double x) {
        double r6434076 = x;
        double r6434077 = 2.30753;
        double r6434078 = 0.27061;
        double r6434079 = r6434076 * r6434078;
        double r6434080 = r6434077 + r6434079;
        double r6434081 = 1.0;
        double r6434082 = 0.99229;
        double r6434083 = 0.04481;
        double r6434084 = r6434076 * r6434083;
        double r6434085 = r6434082 + r6434084;
        double r6434086 = r6434085 * r6434076;
        double r6434087 = r6434081 + r6434086;
        double r6434088 = r6434080 / r6434087;
        double r6434089 = r6434076 - r6434088;
        return r6434089;
}

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 2019174 +o rules:numerics
(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)))))