Average Error: 0.0 → 0.0
Time: 18.6s
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 r69802 = x;
        double r69803 = 2.30753;
        double r69804 = 0.27061;
        double r69805 = r69802 * r69804;
        double r69806 = r69803 + r69805;
        double r69807 = 1.0;
        double r69808 = 0.99229;
        double r69809 = 0.04481;
        double r69810 = r69802 * r69809;
        double r69811 = r69808 + r69810;
        double r69812 = r69811 * r69802;
        double r69813 = r69807 + r69812;
        double r69814 = r69806 / r69813;
        double r69815 = r69802 - r69814;
        return r69815;
}
↓
double f(double x) {
        double r69816 = x;
        double r69817 = 2.30753;
        double r69818 = 0.27061;
        double r69819 = r69816 * r69818;
        double r69820 = r69817 + r69819;
        double r69821 = 1.0;
        double r69822 = 0.99229;
        double r69823 = 0.04481;
        double r69824 = r69816 * r69823;
        double r69825 = r69822 + r69824;
        double r69826 = r69825 * r69816;
        double r69827 = r69821 + r69826;
        double r69828 = r69820 / r69827;
        double r69829 = r69816 - r69828;
        return r69829;
}

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 2019306 +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)))))