Average Error: 0.0 → 0.0
Time: 12.5s
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 r52595 = x;
        double r52596 = 2.30753;
        double r52597 = 0.27061;
        double r52598 = r52595 * r52597;
        double r52599 = r52596 + r52598;
        double r52600 = 1.0;
        double r52601 = 0.99229;
        double r52602 = 0.04481;
        double r52603 = r52595 * r52602;
        double r52604 = r52601 + r52603;
        double r52605 = r52604 * r52595;
        double r52606 = r52600 + r52605;
        double r52607 = r52599 / r52606;
        double r52608 = r52595 - r52607;
        return r52608;
}
↓
double f(double x) {
        double r52609 = x;
        double r52610 = 2.30753;
        double r52611 = 0.27061;
        double r52612 = r52609 * r52611;
        double r52613 = r52610 + r52612;
        double r52614 = 1.0;
        double r52615 = 0.99229;
        double r52616 = 0.04481;
        double r52617 = r52609 * r52616;
        double r52618 = r52615 + r52617;
        double r52619 = r52618 * r52609;
        double r52620 = r52614 + r52619;
        double r52621 = r52613 / r52620;
        double r52622 = r52609 - r52621;
        return r52622;
}

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 2019304 +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)))))