Average Error: 0.0 → 0.0
Time: 20.4s
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 r5929457 = x;
        double r5929458 = 2.30753;
        double r5929459 = 0.27061;
        double r5929460 = r5929457 * r5929459;
        double r5929461 = r5929458 + r5929460;
        double r5929462 = 1.0;
        double r5929463 = 0.99229;
        double r5929464 = 0.04481;
        double r5929465 = r5929457 * r5929464;
        double r5929466 = r5929463 + r5929465;
        double r5929467 = r5929466 * r5929457;
        double r5929468 = r5929462 + r5929467;
        double r5929469 = r5929461 / r5929468;
        double r5929470 = r5929457 - r5929469;
        return r5929470;
}
↓
double f(double x) {
        double r5929471 = x;
        double r5929472 = 2.30753;
        double r5929473 = 0.27061;
        double r5929474 = r5929471 * r5929473;
        double r5929475 = r5929472 + r5929474;
        double r5929476 = 0.04481;
        double r5929477 = r5929476 * r5929471;
        double r5929478 = 0.99229;
        double r5929479 = r5929477 + r5929478;
        double r5929480 = r5929479 * r5929471;
        double r5929481 = 1.0;
        double r5929482 = r5929480 + r5929481;
        double r5929483 = r5929475 / r5929482;
        double r5929484 = r5929471 - r5929483;
        return r5929484;
}

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 2019168 
(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)))))