Average Error: 0.0 → 0.0
Time: 3.2s
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 r126313 = x;
        double r126314 = 2.30753;
        double r126315 = 0.27061;
        double r126316 = r126313 * r126315;
        double r126317 = r126314 + r126316;
        double r126318 = 1.0;
        double r126319 = 0.99229;
        double r126320 = 0.04481;
        double r126321 = r126313 * r126320;
        double r126322 = r126319 + r126321;
        double r126323 = r126322 * r126313;
        double r126324 = r126318 + r126323;
        double r126325 = r126317 / r126324;
        double r126326 = r126313 - r126325;
        return r126326;
}
↓
double f(double x) {
        double r126327 = x;
        double r126328 = 2.30753;
        double r126329 = 0.27061;
        double r126330 = r126327 * r126329;
        double r126331 = r126328 + r126330;
        double r126332 = 1.0;
        double r126333 = 0.99229;
        double r126334 = 0.04481;
        double r126335 = r126327 * r126334;
        double r126336 = r126333 + r126335;
        double r126337 = r126336 * r126327;
        double r126338 = r126332 + r126337;
        double r126339 = r126331 / r126338;
        double r126340 = r126327 - r126339;
        return r126340;
}

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 2019356 
(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)))))