Average Error: 0.0 → 0.0
Time: 13.6s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
double f(double x) {
        double r82329 = x;
        double r82330 = 2.30753;
        double r82331 = 0.27061;
        double r82332 = r82329 * r82331;
        double r82333 = r82330 + r82332;
        double r82334 = 1.0;
        double r82335 = 0.99229;
        double r82336 = 0.04481;
        double r82337 = r82329 * r82336;
        double r82338 = r82335 + r82337;
        double r82339 = r82338 * r82329;
        double r82340 = r82334 + r82339;
        double r82341 = r82333 / r82340;
        double r82342 = r82329 - r82341;
        return r82342;
}
↓
double f(double x) {
        double r82343 = x;
        double r82344 = 2.30753;
        double r82345 = 0.27061;
        double r82346 = r82343 * r82345;
        double r82347 = r82344 + r82346;
        double r82348 = 1.0;
        double r82349 = 1.0;
        double r82350 = 0.99229;
        double r82351 = 0.04481;
        double r82352 = r82343 * r82351;
        double r82353 = r82350 + r82352;
        double r82354 = r82353 * r82343;
        double r82355 = r82349 + r82354;
        double r82356 = r82348 / r82355;
        double r82357 = r82347 * r82356;
        double r82358 = r82343 - r82357;
        return r82358;
}

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. Using strategy rm

  3. Applied div-inv0.0

    \[\leadsto x - \color{blue}{\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}}\]

  4. Final simplification0.0

    \[\leadsto x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]

Reproduce

herbie shell --seed 2019305 
(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)))))