Average Error: 0.0 → 0.0
Time: 23.4s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \frac{1}{\sqrt[3]{\left(\frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812} \cdot \frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}\right) \cdot \frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \frac{1}{\sqrt[3]{\left(\frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812} \cdot \frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}\right) \cdot \frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}}
double f(double x) {
        double r10165449 = x;
        double r10165450 = 2.30753;
        double r10165451 = 0.27061;
        double r10165452 = r10165449 * r10165451;
        double r10165453 = r10165450 + r10165452;
        double r10165454 = 1.0;
        double r10165455 = 0.99229;
        double r10165456 = 0.04481;
        double r10165457 = r10165449 * r10165456;
        double r10165458 = r10165455 + r10165457;
        double r10165459 = r10165458 * r10165449;
        double r10165460 = r10165454 + r10165459;
        double r10165461 = r10165453 / r10165460;
        double r10165462 = r10165449 - r10165461;
        return r10165462;
}
↓
double f(double x) {
        double r10165463 = x;
        double r10165464 = 1.0;
        double r10165465 = 1.0;
        double r10165466 = 0.99229;
        double r10165467 = 0.04481;
        double r10165468 = r10165463 * r10165467;
        double r10165469 = r10165466 + r10165468;
        double r10165470 = r10165469 * r10165463;
        double r10165471 = r10165465 + r10165470;
        double r10165472 = 2.30753;
        double r10165473 = 0.27061;
        double r10165474 = r10165463 * r10165473;
        double r10165475 = r10165472 + r10165474;
        double r10165476 = r10165471 / r10165475;
        double r10165477 = r10165476 * r10165476;
        double r10165478 = r10165477 * r10165476;
        double r10165479 = cbrt(r10165478);
        double r10165480 = r10165464 / r10165479;
        double r10165481 = r10165463 - r10165480;
        return r10165481;
}

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 clear-num0.0

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

  5. Applied add-cbrt-cube0.0

    \[\leadsto x - \frac{1}{\color{blue}{\sqrt[3]{\left(\frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812} \cdot \frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}\right) \cdot \frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}}}\]

  6. Final simplification0.0

    \[\leadsto x - \frac{1}{\sqrt[3]{\left(\frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812} \cdot \frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}\right) \cdot \frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}}\]

Reproduce

herbie shell --seed 2019173 
(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)))))