Average Error: 0.0 → 0.0
Time: 15.1s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \sqrt[3]{\left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x + 1} \cdot \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x + 1}\right) \cdot \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x + 1}}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \sqrt[3]{\left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x + 1} \cdot \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x + 1}\right) \cdot \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x + 1}}
double f(double x) {
        double r4644525 = x;
        double r4644526 = 2.30753;
        double r4644527 = 0.27061;
        double r4644528 = r4644525 * r4644527;
        double r4644529 = r4644526 + r4644528;
        double r4644530 = 1.0;
        double r4644531 = 0.99229;
        double r4644532 = 0.04481;
        double r4644533 = r4644525 * r4644532;
        double r4644534 = r4644531 + r4644533;
        double r4644535 = r4644534 * r4644525;
        double r4644536 = r4644530 + r4644535;
        double r4644537 = r4644529 / r4644536;
        double r4644538 = r4644525 - r4644537;
        return r4644538;
}
↓
double f(double x) {
        double r4644539 = x;
        double r4644540 = 2.30753;
        double r4644541 = 0.27061;
        double r4644542 = r4644539 * r4644541;
        double r4644543 = r4644540 + r4644542;
        double r4644544 = 0.04481;
        double r4644545 = r4644544 * r4644539;
        double r4644546 = 0.99229;
        double r4644547 = r4644545 + r4644546;
        double r4644548 = r4644547 * r4644539;
        double r4644549 = 1.0;
        double r4644550 = r4644548 + r4644549;
        double r4644551 = r4644543 / r4644550;
        double r4644552 = r4644551 * r4644551;
        double r4644553 = r4644552 * r4644551;
        double r4644554 = cbrt(r4644553);
        double r4644555 = r4644539 - r4644554;
        return r4644555;
}

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 add-cbrt-cube0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 
(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)))))