Average Error: 0.0 → 0.0
Time: 3.5s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(\left(\sqrt[3]{0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469} \cdot \sqrt[3]{0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469}\right) \cdot \sqrt[3]{0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469}\right)} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(\left(\sqrt[3]{0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469} \cdot \sqrt[3]{0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469}\right) \cdot \sqrt[3]{0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469}\right)} - x
double f(double x) {
        double r77629 = 2.30753;
        double r77630 = x;
        double r77631 = 0.27061;
        double r77632 = r77630 * r77631;
        double r77633 = r77629 + r77632;
        double r77634 = 1.0;
        double r77635 = 0.99229;
        double r77636 = 0.04481;
        double r77637 = r77630 * r77636;
        double r77638 = r77635 + r77637;
        double r77639 = r77630 * r77638;
        double r77640 = r77634 + r77639;
        double r77641 = r77633 / r77640;
        double r77642 = r77641 - r77630;
        return r77642;
}
↓
double f(double x) {
        double r77643 = 2.30753;
        double r77644 = x;
        double r77645 = 0.27061;
        double r77646 = r77644 * r77645;
        double r77647 = r77643 + r77646;
        double r77648 = 1.0;
        double r77649 = 0.99229;
        double r77650 = 0.04481;
        double r77651 = r77644 * r77650;
        double r77652 = r77649 + r77651;
        double r77653 = cbrt(r77652);
        double r77654 = r77653 * r77653;
        double r77655 = r77654 * r77653;
        double r77656 = r77644 * r77655;
        double r77657 = r77648 + r77656;
        double r77658 = r77647 / r77657;
        double r77659 = r77658 - r77644;
        return r77659;
}

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

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

  3. Applied add-cube-cbrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019352 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x))