Average Error: 0.0 → 0.0
Time: 18.6s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \sqrt[3]{\left(x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)\right) \cdot \left(\left(x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)\right) \cdot \left(x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)\right)\right)}} - x\right)\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \sqrt[3]{\left(x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)\right) \cdot \left(\left(x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)\right) \cdot \left(x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)\right)\right)}} - x\right)
double f(double x) {
        double r5601711 = 0.70711;
        double r5601712 = 2.30753;
        double r5601713 = x;
        double r5601714 = 0.27061;
        double r5601715 = r5601713 * r5601714;
        double r5601716 = r5601712 + r5601715;
        double r5601717 = 1.0;
        double r5601718 = 0.99229;
        double r5601719 = 0.04481;
        double r5601720 = r5601713 * r5601719;
        double r5601721 = r5601718 + r5601720;
        double r5601722 = r5601713 * r5601721;
        double r5601723 = r5601717 + r5601722;
        double r5601724 = r5601716 / r5601723;
        double r5601725 = r5601724 - r5601713;
        double r5601726 = r5601711 * r5601725;
        return r5601726;
}
↓
double f(double x) {
        double r5601727 = 0.70711;
        double r5601728 = 2.30753;
        double r5601729 = x;
        double r5601730 = 0.27061;
        double r5601731 = r5601729 * r5601730;
        double r5601732 = r5601728 + r5601731;
        double r5601733 = 1.0;
        double r5601734 = 0.04481;
        double r5601735 = r5601734 * r5601729;
        double r5601736 = 0.99229;
        double r5601737 = r5601735 + r5601736;
        double r5601738 = r5601729 * r5601737;
        double r5601739 = r5601738 * r5601738;
        double r5601740 = r5601738 * r5601739;
        double r5601741 = cbrt(r5601740);
        double r5601742 = r5601733 + r5601741;
        double r5601743 = r5601732 / r5601742;
        double r5601744 = r5601743 - r5601729;
        double r5601745 = r5601727 * r5601744;
        return r5601745;
}

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

    \[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \color{blue}{\sqrt[3]{\left(\left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right) \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}}} - x\right)\]

  4. Applied add-cbrt-cube0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \color{blue}{\sqrt[3]{\left(x \cdot x\right) \cdot x}} \cdot \sqrt[3]{\left(\left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right) \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}} - x\right)\]

  5. Applied cbrt-unprod0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \color{blue}{\sqrt[3]{\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(\left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right) \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)}}} - x\right)\]

  6. Simplified0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \sqrt[3]{\color{blue}{\left(\left(\left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x\right) \cdot \left(\left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x\right)\right) \cdot \left(\left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot x\right)}}} - x\right)\]

  7. Final simplification0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \sqrt[3]{\left(x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)\right) \cdot \left(\left(x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)\right) \cdot \left(x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)\right)\right)}} - x\right)\]

Reproduce

herbie shell --seed 2019170 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))