Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \left(\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}} - x\right)\]
0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)
↓
0.707110000000000016 \cdot \left(\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}} - x\right)
double f(double x) {
        double r139694 = 0.70711;
        double r139695 = 2.30753;
        double r139696 = x;
        double r139697 = 0.27061;
        double r139698 = r139696 * r139697;
        double r139699 = r139695 + r139698;
        double r139700 = 1.0;
        double r139701 = 0.99229;
        double r139702 = 0.04481;
        double r139703 = r139696 * r139702;
        double r139704 = r139701 + r139703;
        double r139705 = r139696 * r139704;
        double r139706 = r139700 + r139705;
        double r139707 = r139699 / r139706;
        double r139708 = r139707 - r139696;
        double r139709 = r139694 * r139708;
        return r139709;
}
↓
double f(double x) {
        double r139710 = 0.70711;
        double r139711 = 2.30753;
        double r139712 = x;
        double r139713 = 0.27061;
        double r139714 = r139712 * r139713;
        double r139715 = r139711 + r139714;
        double r139716 = 1.0;
        double r139717 = 0.99229;
        double r139718 = 0.04481;
        double r139719 = r139712 * r139718;
        double r139720 = r139717 + r139719;
        double r139721 = r139712 * r139720;
        double r139722 = r139716 + r139721;
        double r139723 = r139715 / r139722;
        double r139724 = 3.0;
        double r139725 = pow(r139723, r139724);
        double r139726 = cbrt(r139725);
        double r139727 = r139726 - r139712;
        double r139728 = r139710 * r139727;
        return r139728;
}

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

    \[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto 0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{\color{blue}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)}}} - x\right)\]

  4. Applied add-cbrt-cube21.5

    \[\leadsto 0.707110000000000016 \cdot \left(\frac{\color{blue}{\sqrt[3]{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)}} - x\right)\]

  5. Applied cbrt-undiv21.5

    \[\leadsto 0.707110000000000016 \cdot \left(\color{blue}{\sqrt[3]{\frac{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}{\left(\left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)}}} - x\right)\]

  6. Simplified0.0

    \[\leadsto 0.707110000000000016 \cdot \left(\sqrt[3]{\color{blue}{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}}} - x\right)\]

  7. Final simplification0.0

    \[\leadsto 0.707110000000000016 \cdot \left(\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}} - x\right)\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x)))