Average Error: 0.0 → 0.0
Time: 9.0s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \frac{\frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} + 0.707110000000000016 \cdot \left(-x\right)\]
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 \frac{\frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} + 0.707110000000000016 \cdot \left(-x\right)
double f(double x) {
        double r131820 = 0.70711;
        double r131821 = 2.30753;
        double r131822 = x;
        double r131823 = 0.27061;
        double r131824 = r131822 * r131823;
        double r131825 = r131821 + r131824;
        double r131826 = 1.0;
        double r131827 = 0.99229;
        double r131828 = 0.04481;
        double r131829 = r131822 * r131828;
        double r131830 = r131827 + r131829;
        double r131831 = r131822 * r131830;
        double r131832 = r131826 + r131831;
        double r131833 = r131825 / r131832;
        double r131834 = r131833 - r131822;
        double r131835 = r131820 * r131834;
        return r131835;
}
↓
double f(double x) {
        double r131836 = 0.70711;
        double r131837 = 2.30753;
        double r131838 = x;
        double r131839 = 0.27061;
        double r131840 = r131838 * r131839;
        double r131841 = r131837 + r131840;
        double r131842 = 1.0;
        double r131843 = 0.99229;
        double r131844 = 0.04481;
        double r131845 = r131838 * r131844;
        double r131846 = r131843 + r131845;
        double r131847 = r131838 * r131846;
        double r131848 = r131842 + r131847;
        double r131849 = cbrt(r131848);
        double r131850 = r131841 / r131849;
        double r131851 = r131850 / r131849;
        double r131852 = r131851 / r131849;
        double r131853 = r131836 * r131852;
        double r131854 = -r131838;
        double r131855 = r131836 * r131854;
        double r131856 = r131853 + r131855;
        return r131856;
}

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 sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  6. Applied add-cube-cbrt0.0

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

  7. Applied *-un-lft-identity0.0

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

  8. Applied times-frac0.0

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

  9. Applied associate-*r*0.0

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

  10. Simplified0.0

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

  12. Applied div-inv0.0

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

  13. Applied associate-*l*0.0

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

  14. Simplified0.0

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

  15. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 
(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)))