Average Error: 9.9 → 9.9
Time: 10.0s
Precision: 64
\[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]
↓
\[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]
\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)
↓
\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)
double f(double t, double l, double Om, double Omc) {
        double r79831 = 1.0;
        double r79832 = Om;
        double r79833 = Omc;
        double r79834 = r79832 / r79833;
        double r79835 = 2.0;
        double r79836 = pow(r79834, r79835);
        double r79837 = r79831 - r79836;
        double r79838 = t;
        double r79839 = l;
        double r79840 = r79838 / r79839;
        double r79841 = pow(r79840, r79835);
        double r79842 = r79835 * r79841;
        double r79843 = r79831 + r79842;
        double r79844 = r79837 / r79843;
        double r79845 = sqrt(r79844);
        double r79846 = asin(r79845);
        return r79846;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r79847 = 1.0;
        double r79848 = Om;
        double r79849 = Omc;
        double r79850 = r79848 / r79849;
        double r79851 = 2.0;
        double r79852 = pow(r79850, r79851);
        double r79853 = r79847 - r79852;
        double r79854 = t;
        double r79855 = l;
        double r79856 = r79854 / r79855;
        double r79857 = pow(r79856, r79851);
        double r79858 = r79851 * r79857;
        double r79859 = r79847 + r79858;
        double r79860 = r79853 / r79859;
        double r79861 = sqrt(r79860);
        double r79862 = asin(r79861);
        return r79862;
}

Error

Bits error versus t

Bits error versus l

Bits error versus Om

Bits error versus Omc

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 9.9

    \[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]

  2. Final simplification9.9

    \[\leadsto \sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]

Reproduce

herbie shell --seed 2020024 
(FPCore (t l Om Omc)
  :name "Toniolo and Linder, Equation (2)"
  :precision binary64
  (asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2)))))))