Average Error: 9.9 → 9.9
Time: 9.1s
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 r66878 = 1.0;
        double r66879 = Om;
        double r66880 = Omc;
        double r66881 = r66879 / r66880;
        double r66882 = 2.0;
        double r66883 = pow(r66881, r66882);
        double r66884 = r66878 - r66883;
        double r66885 = t;
        double r66886 = l;
        double r66887 = r66885 / r66886;
        double r66888 = pow(r66887, r66882);
        double r66889 = r66882 * r66888;
        double r66890 = r66878 + r66889;
        double r66891 = r66884 / r66890;
        double r66892 = sqrt(r66891);
        double r66893 = asin(r66892);
        return r66893;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r66894 = 1.0;
        double r66895 = Om;
        double r66896 = Omc;
        double r66897 = r66895 / r66896;
        double r66898 = 2.0;
        double r66899 = pow(r66897, r66898);
        double r66900 = r66894 - r66899;
        double r66901 = t;
        double r66902 = l;
        double r66903 = r66901 / r66902;
        double r66904 = pow(r66903, r66898);
        double r66905 = r66898 * r66904;
        double r66906 = r66894 + r66905;
        double r66907 = r66900 / r66906;
        double r66908 = sqrt(r66907);
        double r66909 = asin(r66908);
        return r66909;
}

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 2020065 
(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)))))))