Average Error: 10.6 → 10.6
Time: 25.8s
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 r60897 = 1.0;
        double r60898 = Om;
        double r60899 = Omc;
        double r60900 = r60898 / r60899;
        double r60901 = 2.0;
        double r60902 = pow(r60900, r60901);
        double r60903 = r60897 - r60902;
        double r60904 = t;
        double r60905 = l;
        double r60906 = r60904 / r60905;
        double r60907 = pow(r60906, r60901);
        double r60908 = r60901 * r60907;
        double r60909 = r60897 + r60908;
        double r60910 = r60903 / r60909;
        double r60911 = sqrt(r60910);
        double r60912 = asin(r60911);
        return r60912;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r60913 = 1.0;
        double r60914 = Om;
        double r60915 = Omc;
        double r60916 = r60914 / r60915;
        double r60917 = 2.0;
        double r60918 = pow(r60916, r60917);
        double r60919 = r60913 - r60918;
        double r60920 = t;
        double r60921 = l;
        double r60922 = r60920 / r60921;
        double r60923 = pow(r60922, r60917);
        double r60924 = r60917 * r60923;
        double r60925 = r60913 + r60924;
        double r60926 = r60919 / r60925;
        double r60927 = sqrt(r60926);
        double r60928 = asin(r60927);
        return r60928;
}

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 10.6

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

  2. Final simplification10.6

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

Reproduce

herbie shell --seed 2019294 
(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)))))))