Average Error: 10.6 → 10.6
Time: 24.8s
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 r63909 = 1.0;
        double r63910 = Om;
        double r63911 = Omc;
        double r63912 = r63910 / r63911;
        double r63913 = 2.0;
        double r63914 = pow(r63912, r63913);
        double r63915 = r63909 - r63914;
        double r63916 = t;
        double r63917 = l;
        double r63918 = r63916 / r63917;
        double r63919 = pow(r63918, r63913);
        double r63920 = r63913 * r63919;
        double r63921 = r63909 + r63920;
        double r63922 = r63915 / r63921;
        double r63923 = sqrt(r63922);
        double r63924 = asin(r63923);
        return r63924;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r63925 = 1.0;
        double r63926 = Om;
        double r63927 = Omc;
        double r63928 = r63926 / r63927;
        double r63929 = 2.0;
        double r63930 = pow(r63928, r63929);
        double r63931 = r63925 - r63930;
        double r63932 = t;
        double r63933 = l;
        double r63934 = r63932 / r63933;
        double r63935 = pow(r63934, r63929);
        double r63936 = r63929 * r63935;
        double r63937 = r63925 + r63936;
        double r63938 = r63931 / r63937;
        double r63939 = sqrt(r63938);
        double r63940 = asin(r63939);
        return r63940;
}

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 2019208 
(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)))))))