Average Error: 10.2 → 10.2
Time: 8.5s
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 r66813 = 1.0;
        double r66814 = Om;
        double r66815 = Omc;
        double r66816 = r66814 / r66815;
        double r66817 = 2.0;
        double r66818 = pow(r66816, r66817);
        double r66819 = r66813 - r66818;
        double r66820 = t;
        double r66821 = l;
        double r66822 = r66820 / r66821;
        double r66823 = pow(r66822, r66817);
        double r66824 = r66817 * r66823;
        double r66825 = r66813 + r66824;
        double r66826 = r66819 / r66825;
        double r66827 = sqrt(r66826);
        double r66828 = asin(r66827);
        return r66828;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r66829 = 1.0;
        double r66830 = Om;
        double r66831 = Omc;
        double r66832 = r66830 / r66831;
        double r66833 = 2.0;
        double r66834 = pow(r66832, r66833);
        double r66835 = r66829 - r66834;
        double r66836 = t;
        double r66837 = l;
        double r66838 = r66836 / r66837;
        double r66839 = pow(r66838, r66833);
        double r66840 = r66833 * r66839;
        double r66841 = r66829 + r66840;
        double r66842 = r66835 / r66841;
        double r66843 = sqrt(r66842);
        double r66844 = asin(r66843);
        return r66844;
}

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 10.2

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

  2. Final simplification10.2

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

Reproduce

herbie shell --seed 2020047 
(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)))))))