Average Error: 10.1 → 10.1
Time: 17.8s
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 r61748 = 1.0;
        double r61749 = Om;
        double r61750 = Omc;
        double r61751 = r61749 / r61750;
        double r61752 = 2.0;
        double r61753 = pow(r61751, r61752);
        double r61754 = r61748 - r61753;
        double r61755 = t;
        double r61756 = l;
        double r61757 = r61755 / r61756;
        double r61758 = pow(r61757, r61752);
        double r61759 = r61752 * r61758;
        double r61760 = r61748 + r61759;
        double r61761 = r61754 / r61760;
        double r61762 = sqrt(r61761);
        double r61763 = asin(r61762);
        return r61763;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r61764 = 1.0;
        double r61765 = Om;
        double r61766 = Omc;
        double r61767 = r61765 / r61766;
        double r61768 = 2.0;
        double r61769 = pow(r61767, r61768);
        double r61770 = r61764 - r61769;
        double r61771 = t;
        double r61772 = l;
        double r61773 = r61771 / r61772;
        double r61774 = pow(r61773, r61768);
        double r61775 = r61768 * r61774;
        double r61776 = r61764 + r61775;
        double r61777 = r61770 / r61776;
        double r61778 = sqrt(r61777);
        double r61779 = asin(r61778);
        return r61779;
}

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 10.1

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

  2. Final simplification10.1

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

Reproduce

herbie shell --seed 2019308 
(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)))))))