Average Error: 10.1 → 10.1
Time: 11.0s
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 r72719 = 1.0;
        double r72720 = Om;
        double r72721 = Omc;
        double r72722 = r72720 / r72721;
        double r72723 = 2.0;
        double r72724 = pow(r72722, r72723);
        double r72725 = r72719 - r72724;
        double r72726 = t;
        double r72727 = l;
        double r72728 = r72726 / r72727;
        double r72729 = pow(r72728, r72723);
        double r72730 = r72723 * r72729;
        double r72731 = r72719 + r72730;
        double r72732 = r72725 / r72731;
        double r72733 = sqrt(r72732);
        double r72734 = asin(r72733);
        return r72734;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r72735 = 1.0;
        double r72736 = Om;
        double r72737 = Omc;
        double r72738 = r72736 / r72737;
        double r72739 = 2.0;
        double r72740 = pow(r72738, r72739);
        double r72741 = r72735 - r72740;
        double r72742 = t;
        double r72743 = l;
        double r72744 = r72742 / r72743;
        double r72745 = pow(r72744, r72739);
        double r72746 = r72739 * r72745;
        double r72747 = r72735 + r72746;
        double r72748 = r72741 / r72747;
        double r72749 = sqrt(r72748);
        double r72750 = asin(r72749);
        return r72750;
}

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 2019362 
(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)))))))