Average Error: 10.1 → 10.1
Time: 18.0s
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 r80987 = 1.0;
        double r80988 = Om;
        double r80989 = Omc;
        double r80990 = r80988 / r80989;
        double r80991 = 2.0;
        double r80992 = pow(r80990, r80991);
        double r80993 = r80987 - r80992;
        double r80994 = t;
        double r80995 = l;
        double r80996 = r80994 / r80995;
        double r80997 = pow(r80996, r80991);
        double r80998 = r80991 * r80997;
        double r80999 = r80987 + r80998;
        double r81000 = r80993 / r80999;
        double r81001 = sqrt(r81000);
        double r81002 = asin(r81001);
        return r81002;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r81003 = 1.0;
        double r81004 = Om;
        double r81005 = Omc;
        double r81006 = r81004 / r81005;
        double r81007 = 2.0;
        double r81008 = pow(r81006, r81007);
        double r81009 = r81003 - r81008;
        double r81010 = t;
        double r81011 = l;
        double r81012 = r81010 / r81011;
        double r81013 = pow(r81012, r81007);
        double r81014 = r81007 * r81013;
        double r81015 = r81003 + r81014;
        double r81016 = r81009 / r81015;
        double r81017 = sqrt(r81016);
        double r81018 = asin(r81017);
        return r81018;
}

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 2020043 
(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)))))))