Average Error: 10.1 → 10.1
Time: 9.5s
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 r64989 = 1.0;
        double r64990 = Om;
        double r64991 = Omc;
        double r64992 = r64990 / r64991;
        double r64993 = 2.0;
        double r64994 = pow(r64992, r64993);
        double r64995 = r64989 - r64994;
        double r64996 = t;
        double r64997 = l;
        double r64998 = r64996 / r64997;
        double r64999 = pow(r64998, r64993);
        double r65000 = r64993 * r64999;
        double r65001 = r64989 + r65000;
        double r65002 = r64995 / r65001;
        double r65003 = sqrt(r65002);
        double r65004 = asin(r65003);
        return r65004;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r65005 = 1.0;
        double r65006 = Om;
        double r65007 = Omc;
        double r65008 = r65006 / r65007;
        double r65009 = 2.0;
        double r65010 = pow(r65008, r65009);
        double r65011 = r65005 - r65010;
        double r65012 = t;
        double r65013 = l;
        double r65014 = r65012 / r65013;
        double r65015 = pow(r65014, r65009);
        double r65016 = r65009 * r65015;
        double r65017 = r65005 + r65016;
        double r65018 = r65011 / r65017;
        double r65019 = sqrt(r65018);
        double r65020 = asin(r65019);
        return r65020;
}

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 2020089 
(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)))))))